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Steven Strogatz on the Humanity of Math — Transcript

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0:00About 5 years ago, I experimented with
0:02starting up a podcast, called it the
0:043B1B podcast. And essentially, I spent a
0:06summer having various conversations with
0:08a lot of mathematicians, a lot of
0:10content creators. And at the time, at
0:12the end of that summer, I remember
0:13reflecting, okay, this is fun. I could
0:15totally keep doing this, but does the
0:17world really need another podcast? And
0:19also, I just kind of want to concentrate
0:20most of my time making videos. That was
0:222021. The world is pretty different here
0:25in 2026. In particular, the math world
0:28has been completely on fire describing
0:30what is happening to mathematics in the
0:32presence of AI. And in particular, I
0:34think a lot of people have just been
0:35stepping back and reflecting on what is
0:37mathematics to them. What is valuable
0:39about it? What is it that they want to
0:41keep about the culture? Where are they
0:42worried? Where are they excited? And
0:44I've been having a lot of these
0:45conversations anyway. So, I decided,
0:47hey, let's just spin up the podcast
0:49again and share these conversations with
0:50some of you.
0:55For this first episode of the revamp, I
0:57had on Steven Strogats. Always a delight
0:59to talk to, always a great storyteller,
1:01and he always just has something
1:02completely unexpected uh that he says in
1:05any conversation that I have with him on
1:07or offline. So, I think you're really
1:09going to enjoy this one. The other thing
1:10helping to make the revamp possible is
1:12that I've been taking on more of a team
1:14this [music] year. And so in particular,
1:15this podcast comes to you much thanks to
1:17a new producer, Ashley. So many thanks
1:19to her. The conversation itself you're
1:21about to hear will be uninterrupted by
1:23sponsor reads. But if you do want to
1:25support Three Blue and Brown and its
1:26associated projects, the Patreon page is
1:28the best place to do that. There's perks
1:30like early views of new videos.
1:31Alternatively, if any of you are looking
1:33for new jobs or new careers, I have a
1:36set of partner companies you can find at
1:373b1B.co/talent
1:39who are actively recruiting and
1:41interested in hiring people like you.
1:43the kind of people who are deeply
1:44curious about and engaged with math and
1:46its surrounding fields. With that, let's
1:48dive into the conversation with Steve
1:49Strogatz.
1:58>> AI is the conversation among
2:00mathematicians.
2:00>> It is and we ought to talk about it. I
2:02I'm very I change my mind every day. I'd
2:05like to hear what you think.
2:07>> Um
2:07>> Well, okay. What how how have you
2:09changed your mind like in the last year?
2:10What have been some things that have
2:12changed your mind? [laughter]
2:14>> Well, it's a question of whether grief
2:17is the right reaction or ecstasy or
2:20exhilaration
2:22or just massive uncertainty. Um,
2:25>> right this moment of of those of the
2:27four that you just listened listed,
2:29what's the most salient in your mind
2:30right now?
2:31>> I'm trying very hard to be exhilarated.
2:36I I feel like I have some responsibility
2:39to encourage younger people to keep keep
2:43up the fight to not you know like if you
2:46go too hard on grief
2:49there is a sense that like is the
2:51subject dead? Is math over? And if so
2:56uh you know I mean imagine being even
2:59younger than you are. How would a person
3:02feel? would they think I I can't, you
3:04know, I love this subject and now I
3:06can't go into it. I don't I don't want
3:08to send that message. On the other hand,
3:10I don't want to be unrealistic. If
3:13that's the truth, maybe we ought to face
3:15the truth. It's very confusing because
3:17no one knows the truth, right? There's
3:19so much uncertainty about what's going
3:20to happen.
3:21>> This is actually the first question on
3:23my list is what are you telling students
3:25right now? because I I will make a video
3:27like record some video that's basically
3:28just uh specifically addressed at those
3:31students who were maybe thinking of
3:32going into a math PhD.
3:34>> Um and the the hard part of it is like I
3:37don't know the future. I'm not going to
3:38pretend like I do. But I also have some
3:41somewhat firm like predictions or
3:43opinions that I think lend a certain
3:45optimism there. But I don't want to lead
3:47[clears throat] the witness at all. I'm
3:49curious. Student [laughter] student
3:50walks into your office. They're like,
3:52"Professor Strogats, I have loved math
3:54all of my life. I thought I wanted to be
3:55a mathematician, but I'm I'm looking at
3:57everything that's happening now, and I'm
3:59I'm wondering if I'm walking into a dead
4:00field. You in your office on the other
4:03side of that desk, what do you tell
4:04them?
4:06What I'm telling them as of today
4:09[laughter]
4:10is
4:12um it might actually be a wonderful time
4:15to go into math. I don't want to put too
4:18definitive uh
4:21I can't say it with my full heart
4:22because there's so much uncertainty but
4:24to the extent that I can figure it out
4:27it seems like AI might be a great
4:29equalizer in the sense that there was a
4:32time when technical power was the number
4:36one strength that a mathematician
4:39needed. So if you are a really good
4:41problem solver
4:43uh fast, deep, widely knowledgeable,
4:47able to follow intricate chains of
4:50reasoning, construct them, all those
4:53kinds of things that you think of as
4:54being good at math in the problem
4:56solving sense.
4:58Uh those used to be
5:02like the quintessential aspects of being
5:04a strong highcaliber mathematician.
5:08And I feel like those skills are less in
5:11demand now and probably in the years to
5:14come. Not that they're nothing, but
5:18let's think of other things that make
5:19people good mathematicians or good
5:21researchers generally. Curiosity,
5:25taste, deciding what's interesting, the
5:28ability to tell a good story, to to
5:31connect to the real world, to connect to
5:34other parts of math, those kinds of
5:37things. if you were technically weak or
5:39average,
5:41you couldn't really play at a very high
5:43level. But now I think you can. And so
5:48the other day I was talking to a group
5:50of students. We have like the math club
5:52and they've been asking professors to
5:54come and talk to them about what's
5:55happening. And usually we have a panel
5:57of four or five people and we all have
5:59different takes on this. And I don't
6:01know if I connected with the students
6:03the other day, but what I was thinking,
6:05I mean, I have two kids who are 24 and
6:0726 right now, and I think about their
6:10futures all the time. Um, they have
6:13taught me this word, which you will
6:15know. Riz, [laughter]
6:20you know where I'm going. Like charisma.
6:22>> Yeah. Yeah. Yeah. Is it okay? I think
6:24Tell me where you're going.
6:25>> Have I said it wrong? [laughter]
6:27>> No. No. You said as far as Hey, we're
6:29talking below my generation at this
6:30point. I know, right? This is
6:32>> um but yeah, commenting on whether the
6:35AI has RZ or not.
6:36>> No, not the AI. That RZ is in more and
6:39more demand because it's something that
6:41only people have.
6:43>> And I'm starting to think what makes a
6:45future mathematician or a future math
6:48professor is your unique brand. I hate
6:52to say it that way. That sounds like
6:54business. I don't mean it that way. I
6:56mean your uniqueness as like think of
6:58actually I you're a perfect example. You
7:00have somehow I may be too embarrassing
7:02to be pointing at you but you you picked
7:05something that you love. I mean you're a
7:08well okay it will be too embarrass I'm
7:10getting embarrassed on your behalf to
7:12saying it but the things that you seem
7:14to like to do explaining crafting
7:16explanations being visual
7:19it's something that means a lot to you.
7:21You obviously love the subject, but you
7:22found your angle
7:24>> and it turns out I hope it's been very
7:28fulfilling for you and it's very
7:32um it's a gift to the rest of the
7:35universe what you have given us and I
7:37think other people can try to do the
7:40same thing in their own way. What is it
7:42that really moves them? Not just their
7:45passion like what are they good at?
7:47what's their
7:49their fundamentally
7:51distinctive thing whatever that is
7:54>> you can now do that in a way that you
7:56couldn't before AI because AI has been
7:59this equalizer in that it can do the
8:02lemas it can do the proofs
8:04>> if you can ask the right questions if
8:06you can tell the good story if you can
8:08make the cool connection you're in the
8:10game in a way that you never were before
8:13>> I love this take that I mean yeah what
8:15what we're selecting for is an element
8:16of mathematical riz and the the uh the
8:19the PhDs to be are not differentiated
8:21based on pure problem solving abilities.
8:23I want to get back to problem solving
8:25later actually because I think I think
8:27there's something nuanced to to to get
8:28into there. Yeah. Okay. Um but simply on
8:32the side of what what is math or what is
8:34the practice of doing math outside of
8:35it, you know, pointing out like you I
8:38think you are you are very emblematic of
8:41one of the more charismatic
8:42mathematicians out there and deservedly
8:45like well respected for it just in that
8:47I think you have you have a way with
8:49with a microphone. You have a way with
8:51people. You have a way on a stage. you
8:52have a way in your books that really
8:54comes out that's clearly not you're an
8:56amazing problem solver but it's it's
8:58clearly something more than that that
8:59that's drawing people in. Um and so I
9:02think a natural response some people
9:04might have though would be but surely
9:07all of that is something that you can
9:09distill and what's to say that you know
9:12the models aren't going to get better
9:13than that? Um you know
9:15>> I've wondered about that a lot myself.
9:17>> Yeah. So I um I I had written up this
9:20post on like perhaps academic math
9:21should elevate the status of uh of kind
9:25of the the explanatory aspects of
9:26>> I saw this on Terry Ta's blog right
9:29>> for Terry Tow's blog and one of the most
9:31common replies on there was like sure
9:32but like what happens once uh AI is a
9:35super superhuman expositor you know it's
9:37it's super human at doing that what role
9:40is that as I'm curious how you would
9:41respond um yeah on that
9:43>> question my answer to that is
9:45I think I basically accept the premise
9:48first of all that right now first of all
9:52let's talk about right now and let's
9:53talk about the future right now
9:57the AIs are not good at asking questions
10:00we're seeing this in uh math at the
10:02frontier that they are not inventing new
10:06theories you know we'd make this
10:08distinction problem solving and theory
10:10building they've shown them to be
10:12superhuman in problem solving and
10:16They're subhuman compared to the very
10:18best in theory building.
10:21>> Mhm.
10:22>> They're not. Now, you could say no
10:24surprise. They're not trained to do
10:25that. In fact, I I've tried to get them
10:28to make up test questions. I just gave a
10:31prelim exam today and just for
10:35curiosity, I asked, you know, make up
10:36some questions for my complex analysis
10:38exam.
10:40>> Not very good, not terrible.
10:42>> In what way, how did it fail? Like what
10:44was it doing that you wouldn't have?
10:46Well, they were competent. I mean, they
10:49were pedestrian. They were like any
10:51textbook. They weren't particularly
10:54interesting. But maybe that's good.
10:55Actually, it's usually a good uristic
10:57that if the question is too interesting
10:59to the professor for a test question.
11:02[laughter] That's a bad sign. It's going
11:04to be too hard. And the students are
11:06under pressure. They don't want an
11:07interesting question. They want a
11:08straightforward question. So, maybe I
11:10shouldn't say that they weren't good.
11:12They they weren't interesting to me.
11:14They weren't juicy questions that would
11:16challenge my best students. They were
11:18very routine. But but that really wasn't
11:20where I was trying to go. I mean, in the
11:23as far as research math, they're so far
11:25not very good at
11:28at um building new concepts.
11:31Now, maybe we haven't trained them to do
11:33it. We haven't trained them to ask
11:34questions. We've been training them to
11:36try to answer questions and they've
11:38gotten good at that. So those people who
11:40say look taste
11:42even charisma asking good questions
11:45building theory just like we teach our
11:48good grad students to do that I mean it
11:52these are teachable skills they're hard
11:54there are very few people who know how
11:55to teach for instance the art of
11:57discovery
11:59um
12:00but there are people who have thought
12:01about it and so presumably anything that
12:04you could teach a person you could teach
12:05an AI and at some point they will be
12:08superhuman at all of those things and I
12:11think I sort of believe that I I it's
12:14not happening yet. I do imagine it
12:16happening in the future. I have a lot of
12:18good colleagues who would say this is
12:20false this is not going to happen the
12:22storytelling. Yeah. So I don't know this
12:25is open.
12:26>> Yeah we let's take it as a postulate
12:28just you know maybe you don't believe it
12:30will happen but it's interesting to to
12:31engage with. Yeah. What would what would
12:33happen in that future? Um so in in that
12:35scenario yeah if we stipulate that they
12:37will be like Jacob Zimmerman has said
12:39that right in his one of his interviews
12:41the interview he said it in a lot of his
12:42interviews but in his interview with um
12:45Siobhan Roberts for the notices of the
12:48American Math Society he says he thinks
12:52that uh they will just be better at
12:55everything. They the AIS will be better
12:57at problem solving at taste at theory
12:59building all of it. And then he goes on
13:01to say it will make being a
13:02mathematician not a profession in the
13:05future.
13:06>> This is where I I disagree and I'm I'm
13:10curious if I'm simply holding on to a
13:12I'm not even a like practicing
13:14mathematician in an academic sense,
13:15right? Like I I I have a career that's
13:17pretty independent. But nevertheless, I
13:19wonder if I'm kind of biased by the by
13:20the love of mathematicians. And so one
13:23of the things I want to do both in this
13:25conversation and others like it is to
13:26kind of like see if I if I'm blinded by
13:30something because I can get into why I
13:32disagree but yeah what's your take there
13:34in that everything you can do I can do
13:35better future because that's okay.
13:38Right. So that I just to come to my
13:40punchline and it's a very tentative
13:42punchline like just about everything I'm
13:44going to say on this broad topic of math
13:46and AI. But what I feel today and have
13:50felt for the past few days is um
13:56is that I think we're going to find
13:57humanity more and more precious as we
14:01become dwarfed by the capacity of AI in
14:04intellectual matters that our
14:08our foibless our fragility are to air as
14:12human you know those qualities I think
14:15we're going to start to feel affection
14:16for that when I watch let's take a few
14:19examples music or chess not perfect
14:21analogies but let's just talk about
14:23those two when I watch the great grand
14:25masters playing at the world
14:26championship caliber level
14:29and there are many other chess fans
14:31watching them you see them nowadays
14:35uh as they're playing with a chess
14:39engine running simultaneously showing
14:42who's actually better in a given
14:43position sometimes a player will make a
14:46move and instantly the evaluation bar
14:48will drop. Someone has just blundered
14:51and it's a very dramatic moment. Often
14:53the drama is heightened
14:55by the commentators not running the
14:58engines at the same time. So they don't
14:59know what has happened, but you and the
15:01audience know. Oh my god. So then it's a
15:04question of will the commentators
15:05realize, will the players realize
15:09I think there's something very sweet
15:11about it because it's
15:13we're we're people. This is what
15:15happens. We're not perfect. and and uh
15:18likewise I think of the movie Shine
15:21which may be well before your time but
15:22Shine was a story of a pianist named
15:26David Hcgot
15:28um who was a very promising brilliant
15:31young pianist who won some international
15:34competition if I remember right and then
15:38something went wrong like maybe I don't
15:41remember what his diagnosis was but he
15:43had some sort of disorder mentally that
15:46that essentially ruined his musical
15:48career and and to a large extent his
15:51life. But at some point he he came back
15:54and recovered and played after all these
15:58years even after the movie made him
16:00famous
16:01and his playing was not perfect but it
16:04was so filled with humanity
16:07>> and so touching and and passionate and
16:11marvelous that who cares. Of course it's
16:13not perfect. If I listen to Paul Simon
16:16sing now at 80 something years old, I
16:18love Paul Simon. I don't care that he
16:20can't sing anymore. I that's my guy. I
16:22want to hear him. So I'm starting to
16:24think, is that what's in store for us?
16:26That we are going to be these blundering
16:28offkey mathematicians who are weak
16:31compared to the right. I mean obviously
16:33a machine could play everything David
16:36Hcco could play perfectly.
16:38>> Do we want that? Do we really want that?
16:40Maybe. But we might also want the
16:43imperfection, the beautiful humanity. So
16:46maybe that's what what's in store for
16:48us. That we're going to be second rate
16:49mathematicians, but we can still love
16:51it. And and uh I don't know. Okay. So
16:56I'm going to be quiet. Let me hear your
16:58thinking.
16:58>> No, no, no, no. I love Well, I I'm I'm
17:00going to continue on with this a little.
17:01I'll I'll I'll spare my thoughts for for
17:03at least another minute or [laughter]
17:04two
17:05>> in the So,
17:06>> okay,
17:07>> one of the most classic sentiments that
17:08we share with students is that math is
17:10not a spectator sport.
17:12>> Um, and so this sets a certain irony on
17:15the comparisons to chess or the
17:17comparisons to go where people will
17:19point out, hey, you know, chess was more
17:21than alive after the deep blue moment
17:23and go stays more than alive after the
17:24alpha go moment. Um but one of the
17:27differentiators with math would be that
17:28I think a lot of people found found this
17:30charm at the idea of being at the
17:32forefront of pushing forward of being
17:34these these pioneers. Um and and if it
17:37is going to be this emphasis on the
17:39humanity and I absolutely agree that
17:41there is there is humanity to be had in
17:43math and I'd love to like dig deep into
17:44to where it is.
17:46>> What what does that actually look like?
17:48Because I think as stated so far the
17:50view of to heir is to human and focusing
17:52on you know the stumbling nature of it
17:54but there is you know we have this
17:56relationship with Paul Simon so it
17:57doesn't matter if he's 80 because the
17:59you know it's we're like going from
18:01that. What is it that you can tell to a
18:04a budding math PhD or prospective PhD on
18:08kind of what what's in store for their
18:09future? Uh because it can't be that like
18:12people will delight in marveling at your
18:15inability,
18:17right? And so there there's
18:18>> I think what I'm talking about there my
18:20yeah maybe I should sharpen this because
18:22this is a work in progress these ideas.
18:24Um, I don't have a manifesto for you,
18:27but there's pure math where and of the
18:30purist type where people will not use
18:32AI. I have a friend who's a writing
18:35teacher here, Jay Robert Lennon. He's a
18:37brilliant novelist. He he hates AI
18:41for what it's doing to his art art,
18:44which is creative writing, you know,
18:47fiction. and um he thinks it has nothing
18:51to offer because writing is about what's
18:54in you, your life, what you bring to the
18:57page. So he doesn't want to write, he
19:00does has doesn't want to look at AI,
19:02wants no help at all from that thing and
19:04doesn't want his students using it. And
19:06I think there are going to be artisal
19:08mathematicians who will feel the same
19:10way and they don't want to hear from AI.
19:13they're just going to work by themselves
19:15and with their and also you know there's
19:17this whole social dimension me and you
19:19explaining things to each other that's a
19:21big part of the fun of math and um it
19:25causes people to become close to have
19:27friendships to really connect and they
19:30don't want anything impairing that.
19:32Okay. Now there's also though for your
19:35question about the young mathematician
19:36who wants to be at the frontier and
19:39there are a lot of people who feel like
19:40that
19:42and that's a really good motivation. I
19:45mean I certainly remember being excited
19:47with the thought I'm going to make a
19:48discovery. It's a very exciting feeling
19:51and very motivating. So I think that
19:54then the realistic view is you've got
19:56this fantastic new tool. You've got this
19:59superpowered
20:00artificial intelligence. That's your
20:02C3PO.
20:04That's hopefully not HAL, you know, in
20:07[laughter] 2001 of Space Odyssey.
20:09Certainly hopefully not, you know,
20:11Terminator 2, whatever this thing is
20:16in this in this happy future that I like
20:18to think about for a minute where it's
20:20your sidekick at your service, sort of
20:23like computers have been up till now.
20:26Who know the sky's is the limit. what
20:28you could do with that thing. You can
20:30ask questions. You can start a like you
20:32want to cure cancer,
20:34go to it. You know, there may be all
20:36kinds of profound math that can help
20:38with biomed problems, with new energy
20:42sources, with dealing with the climate
20:44problem, with AI safety itself. I mean,
20:48there are whole fields that haven't even
20:49been mathematized yet that people don't
20:51even realize there's math in this in
20:53anthropology or, I don't know, make up
20:56something. So if the the bottleneck in
21:00the past was mathematical strength,
21:02that's not a bottleneck. Now it's just
21:04what your imagination can do, what your
21:06creativity and taste and desires can do.
21:09And so I h happen to feel it might be
21:11like a golden age for applied math. I
21:14think for the most hermetically sealed
21:17pure math,
21:19if you also want to be a mountain
21:20climber and reach the top first,
21:24that's just not going to be that easy to
21:26do anymore. But I still think there's a
21:28lot of worthwhile mathematical endeavors
21:32uh that you can have fun and be the
21:34first if you care about that and really
21:36make worldshaking discoveries.
21:40And I think realistically a lot of maybe
21:42people who had gone into the field with
21:44that anticipation of being you know the
21:46first to top the mountain almost all of
21:48them reach some point of maturity on
21:49realizing that the most enriching parts
21:51of the field are the more communal
21:53aspects and that
21:55>> and and also a lot of people I talk to
21:57um delight simply in knowing right they
21:59just they just like follow that Hbert
22:01phrase on like we can know and we must
22:02know and whether they're the first one
22:04to get there or not they just delight at
22:06the idea of of seeing what that truth is
22:09for something that they engaged with so
22:10long.
22:11>> Um I mean you you touch on applied
22:13versus pure which is one of the topics I
22:15wanted to hit here because a lot of
22:18conversations with mathematicians that
22:20I'll have. It's almost as if the the
22:22prospect of the solution to a problem
22:24being useful is not in the conversation.
22:27People will describe [laughter] like oh
22:28what people don't understand is like
22:30math is about much more than just the
22:32proof. It's all of the you know
22:33constructs that you make in the effort
22:35of the proof. Sure. uh the the goal of
22:37math is to advance human understanding.
22:39Um that human understanding comes from
22:41the process. It doesn't come from the
22:42results. A lot of deep truth in there.
22:45But then if I talk to someone outside of
22:46math, they're like, I've been reading
22:48all these headlines about uh you know uh
22:51grand problems being solved, is that
22:54good? Is like and are are we able to do
22:56better things in the world now? Like
22:58surely if the mathematicians cared
22:59deeply about this Millennium Prize
23:01problem and it's solved, does that give
23:02us anything now? And it it shines a
23:04light on this question of what was the
23:06what was the the purpose of those as
23:09being the the goalposts, but then
23:11applied math maybe stands to be
23:13particularly interesting here where I'm
23:15I'm curious to hear your take on whether
23:17the solutions to problems are the point
23:21or if even in an applied setting, not a
23:23pure setting, we have to be more nuanced
23:25about what is math and that simply
23:27solving the problem as stated, you know,
23:30AI or otherwise is not quite what people
23:33are it and there's some more uh human,
23:36you know, pushing pushing forward human
23:38understanding aspect of it. Um, in an
23:40applied setting, is it fair to say, hey,
23:42if you have a magical problem solving
23:44machine, that's that is strictly good
23:46that just pushes forward things as we
23:48want. Pedal to the metal. Let's let's
23:50let it start improving the world.
23:52>> Such a rich vein you're tapping into
23:55here. This is tough. Um, I I find it
23:58hard to give an organized response to
24:00this. So, let me just try flying out in
24:03a lot of different directions and I'm
24:05going to hope you can pull me back in if
24:07they get too [laughter]
24:09because there's so many things to talk
24:11about here and I don't have
24:15I don't have a sharp formulation of
24:16this. I've thought about this a lot. Um,
24:20okay, let's first talk about
24:21understanding versus results
24:25in both pure and applied
24:28math.
24:30Um all of us like
24:34understanding feels good. Aha moments,
24:37eureka moments. Okay. So there's in fact
24:39a friend of mine pointed out to me
24:41recently that Allison Gopnik
24:44who I think is a psychologist wrote an
24:46article with a title can't remember it
24:49but it involves the word orgasm.
24:52something like problemolving as orgasmic
24:56>> or something like that that maybe it's
24:58not problem solving but or maybe it's
25:00like the orgasm of understanding
25:02something like that that there's some
25:04kind of truly delightful feeling when
25:08you understand something like right up
25:11there with the best feelings you can
25:14have. So we like understanding for that
25:16reason. We also like understanding
25:19in both pure and applied math
25:23for its generative nature. When you
25:26understand something well or have
25:29insight, it leads you to new questions
25:32to new ideas to see connections and it
25:36produces it's fruitful right it creates
25:40more activity more buzz in your own head
25:42in the community's head in your friends.
25:44So, so okay. So, understanding is
25:48pleasurable. It's productive in this
25:50generative sense
25:53and it's been a route to power
25:58>> understanding.
26:01This is what I recently with my
26:03colleague and uh co-author Alex Townson.
26:05We wrote a New York Times piece just a
26:08few weeks. Well, now whatever. So, it
26:10was in late September. Um
26:14we had an article explaining that yeah
26:16you know for the people who are confused
26:18by the pure mathematician saying boohoo
26:22understanding is what we're after not
26:23results the machines are taking away the
26:26results that was never the real purpose
26:29Allah thirst the purpose was human
26:31understanding and you're wreck you're
26:33ruining it's like you know you're
26:35destroying the landscape um you're
26:38blowing up the lighouses you're nuking
26:40okay there's been all this kind of
26:42language very devastating language and
26:45the public is rightly confused like I
26:47thought you wanted your problem solved
26:49actually no [clears throat] there's a
26:52tribe there is a tribe within pure math
26:54that that deifies understanding as the
26:58they say this is what our subject is
26:59really about following thirsten I mean
27:01I'm in Thirstston's office I have the
27:04[laughter] I'm breathing molecules of
27:06thirsten I'm sure every day so uh and I
27:10love his essay on proof and prog
27:11progress in mathematics. So absolutely
27:14there's a subculture and maybe the
27:16predominant culture in math that sees
27:18understanding. I'm talking about pure
27:19math. Understanding is the beall and
27:21endall and that to the extent that
27:24problem solving leads us to greater
27:26understanding
27:28problems are worthy activities. Now
27:31there is another culture like an Eddish
27:33culture. Um and there are disciples and
27:37and former collaborators of Erdish
27:39people like Joel Spencer. I just got an
27:40email from him the other day saying and
27:43I think Jacob Zimmerman would be another
27:44one. There's a lot of great
27:45mathematicians. Let's just still focus
27:48on pure mathematicians who think you got
27:51it backwards. It's it's that
27:54understanding is helpful in so far as it
27:56lets us solve problems
27:58>> and that problems are the units of math.
28:01>> If people haven't read it, Tim Gowers
28:04has an excellent post or or essay on the
28:06two cultures of mathematics.
28:07>> Yeah. The two cultures.
28:08>> Yeah. the problem solvers, the theory
28:10builders is the way he phrases it. Um
28:13Freeman Dyson has his wonderful essay on
28:16birds and frogs which is also close but
28:19not quite the same thing to this
28:20distinction.
28:21>> But anyway, the truth is most
28:24mathematicians either pure or applied
28:26recognize that results
28:29and understanding are both important and
28:31some people care more about the problem
28:33solving and some care more about the
28:34understanding. They're both really
28:36important and fun. Okay. But then the
28:40public thinks, "Yeah, but so what?" And
28:44and so that's where applied math comes
28:46in and also pure math because all math
28:49becomes applied at some point. I mean,
28:51that's just an empirical fact. There
28:53really isn't any part of Also, this is
28:55why I say I'm going off in 10 different
28:57directions at once. This is such a
28:59historical anomaly, this species
29:02distinction between pure and applied
29:03math. Don't forget the greatest
29:06mathematicians of all time until the
29:08past hundred years always did both.
29:11>> Yeah. Pure mathematician is a very
29:13recent recent invention.
29:14>> Pure mathematician is a like would Gaus
29:17have said he was a pure mathematician.
29:19He was tracking series. He you know this
29:22asteroid. He was mapping the earth
29:25literally doing mapping when he was
29:26inventing differential geometry.
29:29Reman was very interested in electricity
29:32and magnetism and you know Hilbert even
29:36Hilbert was thinking about general
29:38relativity. So um and obviously Oiler
29:43you know or Newton these people are
29:44absolutely top physicists as well as
29:47mathematicians Kepler too.
29:50>> So Galileo I mean Galileo maybe not so
29:53great with math. He was pretty good but
29:55anyway world caliber people and they
29:58didn't make this distinction. This is a
29:59very peculiar 20th century phenomenon.
30:02Uh okay that maybe was a tangent. Let me
30:04come back off that tangential direction
30:06and back to the core which is on this
30:09question of understanding and why does
30:12understanding matter
30:15pleasurable yes generative yes and a
30:18route to power that's so that just in
30:21case that argument is not familiar
30:24if you understand let's say vector
30:26calculus or quatians at the level that
30:30James Clark Maxwell did in the 1800s
30:33you can then rewrite Right. What Michael
30:35Faraday and Aier discovered and Gaus too
30:39about electricity and magnetism into
30:41four equations.
30:43>> And then you can manipulate those
30:44equations using logic and using your
30:47brain as Maxwell did around the time of
30:50the Civil War in the US.
30:53And um
30:55you make a prediction of something that
30:57no one has ever seen. That there's an
30:59invisible
31:01wave of energy propagating at the speed
31:03of light that we now call an
31:05electromagnetic wave
31:08that you know give it a few years
31:11becomes the basis for television and
31:13radio and cell phones and all kinds of
31:16wireless communication. And that was
31:19only possible because he knew how to do
31:22he he recognized the wave equation a
31:24partial differential equation when he
31:25derived it from doing vector calculus
31:28identities on the four laws of
31:30electricity and magnetism. So my point
31:33is that the understanding that Maxwell
31:35had through math and that Michael
31:37Faraday did not have because he was a
31:40different kind of mind
31:42led Maxwell to be the first person on
31:46the planet to understand what is the
31:47nature of light that light is an
31:50electromagnetic wave. Nobody knew what
31:52light was before Maxwell. Not really.
31:55And so in that blinding flash of insight
31:58um he figured out something that turned
32:01out to change the world. And we could
32:02give so many stories like that whether
32:04it's Schroinger's wave equation or
32:06Durac's prediction of antimatter
32:09or whatever. I mean just it's endless
32:12the the I mean but all these things have
32:14turned into technology
32:16>> right? So from from understanding
32:19general and special relativity, you can
32:21figure out the corrections you need to
32:23make in the atomic clocks to make the
32:25GPS devices work as accurately as they
32:28do. If you didn't understand relativity,
32:32you'd GPS wouldn't work.
32:35>> And so a pertinent question then becomes
32:37if the entity that is coming to those
32:40bits of understanding is not necessarily
32:42human, you know, that the solution is
32:44found and it's not human. um either you
32:47say hey the the um the benefit is lost
32:51because it wasn't a matter of young
32:53Maxwell happening to solve a given
32:55random second order differential
32:56equation. It was the intuitions about
32:58what wave equations feel like that he
33:00then had light up again when he was
33:02engaging with um a certain physics
33:04context that that actually mattered. And
33:06therefore had he just been handed the
33:08solution out of the blue it wouldn't
33:10have have given us the value that was
33:12actually uh influential to the world
33:14which was Maxwell's as a human brains
33:17understanding. I think the other take
33:19could be like well why can't the same
33:21entities that are coming up with you
33:23know solution to the next millennium
33:25prize problem silicon though they might
33:27be um have that downstream effect which
33:29you can have a very positive take on and
33:31say like amazing wonderful like we just
33:34sit back and wait for the usually
33:36decadesl long delay between uh pure math
33:39discovery and application discovered um
33:41to be to be compressed um yeah but
33:44between that dichotomy I'm thinking you
33:46you you need or it is beneficial for
33:48there to be a a loving human mind who is
33:51embraced with it in order to digest it
33:53into application versus
33:55>> Is it true? Is it just a romantic thing
33:57that you just said? Like I mean it
33:59sounds nice, but but I can I mean I love
34:01that you're seeing all the same
34:04>> I mean you're following the same
34:05flowchart of thinking well not the same.
34:08I mean you have your own version of it
34:10but normally when I have this
34:11conversation with people they're not
34:14seeing as far as many moves ahead
34:17because I keep wondering like in this
34:19argument you know say sure um if I have
34:22this entity which can solve the problem
34:24let's say
34:27it can give me answers who says it can't
34:29also give me all the understanding along
34:31the way and all the spin-offs and all
34:33the applications in other words I think
34:36people get confused about the argument
34:38that is easy to make that human
34:40understanding has led to power and
34:42progress and they get confused by the
34:44converse which is that they think does
34:47that mean if humans didn't do it like if
34:50the AIs did it we wouldn't have the same
34:52amount of progress no that doesn't
34:55follow at all in fact I think if the AIs
34:58could get us the answer they would be so
35:02strong they could also get us all the
35:04side spin-offs and everything else too
35:06so I don't think The argument for why
35:09human understanding is important
35:13is that it's because only humans can see
35:16all the connections and the spin-offs. I
35:18just don't believe that's true. I think
35:19the AI will be able to do all of it. So,
35:21I really am very confused here. Let me
35:24put it starkly if that's last sentence
35:26or paragraph was too hard to follow. Um,
35:30here's the real question and I would
35:32love to know what you think about this.
35:34Is is understanding overrated?
35:38>> I think I think that this might be a
35:40real confusion that people Let me make
35:43this argument and I don't know that I
35:44believe it, but just for the sake of
35:46since you like having discussions, let's
35:48have a discussion.
35:50>> You could say that human civilization
35:52didn't have much understanding for I
35:54don't know how old are we as a species?
35:56100,000. I don't know the number. I
35:58should know my anthropology. [laughter]
36:00Like I know that 12,000 years ago we
36:02domesticated dogs because I love dogs.
36:05So I remember that number.
36:06>> I think there's sort of a two 200 to
36:08300,000 years. I'm not an expert here.
36:12Yeah. Of what people would carve out as
36:14our current species.
36:15>> We've been homo sapiens for 200,000.
36:17>> Neither one of us. Hopefully
36:19understanding is overrated and this
36:21specific number doesn't matter for the
36:23>> Yeah, we don't need this number. That's
36:24not the point.
36:25>> [laughter]
36:26>> The the point is for a long time we
36:28didn't understand much. We were relying
36:31on instinct. We were relying on
36:33experience. But things didn't really
36:35make sense in the way that they started
36:37to. And now again some arbitrary number.
36:40Certainly since the enlightenment
36:43>> 6 say if you want to put it with Isaac
36:44Newton we had a different level of
36:47understanding than we had before Newton.
36:49We really mathematized we as a species.
36:53Like take Kepler. I mean Kepler could
36:55see the elliptical orbits, the square
36:59and cube law about the planets. Kepler's
37:02third law. These are numerical patterns.
37:04He couldn't explain them. He just saw
37:05them in the data. And that was great.
37:07The math showed the pattern. But why?
37:11Okay, he couldn't understand them. And
37:13then the next, you know, a few
37:14generations [clears throat] later,
37:15Newton can explain that
37:18not only what Kepler saw, but all of
37:20what Galileo saw too from a deeper
37:23principle set of principles from his his
37:26laws and universal gravitation. And so
37:29that is like a triumph. Uh plus he has
37:32calculus in a in a more systematic
37:34powerful form than those other people
37:36have. And so he can derive all kinds of
37:39stuff with logic and a few principles.
37:42So that is a very powerful advance in
37:44human understanding and that Newtonian
37:47framework of find the differential
37:50equations and solve them more or less
37:53gives us 400 years of progress all the
37:55way through the Schroinger equation
37:58really I mean the Navier Stokes equation
38:00Maxwell's equation
38:01>> this is sounding like a case for
38:02understanding being under this of utmost
38:05importance
38:06>> it's it has been of utmost importance
38:08for 400 years
38:10>> okay
38:11>> and I'm going to argue you temporarily
38:14that there has been a great interlude of
38:17understanding
38:18before this interlude began. We didn't
38:21have much.
38:22Obviously, we had some. We had
38:24Archimedes. We had, you know, the guy
38:27who is whose name is translated as
38:29Elhazen, Iban Alhyam, great Islamic
38:33scholar. Okay. I mean, there were people
38:35for sure.
38:35>> Let's make some sweeping generalizations
38:37and just say like post enlightenment
38:39there was a
38:40>> we don't have to do with the
38:40enlightenment, right? I mean, maybe the
38:42Egyptians with the pyramids. We had a
38:43few thousand years. Let's say that way.
38:46We had a few thousand years of really
38:47kind of building up our understanding.
38:52But I think the window might be closing.
38:55That's that the the interlude is coming
38:57to an end because I think the AIS are
39:00going to get so advanced
39:03that even though they're going to be
39:05good teachers, they're not going to be
39:07good enough because we're limited until
39:10we change our biology. Then we're not
39:12really human. I mean, if we're going to
39:14stay the humans that we are with our
39:16kilohertz clock speed of our neurons,
39:19with the number of whatever it is, a
39:22hundred trillion synapses, I mean,
39:26whatever it is, we have limits
39:28and
39:30we can understand up to a certain level
39:33and that will be it. We're just not
39:35going to be like we already know, you
39:36can't picture the ninth dimension in
39:38space. There's only certain things that
39:40we can do. We can't picture 50 moving
39:43objects moving, you know, spinning
39:45around simultaneously. Psychologists
39:47have studied. So, it's gonna come soon
39:51that we won't understand all kinds of
39:53things that the AIS will tell us. And
39:56so, I I feel like that's going to be the
39:58story that we have this wonderful
39:59glorious interlude when the lights went
40:02on and then the lights are going to go
40:04off. And we're actually sort of lucky
40:07that we're living in a time when
40:09understanding is still meaningful. But
40:11progress will continue. We're going to
40:13have all kinds of fantastic results.
40:15Predict I mean assuming we can survive
40:17this
40:19>> separate question. But if we can survive
40:22super powerful AI and all the other
40:25things coming to the planet,
40:27um
40:29we're going to have we'd have incredible
40:31progress.
40:33When you when you say the or making the
40:36potentially devil's advocate case on
40:38understanding is overrated, you mean in
40:40so far as progressing the the welfare of
40:43humanity or or pushing forward, you
40:46know, a sense of um
40:48>> ability in constructing the world around
40:51us or however you want to measure
40:53progress. You're saying uh we we are we
40:56are fast coming to the point where human
40:58understanding as a meaningful component
41:01of what determines that kind of progress
41:04is of waning significance.
41:06>> Absolutely beautiful summary. Yes, that
41:09it's overrated in that sense that we
41:11think understanding is great because
41:12it's been so helpful to us also because
41:14it's pleasurable.
41:16>> But it's going to stop being that
41:18helpful. No, it will still be
41:20pleasurable.
41:21>> Okay. I mean just like people like to do
41:23crossword puzzles or other things that
41:26involve thinking
41:29um the so that's so there's that view of
41:31it that math will always be here just
41:34like playing the cello or you know I
41:36mean singing these things are just
41:38inherently fun and and actually I sort
41:41of flinched although I don't know if I
41:42visibly flinched when you spoke about
41:44welfare or progress you know because
41:49it's such a narrow construction of
41:51progress that we're talking about here
41:52like building more gadgets, even curing
41:55diseases.
41:57Fine. Those kind of advances are a
41:59certain type of progress.
42:02But what about like spiritual progress
42:04or happiness or kindness or you know
42:08very soft things that are still very
42:11important in life. um maybe the most
42:14important love, being loved, those
42:17things
42:19uh
42:21that is going to persist forever. We
42:23hope and
42:26>> I I really find myself in these
42:27conversations. I always end up wanting
42:30to talk about the meaning of life. I
42:32really think that's what's lurking here.
42:34I know we're supposed to talk about math
42:36with each other, but I I kind of think
42:38that's what we have to talk about is
42:40what are we doing? I mean, what are we
42:42here for, if anything, and what do we
42:44want out of our life? I do think that's
42:46what's at stake, and that's ultimately
42:47what we have to talk about.
42:50>> It's so interesting you land there. I
42:51mean, I think the reason that the math
42:53and AI topic is so relevant even outside
42:57of the math circles is that people talk
42:59about a spiky frontier to AI. There are
43:01certain things it gets good at faster
43:02than others. And in so far as math
43:04exists right at the beginning of one of
43:07those spikes, coding as well might be
43:09another one of them. It stands to be a
43:11microcosm of a broader world on and
43:14mathematicians are especially
43:15interesting because the thing that they
43:17are doing is both useful. You know, you
43:21you you mentioned three different things
43:22that are uh that are what we get out of
43:26understanding. You have the the or
43:27orgasmic side of like it's just nice.
43:30You have um a route to power. Um and
43:32then you also have the generative aspect
43:35of it on like it brings you things. And
43:37if I'm if I'm hearing the argument
43:39correctly, it sounds like what you're
43:41saying is on the generative side that
43:44human understanding won't be as
43:45important on the route to power side. I
43:48mean, maybe we can get to that. That
43:49depends on what human clarified the
43:52distinction about generative versus
43:53power. So there's power in the outside
43:56world, but there's also generative in
43:58the inside world. So generative of more
44:01ideas like you can speak about for to me
44:04pure math is about the orgasm and the
44:07generative
44:08math that keeps recreating new math math
44:11that keeps posing new qu like say let's
44:14take the the quest to solve fair's last
44:16theorem right the prove the fair
44:18conjecture so pure mathematicians love
44:21that story rightly because you know
44:25along the way to try to solve this
44:27problem they invent invent ideas like
44:31ideals in, you know, in algebra. they
44:35discover number fields and examples
44:38where they don't have prime
44:40factorization being unique and like
44:43there's a whole
44:45glorious
44:47imagined world that turns out to spring
44:50up around this question that is
44:52beautiful in its own right and actually
44:55arguably more beautiful and more
44:57important than for MA's last theorem. I
45:00think most serious mathematicians would
45:01say that's not really that theorem or
45:04that conjecture whatever
45:06that was our lighthouse right I mean in
45:08the modern to use the current uh
45:11metaphor that seems to be going around
45:13that that shines the light and then we
45:15create all kinds of other ideas to try
45:18to solve it and those ideas take on a
45:21life of their own they become
45:23I mean they gradually give rise to
45:25something close to the Langland's
45:27program you know like the really big
45:29stuff
45:31that that ends up getting used in wild's
45:34proof modular forms. I mean, I don't
45:36know wilds proof, but it but it sounds
45:38like a really absolutely enormous set of
45:41ideas
45:43gets used that is way more beautiful and
45:46powerful and and generative in this
45:49sense that it's math making more math
45:53and more understanding and lots of other
45:55great results that along the way bing.
45:58Okay, we get from Maslas theorem, but
46:00that's not the point. And this is why
46:02Gaus complained so much about Goldbox
46:04conjecture, right? I mean, Goldbox
46:07conjecture that
46:09every even number is the sum of two
46:12prime numbers still unsolved.
46:16Seems like it in a way a better question
46:18than for last theorem. So simple. And
46:21yet very few mathematicians get all
46:24weepy and excited about goldbox
46:26conjecture because it hasn't been
46:28generative. It doesn't it didn't produce
46:31the same kind of surrounding
46:34superructure of great math. It's like
46:36sort of peripheral. It's kind of out
46:38there not connecting to the great body
46:40of other math. So in this certain
46:42aesthetic
46:45I mean Gaus has some quote I don't
46:47remember the exact wording but it's
46:48something like
46:50ah you know it's easy to make up a
46:52question that you could neither prove
46:54nor find a counter example to and it's
46:57not connected to anything else and
46:59that's of no interest.
47:02So, so it was the peripheral nature of
47:05the of the conjecture goldbox conjecture
47:07that turned off Gaus and I think turned
47:09No, it's not totally true. There is
47:11beautiful math connected to Goldbox
47:13conjecture too, but not as beautiful as
47:15the math and not as interconnected as
47:18Fairma's last theorem. So, according to
47:20certain tribe, this is what pure math is
47:24all about. I, you know, look, this is me
47:27talking about a foreign culture. It's
47:29not really my people. I'm I'm the people
47:32I want to talk about Maxwell, you know,
47:34or
47:35>> or Einstein. I mean, I'm guess I'm a
47:37physicist in mathematicians clothing,
47:40>> but a biologist, too. [laughter]
47:43>> I I think I want to like stay drilled on
47:45the the site because what's what's
47:46salient to the minds of a lot of young
47:48people is just what is the role? One,
47:50will human mathematicians exist? Um
47:53yeah, you know, is it is it dead in the
47:55water to even like go into to a PhD? And
47:57then two, what is the role if they do
47:59exist? And so maybe first I've been
48:01trying to hold my tongue. I don't want
48:03to insert too many of my own opinions.
48:04>> I want your tongue flapping, man.
48:06>> Um [laughter]
48:07I
48:07>> It's your show. Okay, you could be on
48:09that side of the microphone.
48:10>> No. Well, so at the at the very least
48:13>> poke holes in Please poke holes in this.
48:14I just want to at least lay out why I
48:16think like mathematicians will exist,
48:18but it's kind of this wide openen
48:19question on exactly what they do. And
48:21then and then that might set the framing
48:22for how we think about this question of
48:24you know in so far as it's about uh uh
48:27being generative like to whom does that
48:29matter.
48:30>> So just from a from a side point of why
48:32is this a job? Where does the money flow
48:34from for mathematicians I think it's
48:36important to for a young student to have
48:38a clear vision of that in their mind
48:40because it is a very weird job compared
48:42to other portions of the economy. Are we
48:44talking about an academic mathematician
48:46who's a professor or are we but but
48:48there's so many mathematicians with jobs
48:51called data analyst?
48:54>> What what a wonderful Steve Strogat's
48:56answer on like you know
48:57>> true what is a cryptographer who what
49:00who who employs more mathematicians than
49:02anybody? The National Security Agency.
49:05>> Okay, I love this.
49:06>> Okay, you don't mean them. You want to
49:07talk about math professors.
49:09>> And for the sake of clarity, let's let's
49:10let's first talk about professors, but
49:12actually we should zoom out. Um so I
49:14think so first on the side of professors
49:16then let's zoom out. Okay the reason
49:18it's relevant just to focus on the
49:20professors before the zoom out who
49:22trains all the cryptographers who trains
49:24all of the data analysts all of the like
49:26one of the most valuable
49:28>> externalities from the existence of math
49:31departments are all of the people who
49:33like quote unquote fail to go into
49:34academia or like don't end up becoming
49:36professors. you have this just spilling
49:38over of mathematical talent and problem
49:40solving ability out of people that maybe
49:42they pursued a PhD, maybe they uh just
49:45got their undergrad who don't
49:46necessarily go into academia but
49:48importantly they spent a meaningful part
49:51of their formative youth at least
49:52undergrad years maybe grad years in a
49:54math department or something adjacent to
49:56a math department
49:57>> and so so the the question of like do
49:59those math departments exist and the
50:01people doing this training do they exist
50:03I think has has uh has bearing even on
50:06the the most the broader stroked
50:09definition of mathematician that I would
50:10agree with on you on on here. Um but
50:13just on the academic mathematician side
50:15one you've already kind of hit it where
50:16I think if you follow the money flows a
50:18ton of it is just uh educ just teaching
50:21I think on um for for a typical math
50:23department which is unlike other forms
50:25of research where sometimes you know uh
50:27harder sciences are quite expensive to
50:29do the research um and and there's going
50:31to be more that leans on public funding
50:33or or private philanthropic funding. Of
50:35course, math also has that, right? There
50:37is um there are, you know, in the US
50:39like NSF grants that are a meaningful
50:41part of what will support mathematical
50:43research. There's various private
50:44foundations. You have atypical
50:47institutes like if you're a permanent
50:50faculty member at the Institute of
50:51Advanced Study, like teaching is not as
50:53as big a part. Um
50:54>> right,
50:55>> the teaching side of it, this strikes me
50:57as something that's quite AI safe as far
51:00as job security goes in so far as if
51:03universities exist at all. if we have
51:05social structures at all like what we
51:07have now, people really will value the
51:09um the human to human side of that. Um,
51:12and I mean people have have sort of
51:14written about this on how like a pretty
51:17good case study on this is COVID and how
51:19much people hated uh education through a
51:22screen
51:23>> even when it's just an Alex Conoric made
51:25this point in a nice like dialectical
51:27thing. He was I was reading of his
51:28lately uh where it was essentially like
51:31look you already if you have the current
51:33status of ed education ability but
51:35mediated through a screen and people
51:36hated it you know maybe AIS get
51:39superhuman such that even through a
51:41screen they're better but it's a very
51:43social thing going on if we think of
51:44what's actually happening with education
51:46where it's not about clarity of
51:48explanation it's about what motivates
51:50you to learn and if we think of what
51:52motivates people it's their it's their
51:54connections especially peer connections
51:55but also I think mentor or connections
51:57and such. I will care about a topic more
52:00knowing that you Steven Strogats wrote
52:02about it compared to just what the words
52:05on the page in and of themselves can do
52:07like that
52:08>> uh little bit of human to human
52:09connection matters. So if we presume
52:12that teaching still exists um then the
52:15existence of like that as one of the
52:18funding sources towards what goes into
52:20math departments is kind of unaffected
52:22by whether or not AIs can you know solve
52:25problems better or set conjections
52:27conjectures better or set entire
52:30programs like the leng programs better
52:32all of that is this ancillary thing of
52:33what the mathematicians choose to do
52:35with this surplus time that is you know
52:37research [laughter] and some of what's
52:39>> good that you see it that way because
52:41after all historically I mean it's been
52:43changing so much throughout history
52:44right there before there were really I
52:47mean universities are not that old
52:50>> 1200 you know AD or something the first
52:54universities in Europe or or somewhere
52:57about there uh and for a long time it
53:00was all about teaching yeah I mean Isaac
53:02Newton or Isaac Barrow did do some they
53:04did research but they were teachers
53:08And
53:10then after World War II, I mean, that's
53:11the big thing that really changes so
53:14much because for one thing, computers
53:16start to exist,
53:17>> modern computers, but also
53:21because of this vision of this guy
53:23Vanavar Bush that we need research and
53:27we're going to pay with taxpayer dollars
53:29for these professors in math and physics
53:32and science to do research with such
53:35generosity from the public that it's
53:38actually free to go you get paid to go
53:40to graduate school in the sciences to
53:42get a PhD. It's really shocking. I
53:44couldn't believe it that I didn't have
53:45to ask my parents for money [laughter]
53:47to go get a PhD that that they would pay
53:49me to get a PhD. I thought that's just
53:51the greatest thing. Um
53:54>> yeah,
53:55>> now how much longer will it last though?
53:57Because what was why did we get paid to
53:59go to grad school? Was it because of the
54:01Cold War? because the country sort of
54:03thought we need a cadre of serious
54:06technical
54:08people so that we can stay ahead of the
54:10former Soviet Union. I mean it's a very
54:14cynical view of it but I think that was
54:16actually a big like in Congress they
54:19would say that's what science funding
54:22was about for a long time. So this one
54:24is not a done deal on whether public
54:26funding like continues to exist um for
54:29mathematics.
54:30>> But we may become teachers and do a
54:31little research on the side like we
54:34always were.
54:35>> Yeah. Even if you subtracted it all
54:36away, the the career does not die. No, I
54:39if I had
54:39>> No, it doesn't die as teacher.
54:41>> Yeah. Yeah. So if I had to predict, I
54:43would imagine public funding.
54:44>> But let's ask the question. May I ask
54:45you then since I know you wrote about
54:47this? So why why does anyone want to
54:50learn math if
54:52of course the calculators to this right
54:55now can do all kinds of elementary math
54:57calculating tips or balancing your
54:59checkbook. So you
55:03since we're doing the devil's advocate
55:04thing with each other.
55:05>> Yeah. You know what's your argument for
55:08why anyone should learn math in the
55:11future given that you can press the
55:13button on wolf from alpha or now just
55:16ask anthropics cla or chat gpt and so
55:20what would you say why why do you what
55:22because people must be asking you all
55:24the time why should I learn math
55:27>> I think there's there's basically the
55:30artistic answer and then a utilitarian
55:32answer I think the artistic answer stays
55:34pretty stable into for whatever AI
55:36feature you get. And you sort of hit it
55:37on earlier on like just the there is a
55:40very unique kind of joy and edification
55:44that is unlike anything you find almost
55:46anywhere else that uh math has really
55:50cultivated an aesthetic around that it's
55:53joy isn't quite the right word for when
55:55you come to understand something. I I I
55:57think of a very specific clicking moment
55:59that happens for certain kinds of
56:00[laughter]
56:01>> Yeah, clicking like that that click that
56:03happens in the brain. I don't get it
56:05from anything else and it's it's it's
56:07such a joy and it's it's so addictive. I
56:10think certainly there will always be
56:11people who have experienced that and
56:13just want more of it. Um and actually I
56:15think many of the mathematicians I
56:17talked to this is this is actually their
56:19motive for going into the field. It's
56:21not so much they wanted to be the first
56:23to discover something. It's not so much
56:25um you know it's not even yet the
56:27vibrancy of of the culture and the
56:29shared community. I think it's that at
56:30some point when they were younger, they
56:32got addicted to that feeling of whatever
56:34like doing math meant for them and they
56:36they simply wanted to do more of it. And
56:38the most
56:38>> that's what it is.
56:39>> Yeah. The the the the most standard path
56:42for how to do that.
56:42>> I mean, you'll remember that was what
56:44the last time we did this together when
56:46I was on your uh podcast some years ago.
56:50I told that whole story about this
56:51certain triangle problem in high school.
56:54>> Yes.
56:54>> And that was it for me. And that was I
56:56wanted to reproduce that feeling
56:59>> that will always exist. There will be
57:01the people these are the people I'm
57:02often trying to um either speak to with
57:05my videos. You know, they've already had
57:06that feeling and I'm trying I'm trying
57:08to feed the addiction and give them a
57:09couple more of those clicky moments.
57:11Even better would be if it's somebody
57:12who hasn't yet experienced that and I
57:14can offer it to them for for the first
57:16time in some form. So that that's one
57:18answer on on why to continue to learn
57:20math. And this isn't the anything you
57:22can do, I can do better future of AI
57:24where like there's just look, there's
57:26nothing that you're going to be able to
57:27do that the AI couldn't.
57:29>> This is timeless. It's permanent.
57:31>> That is such a wild future to engage
57:33with. First of all, we have to do all
57:35the normal couching on like, you know,
57:36humans are still alive. This is a good
57:38version of the future, not a bad version
57:40of the future. But like in that in that
57:42branch, of course, we're going to focus
57:44on the human flourishing aspect because
57:46what what else is there to focus on? Um
57:49I think we we have some years yet though
57:51that closes that gap on the anything you
57:53can do I can do better.
57:54>> And there's definitely been time and
57:57time again this recurring phenomenon
58:00where the people who learn these
58:02mathematical abstractions come to
58:05appreciate the nature of what it looks
58:08like to sharpen your problem solving
58:10abilities in that context find
58:12themselves unexpectedly useful in
58:14neighboring fields. And this maybe gets
58:16to your point on like what is a
58:17mathematician? are all the you know the
58:18data scientists and the cryptographers
58:20and the machine learning researchers
58:22everybody there the these are these
58:25these people who have just spilled forth
58:27from the the mathematics education
58:29system quite productively and so you
58:32know everybody's writing their their
58:33grants talking about these examples that
58:35you brought up on you know remon uh car
58:38caring about non-ucuklitian geometry
58:40that turns into general relativity later
58:42or pursuit of ferma's last theorem gives
58:44rise to things like elliptic curves
58:46which are then useful
58:47That is one externality that comes from
58:50doing math research and and that
58:51existing as an institution. There's a
58:53much more immediate one in my mind which
58:55is this spillover of just all the highly
58:58educated educated in the sense of
59:00capable of problem solving,
59:01understanding mathematical abstractions,
59:03fluent in that framing frame of thought,
59:06>> just just going elsewhere. anything
59:08that's not academia that they're going
59:09into. Well, not anything like quite a
59:12few of the the things are are productive
59:14um in these in these ways that are hard
59:17to capture in a direct sense and
59:19therefore very good fruit for you know
59:22private philanthropic funding or public
59:24funding or whatever it might be. I you
59:26know maybe there is a future of AI so
59:28good at everything that all of that's
59:30obviated. All the cryptography is
59:31automated all the data analysis is
59:33automated. But at the very least in the
59:35meantime, you don't want to jump the gun
59:37on halting the the system that produces
59:40all of the people fruitful there. Uh and
59:43then you know what whatever it is that
59:45you think is important for making sure
59:47we're on that good version of the future
59:49and not the bad one. You know, I think
59:51of all the people who are jumping ship,
59:54so to speak, from the traditional math
59:56academic career paths, there's some I
59:58know that go into the AI safety side of
1:00:00it, and it's probably a very good thing
1:00:02that the like highly mathematically
1:00:04trained people are trying to bring those
1:00:05chops into, you know, these various
1:00:07problems that they frame their think
1:00:08what you will of like how well posed
1:00:10those problems are or not. It just seems
1:00:11like a very good thing to have people
1:00:13trained in this way, like thinking hard
1:00:15about that. And so from that standpoint,
1:00:19it just seems clear to me something like
1:00:21the institutions we have now of a group
1:00:23of people that we call mathematicians
1:00:26who exist in departments that by and
1:00:28large are just training people in
1:00:30mathematical thought. Some of them to be
1:00:32new mathematicians but a lot of them
1:00:34not. that as an institution strikes me
1:00:36as surprisingly stable compared to a lot
1:00:39of other things where AI progress tends
1:00:41to potentially automate tasks within a
1:00:43job and then and then the job wholesale.
1:00:45And the question then becomes what do
1:00:48those people within this group decide to
1:00:51do on the research side on on uh the all
1:00:56of all of these things where we've come
1:00:57up with proxies in the past. You know
1:00:59what's the significance of the theorem
1:01:01that you proved in your PhD thesis and
1:01:03things like that. they have the choice
1:01:04for what to use as a proxy instead to uh
1:01:08make you know hiring decisions to uh
1:01:11decide on is this a worthy topic for a
1:01:13PhD or not to make tenure decisions.
1:01:15Nobody nobody else is making that choice
1:01:17for them. It is entirely within the
1:01:19community to decide what deserves
1:01:21academic status and not and that I think
1:01:24is a very fruitful I have no idea what
1:01:26the answer is but I think that's a very
1:01:27fruitful question to ask right now.
1:01:28>> I think I mean I do have a feeling about
1:01:30the answer there. It's that it's um
1:01:34it's almost like upvotes on social media
1:01:37that [laughter] if I can do something
1:01:39that you find appealing or that gave
1:01:42your neural circuitry a little shiver of
1:01:46pleasure just to think about it or to
1:01:48see something. And it's not because it
1:01:50was so earthshatteringly new like any AI
1:01:53could have easily produced it at the
1:01:54push of a button.
1:01:56That's not going to be the test anymore.
1:01:58It's just did you enjoy what I created
1:02:01or even what I showed you and and what I
1:02:04made a case for that you should pay
1:02:06attention to it. That's why I think it
1:02:08is related to a kind of charisma
1:02:10salespersonship
1:02:12something like that. It's really about
1:02:13the social dimension that we're giving
1:02:15each other pleasure and you might say
1:02:17for what real purpose that's the
1:02:18purpose.
1:02:19>> Yeah. It's not going to be I mean some
1:02:21of it will be you instrumental like for
1:02:24really solving problems that matter to
1:02:26life or to human well-being or to the
1:02:28planet's well-being
1:02:30but the AIS will be playing a very big
1:02:32role in that even just aside from that
1:02:35like the pure part of math I think it'll
1:02:38be a lot what it is now which is do we
1:02:41do things for each other that are
1:02:42interesting or do we show each other
1:02:44interesting things can we teach each
1:02:46other um and can we have fun doing it
1:02:49together which again I feel is very
1:02:52close to the meaning of life like for an
1:02:55academic person anyway but um I really
1:02:59think we have to ask what do we do with
1:03:02our blip of consciousness you know like
1:03:06ashes to ashes and dust to dust you're
1:03:08you're atoms and for a while you're
1:03:12organized in this astonishing way that
1:03:15gets to feel pleasure and happiness and
1:03:17love and sadness And
1:03:20what are you going to do with that
1:03:23period of however many years it is? And
1:03:27that's always been the question. But I
1:03:29feel like it's forcing a lot of us to
1:03:30become philosophical who haven't thought
1:03:33I mean I happen to like philosophy. I've
1:03:35always liked philosophy. I have not paid
1:03:37much attention to religion in the past
1:03:40but but I'm finding myself reading some
1:03:42of the great religious writings
1:03:45particularly the book of Ecclesiastes
1:03:48which I you know that's the one that
1:03:50gives rise to that song uh the bride the
1:03:53birds turn turn to everything there is a
1:03:57season turn
1:03:59um that that's a line from the from
1:04:01Ecclesiastes in the Old Testament and if
1:04:03you haven't read it uh I don't want to
1:04:05go on a
1:04:07evangelical thing here, but I had not
1:04:09read it until recently, and it's a very
1:04:14unflinching
1:04:16and modern and
1:04:19not particularly um easy to read as far
1:04:22like for a a traditionally pious person,
1:04:25God doesn't appear in it very much.
1:04:28>> What do you mean by unflinching?
1:04:30>> I mean unflinching in that it says there
1:04:32is no meaning.
1:04:35It doesn't give you any comfort at all
1:04:38about um the reason that you're here is
1:04:41because of love or because of doing
1:04:45God's work or about the works that you
1:04:48create. All of that is described as
1:04:51vanity. And it's vanity in a particular
1:04:54sense. It doesn't mean vanity like, oh,
1:04:58you're so vain, you're conceited. It
1:05:00means you're doing everything in vain.
1:05:02>> It's all pointless.
1:05:04It's all vanity. The the Hebrew word is
1:05:07apparently the word for vapor
1:05:10or breath. It's all It's all It's sort
1:05:12of like the concept of dust in the wind.
1:05:15It's It's all vapor. It's all transient.
1:05:17It's really very Buddhist sounding
1:05:20roughly.
1:05:21>> So, what did you take away from it?
1:05:23>> What do I take from it?
1:05:24>> Yeah. Yeah. What do you take away from
1:05:25it?
1:05:25>> What I take from it? I mean there is
1:05:26there are glimmers of hope in it which
1:05:29which are
1:05:31um sentences like
1:05:34this idea that to everything there is a
1:05:36season everything is beautiful in its
1:05:39time it says
1:05:43>> sorry this is my new thing crying on
1:05:45camera [laughter]
1:05:47but this idea everything is beautiful in
1:05:50its time that that we get to have a
1:05:53moment in the sun
1:05:55you know when you get to love, you get
1:05:57to care, you get to be somebody, you get
1:05:59to live out your dreams maybe if you're
1:06:01lucky and that's it. I mean that it's
1:06:04because it's transient because life is
1:06:07so short. That's what makes it precious.
1:06:11These are not original thoughts. I mean
1:06:13these are ancient thoughts but they're
1:06:15right there in this several thousand
1:06:17year old document. And so when I think
1:06:20of what are we doing when we do math if
1:06:22the machines are better than us? Well,
1:06:24Terry Ta's already better than me, you
1:06:26know. I mean, it's not about that. It's
1:06:28about what I get to do by having this
1:06:31conversation with you or with my
1:06:33students or my teachers. That's that's
1:06:36what we get to do while we're alive.
1:06:39>> I mean, you're saying
1:06:41>> I'm saying that's why we're doing it. If
1:06:43it's if math is the thing that gets you
1:06:44up in the morning, do it for that
1:06:47reason. If it's playing your guitar, if
1:06:50it's helping the person at the hospice,
1:06:53you know, whatever it is that gives your
1:06:54life meaning, that's what you've got to
1:06:56cling on to because you're only here for
1:06:58a short time. I I kind of think that's
1:07:00all there is. And the the when I say
1:07:04it's unflinching,
1:07:07it's so unflinching that at the end of
1:07:09it, if you look at this Ecclesiastes,
1:07:13it has a paragraph which is clearly
1:07:15tacked on by later rabbis which says all
1:07:18that is all very nice, but all in fact,
1:07:21what you're really supposed to do is
1:07:23just do what God tells you to do.
1:07:25[snorts]
1:07:26like it's, you know, it gives a very
1:07:27traditional top- down kind of thing that
1:07:30is totally at odds with everything in
1:07:32the rest of the text.
1:07:34>> It's um
1:07:36>> okay, didn't plan to go there, but
1:07:38>> Well, [laughter] no, I I love everything
1:07:40about this because essentially what
1:07:42you're getting at is human flourishing.
1:07:44And if you're saying like if if math is
1:07:46what what feels like a life best lived,
1:07:49you know, to do math, to engage with it,
1:07:51to find these clicking moments, that is
1:07:53the reason to do it. You need no you
1:07:54need no justification even further than
1:07:56that. You don't need to rest on the the
1:07:58fact that your particular contribution
1:08:01is like what what the future hinges on
1:08:03as far as like later utility down the
1:08:06road.
1:08:07>> I want to I do want to talk about that
1:08:09problem solving component of it that I
1:08:11pushed back a bit earlier and and and
1:08:13and connected a bit. you referenced
1:08:15already the story you gave the last time
1:08:18you were on this podcast of a particular
1:08:20problem you were given as a young
1:08:21student that was you know unexpectedly
1:08:24tricky about triangles and and the
1:08:26pursuit and the joy that that came from
1:08:28that.
1:08:28>> Um so I've had and this is going to be a
1:08:31little bit of a long thought but I'll
1:08:32I'll see if I can I can keep it somewhat
1:08:34short. I've I've had this experience
1:08:36many times where you know I find math
1:08:38quite beautiful. I think you find it
1:08:40quite beautiful. there's a certain
1:08:41shared aesthetic among many
1:08:42mathematicians, but then every now and
1:08:44then I'm trying to communicate to
1:08:46someone else what it is I find beautiful
1:08:47in it. And I like to, you know, this is
1:08:49my whole job to some extent. I'm
1:08:50supposed to be able to like convey the
1:08:52[laughter] beauty of math and and and I
1:08:54run up against a regular failure. Um,
1:08:56which is that sometimes somebody who's
1:08:57quite outside of it.
1:08:59>> It's just there's just nothing about it
1:09:00that's clicking the way that I would
1:09:01want. You know, I maybe I talk about the
1:09:03Pythagorean theorem or certain way of
1:09:05seeing it and it's, you know, they're
1:09:07they they nod along and it's not that
1:09:08they don't understand it. It's just
1:09:10something where it's as if I'm seeing a
1:09:12color and they they see it in black and
1:09:14white. They're like, "Look, that's true
1:09:16and everything, but [laughter] I got to
1:09:18be honest, I don't see why this is
1:09:19beautiful."
1:09:20>> And I've thought about this and I think
1:09:22some of what's going on is my my sense
1:09:26of what is beautiful is actually more
1:09:28tied to problem solving than it might
1:09:30seem at first. where I, you know, in my
1:09:33youth was was good at math or in so far
1:09:35as, you know, in the local environments
1:09:37where I was enough to feel that way as,
1:09:40you know, egotistically young man as as
1:09:41as many of us might have been at some
1:09:44point.
1:09:44>> And um and sometimes when there's a
1:09:47given idea that I would see and think
1:09:49like, oh wow, that's that's very
1:09:50beautiful. What that actually would
1:09:52translate to is I can see how this might
1:09:54be useful later or that is a real bolt
1:09:57out of the blue that helped solve this
1:09:58problem and I can like part of me can
1:10:02predict that maybe I can use that same
1:10:04kind of bolt later on were I to come
1:10:06across another problem and seem
1:10:08similarly clever something like
1:10:10generating functions. You know the first
1:10:11time you ever learn about generating
1:10:13functions
1:10:13>> it's just like where did that come from?
1:10:16But [laughter] it's you can sense the
1:10:17generality of it and and you can have
1:10:19the sense that like oo next time I come
1:10:21across this recurrence uh uh property or
1:10:24something like that is a tool that I'm
1:10:26going to be able to bring to bear. And
1:10:27the fact that it's both general and that
1:10:29it's unexpected, this is some of what
1:10:31makes it seem uh beautiful. you I I
1:10:35don't play as as much chess as I I think
1:10:36you do, but sometimes when I see people
1:10:38commentate on like a particular move
1:10:40being beautiful, some component of that
1:10:42is that it's unexpected and it's also
1:10:44that it's um
1:10:46>> you know it's clearly useful. It was a
1:10:48good move to make and that if we say
1:10:50what makes that beautiful I wonder if
1:10:51it's a sense of it's like an intuition
1:10:53to tuck away that maybe can be applied
1:10:55in a future game. And if you try to take
1:10:58the problem solver out of the
1:11:00mathematician or out of the student and
1:11:03if they don't they don't have the same
1:11:05kind of practice of really engaging with
1:11:08and struggling with problems in the same
1:11:10way
1:11:11>> that all of these surrounding things
1:11:13that we're talking about on like oh it's
1:11:14it's math for human flourishing. It's
1:11:16it's this thing that gives you this
1:11:17unparalleled feeling or mathematicians
1:11:20saying it's the lighthouse that's
1:11:21shedding light on this broader landscape
1:11:22but it's the landscape that you care
1:11:24about. I kind of wonder how much of that
1:11:26landscape or how much of that deeper
1:11:28clicking feeling is dependent on being
1:11:31perceived by a problem solver, a person
1:11:34who at some point in their past really
1:11:35engaged with trying to solve hard
1:11:37problems and has unconsciously or
1:11:39otherwise collected a sense of what's
1:11:41going to be useful for that. And this
1:11:43beauty that we're describing and this
1:11:44flourishing that we're describing is
1:11:46tied with that. And so this is a very
1:11:49long way of kind of going
1:11:51>> but I think I'm following you. Yeah, go
1:11:53ahead. you ask the question because I
1:11:54think I know where you're going. if you
1:11:56had had a youth where you didn't have
1:11:59you were given this triangle problem and
1:12:00you could just ask chat GPT or something
1:12:02and it kind of shows you what the answer
1:12:03is or like or or you mentioned Gorsat's
1:12:06theorem in complex analysis um something
1:12:09if that was something that uh you know
1:12:10it's it's just coming out as text from a
1:12:13chatbot like all of the all of the
1:12:14problems that you could have engaged
1:12:16with the mode of of engagement at least
1:12:18in principle maybe also in practice came
1:12:21from the you know quote unquote all
1:12:23knowing AI just giving you the answer
1:12:25>> do Do you think your aesthetic for math
1:12:27would have been affected if that had
1:12:29been your youth?
1:12:32>> Oh, very very much.
1:12:34>> Yes. And um
1:12:38in a very negative way in a very I would
1:12:40be deprived.
1:12:42>> And how so how do we preserve that? Like
1:12:44how do we make sure?
1:12:45>> Yeah. Let me let me try to make this
1:12:46very concrete that uh I have taught
1:12:50three times a course
1:12:54called math explorations
1:12:57and it's a course for people who have a
1:13:00math requirement to graduate and most of
1:13:04them don't want to be there.
1:13:07>> You know, these are government majors,
1:13:10architecture, whatever. They're art
1:13:12history. They're not interested in math.
1:13:14Not really. Some of them are, but most
1:13:17of the people who take it are taking it
1:13:18because their college
1:13:21says you have to satisfy a quantitative
1:13:24reasoning distribution requirement.
1:13:28And um this is thought to be one of the
1:13:30easier ways to do it. Like you could
1:13:33take calculus, but a lot of these
1:13:35students have already taken calculus and
1:13:37may have even gotten a good score on the
1:13:39BC calculus test. That's how they got
1:13:41into Cornell in the first place. but
1:13:44they don't see the point of math or they
1:13:46hated math or maybe they were perfectly
1:13:49good at it and they just whatever. So
1:13:52they don't want to do calculus again. So
1:13:54they're in my course math explorations
1:13:56and just to come to the point since I do
1:13:59feel so long-winded for some reason
1:14:01maybe because I am [laughter]
1:14:04I think it's absolutely essential to
1:14:06give people the experience of doing
1:14:08math. Math appreciation doesn't work
1:14:12without math
1:14:14doesn't really work without doing math.
1:14:18You can appreciate math passively. You
1:14:20know, you could watch Grant or you could
1:14:21watch me talking about the beauty of
1:14:23math or blah blah blah. It doesn't it's
1:14:26not the same. It doesn't produce the
1:14:28necessary thing that makes a person get
1:14:33it unless they do it. Now, it doesn't
1:14:35have to be advanced math. It could be so
1:14:38basic. I mean what I often use as the
1:14:40first activity is is a problem where
1:14:42there's a triangle drawn in the middle
1:14:44of a piece of paper and it's a triangle.
1:14:50Actually the the first activity is I
1:14:52would show you an equilateral triangle
1:14:54and then I give you a scissors and say
1:14:58your goal is to cut out the triangle but
1:15:00you can only make a single straight cut.
1:15:03Have you ever heard this activity?
1:15:05>> I don't think so. No.
1:15:06>> Okay. So there's a triangle. I mean, I
1:15:08could draw one, but I give a blank piece
1:15:09of paper, except it's got a big fat
1:15:11triangle. It's equilateral. Here's your
1:15:13scissor. Cut out the triangle, but you
1:15:15have to cut in a straight line. And then
1:15:18the student thinks, "That's impossible."
1:15:20And then another student says, "Are we
1:15:22allowed to fold the paper?"
1:15:24>> And then you say, "Go ahead." So then
1:15:27the kids are all holding up the paper to
1:15:29the light and get and folding it to get
1:15:31the lines on top of each other. Then
1:15:33they cut and everybody can do it and the
1:15:36triangle drops out and then you hand
1:15:39them another piece of paper that has a
1:15:41square on it
1:15:42>> and then they're kind of actually like
1:15:44it because they did it. They do it
1:15:46again. The square drops out anyway. You
1:15:48do a few simple shapes and everyone can
1:15:50do it. But then
1:15:53you give them a scaling triangle. All
1:15:56three sides are different length.
1:15:59No symmetry. no obvious an you know
1:16:03axis of symmetry or any obvious thing to
1:16:05do with it. And I did this myself in a
1:16:10in a class learning how to teach in this
1:16:12inquirybased style. Um I had never been
1:16:16taught this way. And next to me was my
1:16:18colleague John Gugenheimer who's very
1:16:20fast and smart. and
1:16:24and John is doing something with the
1:16:25paper and he cuts it out and it's it
1:16:27worked
1:16:28>> and I can't figure out what to do and I
1:16:30feel myself getting embarrassed and my
1:16:32face is getting red because I'm really
1:16:34slow and I'm always the slowest and I
1:16:37start feeling what people who hate math
1:16:40feel.
1:16:41Okay. So, it's really good to go through
1:16:43that and then John is now doing a
1:16:45quadrilateral and then he's doing a
1:16:47concave quadrilateral and he everything
1:16:50they give him, he could do it and I'm
1:16:52still stuck on the scaling triangle.
1:16:55Now, um
1:16:58when I do this with the students and I
1:16:59give them the scaling triangle after
1:17:02they've had several successes, nobody in
1:17:05the room can do the scaling triangle.
1:17:06And it like a half hour goes by
1:17:09>> and
1:17:11The interesting thing that happened the
1:17:13first time I taught this was I say I'm
1:17:15like running out of time and the the
1:17:18bell's going to ring and I think okay so
1:17:21I say would you like a hint and then a
1:17:23bunch of students say yes and then all
1:17:26the rest of the students say no
1:17:29>> that's great [laughter]
1:17:30>> because they are actually having a
1:17:32mathematical moment they knew they
1:17:33should be able to do this godamn it they
1:17:36had done these other shapes
1:17:38>> and and so I thought You guys are the
1:17:40best because that's exactly you're
1:17:42already on the right track now that you
1:17:44know that you want to do this and
1:17:47there's no reason this isn't going to do
1:17:49any important thing in the world. This
1:17:51is just a game.
1:17:52>> Yeah.
1:17:53>> I had a kid then write to me and and you
1:17:56have to understand these are all
1:17:57traumatized people. On the first day we
1:17:59have them write on the board what's the
1:18:01first word that comes to mind when they
1:18:03think about math. I got responses like
1:18:06sick, ugly, hate it, embarrassed, you
1:18:10know, some people say beautiful, but
1:18:13um mostly this a class that has a lot of
1:18:17built-in trauma about whatever happened
1:18:19to them in math class. So, but over the
1:18:21weekend I got emails from one student
1:18:23saying, "I thought about this for hours
1:18:26and I find and I fiddled with it and I
1:18:28finally got it to work and I can't tell
1:18:30you the the feeling I'm having right
1:18:33now." But of course he doesn't have to
1:18:34tell me because it's the feeling you're
1:18:36talking about.
1:18:38>> So my goal in this class math
1:18:40explorations is to give everybody
1:18:43find some way to get let them get that
1:18:45feeling because that's the genuine
1:18:47mathematical experience and it doesn't
1:18:50matter that it's such an easy I mean
1:18:51it's a very it's not a deep problem but
1:18:55it gives them the deep experience.
1:18:58>> That's okay. That's great. And I think a
1:19:00perfect example of maybe how to use
1:19:02classroom time effectively for that
1:19:05because the other struggle of course
1:19:06every educator is having is um what to
1:19:09do about homework um when when more and
1:19:12in some sense maybe I'm just a naive
1:19:15outsider. I feel like why are we grading
1:19:17homework anymore? Um at the very least
1:19:19stop grading it. And then and then the
1:19:21question is you know how do you how do
1:19:22you motivate people to want to practice
1:19:24or maybe how do you shift that practice
1:19:26time to be in a in a communal
1:19:27environment instead of relying on
1:19:30someone's like internal motivation to to
1:19:33do that practice just for its own sake
1:19:35or just for the sake of the proctored
1:19:37quiz that you'll take the next day. Um
1:19:39these kinds of experiences though that
1:19:40this feels like just a much better use
1:19:42of time in the classroom to
1:19:44>> well yes and no because it's very slow.
1:19:48The students come out after after a
1:19:50whole semester of doing this. I mean, I
1:19:52have all these Let me say this comes
1:19:54from a series of books that you can look
1:19:57up on the internet, they're free, called
1:20:01Discovering the Art of Mathematics.
1:20:04All right, discovering the Art of
1:20:05Mathematics. If you type that exact
1:20:09phrase into your search engine, you'll
1:20:11be led to a place called Westfield State
1:20:13College.
1:20:14And um West maybe you're doing it as we
1:20:18speak.
1:20:19>> Yeah, I was curious.
1:20:20>> They they have uh like 11 PDFs of um
1:20:25math and music, math and dance. It's all
1:20:28about art. It's for liberal arts
1:20:29students and it's constant. I mean, it's
1:20:33so many brilliant activities of this
1:20:35type that are really hands-on. You could
1:20:38do it at high school level. You could
1:20:40even probably do it at middle school
1:20:42level, but we use it at college and it's
1:20:44meant for college students. Uh, and
1:20:48there's a whole psychology explained
1:20:50about inquirybased learning. But at the
1:20:52end of the semester, you could ask, have
1:20:54the students learned how much math have
1:20:56they learned? And by conventional
1:20:58measures, you would say very little.
1:21:01>> But I would say they've learned a lot.
1:21:04>> And I've the main thing is I've changed
1:21:06their attitude. They're now ready.
1:21:08They're now ready. And some of them say,
1:21:11"I don't still don't want to do math."
1:21:13But now I understand why people love
1:21:14math. They get it. They do get it. They
1:21:18all get it.
1:21:19>> It's I mean that that strikes me as much
1:21:21more useful than whatever because the
1:21:23major requirement you named it. So like
1:21:24quantitative reasoning or something
1:21:26called as an this is this is
1:21:29categorically not quantitative. At least
1:21:31the the example at the beginning
1:21:33>> the word quantitative wouldn't apply
1:21:34there. And in fact, I actually think
1:21:37almost all of what happens in a math
1:21:39department at a college level, I
1:21:42wouldn't call quantitative reasoning.
1:21:44Um, I mean, of course, some of it is,
1:21:46but if if if someone wants to justify
1:21:48like what is it that someone's getting
1:21:49out of the the math classes or a math
1:21:51major or that kind of training that's
1:21:52brought into the rest of the world, like
1:21:55everybody usually goes towards that word
1:21:58quantitative, you know, this is this is
1:22:00what makes it a transferable skill and
1:22:02everything. I think there
1:22:03[clears throat] are many better paths
1:22:03towards quantitative reasoning.
1:22:05>> Well, we could do that. I mean, you
1:22:07could say, why why am I not teaching
1:22:08them financial literacy? Well, that's
1:22:10useful, too. But this is something else.
1:22:12I'm trying to teach them
1:22:14>> what they missed and and what it is that
1:22:18people who love math love about it.
1:22:20>> They do get that. Is that worth
1:22:22anything? I don't know. I think it is.
1:22:25>> I agree. I agree. I also think this is a
1:22:27great way to get at it where you
1:22:28especially if there's trauma going in,
1:22:30you want to make sure to uh like put a
1:22:34balm over that trauma before you proceed
1:22:37forward in whatever it is that you're
1:22:38trying to get out rather than just like
1:22:40hammering in more problems of a certain
1:22:42type.
1:22:42>> Yeah.
1:22:43Um
1:22:46I think this might have some
1:22:47relationship with the other questions on
1:22:50what is it that we're doing math for or
1:22:52what is it that in some sense this is
1:22:55not does not have direct bearing on what
1:22:57do the mathematicians of the future do
1:22:58or a perspective student right now
1:23:00contemplating if they should go into a
1:23:02PhD and wondering if they should be
1:23:04optimistic or pessimistic. you know, a
1:23:06vision of uh teaching the liberal arts
1:23:08majors to maybe barely appreciate what
1:23:10they find beautiful by like folding
1:23:12paper in the right way. To some people
1:23:14that would be a, you know, a positive
1:23:16aspect of it. But I think to some people
1:23:18maybe they would they would fear like oh
1:23:20if this is all about sharing the
1:23:22flourishing of math and if uh uh if this
1:23:25is an example of what that looks like
1:23:27somehow that might somehow that might
1:23:31not quite leave the taste in their their
1:23:32mouth that they they were hoping for as
1:23:34far as like existing at the frontier and
1:23:36and really really wallowing in that um
1:23:39and enjoying that side of it. I'm I'm a
1:23:41little bit curious for you because you
1:23:44because you walk so many different
1:23:46lines. You educate and in college you
1:23:50have done phenomenal research. You have
1:23:52done various bits of popularization like
1:23:54how these how these weave together for
1:23:56you. How important is the education side
1:23:59and doing classes like this to more um
1:24:02more applied research that you might do?
1:24:05Or how important are [clears throat]
1:24:06like you just wrote this book big math.
1:24:08Um you've wrote many excellent books
1:24:09through your past. How important is that
1:24:12act of writing and and really turning
1:24:13math outward and kind of in some sense
1:24:16stepping below where you could be as far
1:24:18as you know uh proximity to the
1:24:20frontier. Um how how related are those
1:24:24other activities to the the applied
1:24:27research that you will do or have done
1:24:28throughout your career?
1:24:29>> Yeah. Uh my answer is peculiar literally
1:24:33peculiar to me you know it's it's
1:24:36idiosyncratic. It's not this wouldn't be
1:24:38the standard answer but but I always
1:24:42wanted to be a teacher. That's you know
1:24:45if I have to start writing my own eulogy
1:24:48or putting thinking about what goes on
1:24:49my gravestone I was a a teacher not a
1:24:53researcher in my heart. I mean a re to
1:24:56do research is to teach myself and to
1:24:59teach the world whatever I discovered or
1:25:02my colleagues and I discovered together.
1:25:05But I think of the fundamental activity
1:25:06as teaching and learning. I did have
1:25:09this one experience where I was working
1:25:10at a college at one point where the
1:25:13students weren't getting what I was
1:25:15trying to teach. And I found that very
1:25:17disappointing. No matter what I any
1:25:19trick I use, it just wasn't working. And
1:25:22that made me feel I have to be at a
1:25:25place where the students can get what
1:25:28I'm trying to impart. And so for that
1:25:32reason I felt I have to be I mean this
1:25:35is going to sound very crass
1:25:38that I have to be a good enough
1:25:39researcher that I can end up at the kind
1:25:41of place I want to be at.
1:25:44>> And
1:25:47um so I had seen very good teachers in
1:25:52college at Princeton who didn't get
1:25:54tenure because in my mind I thought they
1:25:56didn't publish enough. probably wasn't
1:25:58exactly that. They probably didn't
1:26:00publish good enough stuff,
1:26:04but but whatever. I knew that their
1:26:07research was what sank them.
1:26:09>> And so I always felt
1:26:12I have to try to be the best researcher
1:26:14I can be so that I can teach the way I
1:26:16want to teach.
1:26:18>> That's very interesting. I had no idea.
1:26:19It was it was such a twisted teaching.
1:26:22That's such a twisted way of what's the
1:26:24research for so that I can teach
1:26:26[laughter] good enough students. And
1:26:29>> that was really in my head. I'm not
1:26:31kidding. Now
1:26:33>> I I don't want to put too much of an
1:26:36emphasis on it because I do love
1:26:38research. I don't want to oversimplify.
1:26:41I love the mystery. I'm deeply in love
1:26:44with math and science and the universe
1:26:48and you know all of it. All of learning
1:26:50in fact. I mean not just the science and
1:26:52math part
1:26:54just really loved being a student my
1:26:56whole life and I just wanted a chance to
1:26:58do that to teach to learn and research
1:27:01is a big part of that and so is writing
1:27:03for the public and so is doing this
1:27:05conversation you know I mean it's all to
1:27:08me this it's the thing I want to do with
1:27:10my life with my my short time
1:27:13so that's it I mean but the research has
1:27:17been really thrilling along the way
1:27:18because I've had such good students I
1:27:20That's the other nice thing. When you
1:27:22work at a topflight place, you get
1:27:25really brilliant, creative, ambitious,
1:27:27hungry, mountain climbing. In some
1:27:29cases, literally, I had mountain
1:27:31climbers. My most famous student, Duncan
1:27:33Watts, really was an outdoors person who
1:27:36would hang by his fingertips off of
1:27:39deathdeying cliffs. I mean, he was like
1:27:41not quite the guy in Free Solo, but I
1:27:44mean, he's a crazy rock climber.
1:27:46And um so I got to have adventures with
1:27:49people like him. and you know had
1:27:51something like 25 PhD students and lots
1:27:54of postocs and and brilliant
1:27:57collaborators. My friend Renie Moro my
1:27:59lifelong friend I mean we've had great
1:28:01adventures which is what research is but
1:28:04we had them together. I mean it really
1:28:06is about going through life with people
1:28:09you care about.
1:28:11Keep coming back to that.
1:28:13>> Yeah. I mean the the fact that you keep
1:28:15coming back to that speaks to something
1:28:17um both in terms of just what you want
1:28:18what you personally want mathematics to
1:28:20be but what I expect a lot of other
1:28:22people would too.
1:28:22>> Yeah.
1:28:23>> I think the the last line of questioning
1:28:25I want to get at here would be
1:28:28>> on on this topic of mathematicians kind
1:28:31of get to decide what the field might be
1:28:32or if we if we if we run with that for a
1:28:35moment um and it's in this tumult
1:28:38because some of the traditional proxies
1:28:39are no longer as useful as they once
1:28:42were. Um I mean you you set a very good
1:28:44example here on all of the other things
1:28:47that you can pursue while like in the
1:28:52service of valuing these these more
1:28:54human aspects of math and it's not
1:28:56necessarily about the significance of a
1:28:58theorem that was proved um you know can
1:29:00maybe focus on more application but is
1:29:02it what I'm hearing here is it's not
1:29:03even as much about that as it is you
1:29:05just wanting to wallow in the knowledge
1:29:07and help impart that to others whether
1:29:08it's your students directly or the
1:29:10people reading your books. What do you
1:29:12think the
1:29:14what if you were, you know, in charge of
1:29:16maybe one math department or could sweep
1:29:18sweep a magic wand and instill the
1:29:20culture with a sense of what to value?
1:29:22What what do you think should be valued
1:29:25in making decisions around hiring,
1:29:27making decisions around tenure, deciding
1:29:29what people pursue, what people what is
1:29:32a math PhD, right? Just five years from
1:29:34now, let's do student entering now, like
1:29:36publish the PhD. What is what does it
1:29:38actually entail?
1:29:40uh what comes to your mind as uh as
1:29:44emblematic of of all of these things
1:29:46that we want to value?
1:29:47>> That's very very baffling question. I I
1:29:49mean I have an instinctive answer and
1:29:51it's going to sound evasive but it's
1:29:53what clearly comes to my mind first
1:29:56which is um
1:30:00I have a very profound respect for
1:30:02individuality of people's taste. I don't
1:30:06it's I'm escaping really answering. I
1:30:09don't want to be prescriptive. I know it
1:30:11when I see it. If if a person is given
1:30:14the freedom to do math that's meaningful
1:30:16to them, whatever that means, and that's
1:30:19the part that's so nebulous.
1:30:23Um, but if they're somehow their heart
1:30:25and soul and mind in maybe AI tools are
1:30:29all put in the most powerful way and the
1:30:33most incisive and penetrating and,
1:30:37you know, offbeat. I just want to see
1:30:39that person express themsself
1:30:43in their unique way to do something with
1:30:46math. That's what I want. And I want to
1:30:48have everyone have the freedom to do
1:30:50that. Now, you could say that's not a
1:30:52requirement at all. I know that's why
1:30:55it's such a bad answer, but that's
1:30:56actually what I would want. It's
1:30:58actually a great answer because I think
1:31:00it's one of the reasons for optimism in
1:31:02in making the case like why is this not
1:31:04only is it a fine time to go into math,
1:31:05I think it's arguable this is one of the
1:31:07best times to go into math precisely
1:31:09because the culture is in such an
1:31:10upheaval on people are deciding what
1:31:12even is this. Therefore, if you are an
1:31:14entering PhD student, you get to
1:31:16basically you have more you might not
1:31:18have infinite freedom, but you have more
1:31:20freedom than you
1:31:20>> have more freedom than ever before
1:31:22>> to say like I'm going to plant a flag
1:31:25that says this is what I think it should
1:31:26be. Like had I had I um decided, you
1:31:31know, when I was starting three blue and
1:31:32brown, I want to do this under the guise
1:31:35of this being my PhD thesis in a pure
1:31:37math department, you know, 10 or 15
1:31:39years ago. That never that just never
1:31:41would have worked. it would have
1:31:42required a very peculiar department to
1:31:44even like consider that. I don't know if
1:31:46I could now, but if it was a younger
1:31:48version of me and I was heading out
1:31:49doing the same thing, I actually think I
1:31:52could basically take the kind of stuff
1:31:53that I've been doing and make a case for
1:31:56like
1:31:56>> uh hey, we're deciding what match.
1:31:58>> It's a very remarkable thing actually. I
1:32:00mean, you did you did create a whole
1:32:02genre. I mean, you made a whole life and
1:32:04I can remember when we used to talk
1:32:06about this near the beginning and we
1:32:08were thinking about different ways for
1:32:10you to live this life that you were
1:32:12imagining and you've you seem to be
1:32:16pulling it off
1:32:18thanks to YouTube, thanks to the
1:32:20internet and thanks to you.
1:32:22>> I had I had various lucky things that
1:32:25happened such that this whole thing
1:32:26could exist outside of um you know
1:32:28traditional funding mechanisms or
1:32:30academia or things like that. But as far
1:32:32as other things that being a
1:32:34mathematician can be or pushing forward
1:32:36human understanding whatever that means
1:32:37can be and maybe for some people that
1:32:40really is they want to stay at the
1:32:41forefront of knowledge and what a PhD
1:32:43looks like. They spin off their AIs to
1:32:46discover like hundreds and thousands of
1:32:47theorems in a particular domain and they
1:32:49are the taste maker to decide what is
1:32:51the network between these and their
1:32:53thesis looks like a book that is an
1:32:54entirely new field and they are trying
1:32:56to like caress it into a sort of
1:32:58understanding that's compelling to
1:32:59others but it covers a hundred times as
1:33:01much as what
1:33:02>> that's amazing that is actually a vision
1:33:05>> it could be that it could be that
1:33:07>> I think one analogy I often turn to is
1:33:09and this is near and dear to your work
1:33:11also is like the origins of chaos theory
1:33:13where we think of that as being you
1:33:15could have defined the theorems of chaos
1:33:17theory without um computers existing but
1:33:19somehow observing the phenomena required
1:33:21to even realize this is a theory worth
1:33:24uh defining required automated
1:33:27computation such that you could run
1:33:28millions or billions of computations and
1:33:31>> it's so interesting this example because
1:33:32it was invented by someone without a
1:33:34computer
1:33:36>> I mean pankare had this problem that it
1:33:39was in his head and hardly anybody could
1:33:41understand what was in
1:33:43Even when he explained it, they still
1:33:45didn't get it. That's why it took
1:33:47>> 60 years till Loren could put it on the
1:33:50computer. And so now we understood what
1:33:52Ponare was saying.
1:33:54>> But actually Pankare saw most of it. We
1:33:56could see it in his writing.
1:33:58>> I guess maybe the the case then is not
1:34:00so like the poner might exist, but who
1:34:02is the Loren for a
1:34:04>> he's a tree falling in the forest that
1:34:06nobody hears, right? That's the thing.
1:34:08Plonare was so early and so far ahead
1:34:12that only Burkoff could understand him.
1:34:15You know, I mean those guys really plus
1:34:17they were doing something that was so
1:34:19wrong in terms of this was when
1:34:22relativity was happening. This is when
1:34:23quantum mechanics was being born. Nobody
1:34:25wanted to hear about classical
1:34:27mechanics. I mean that was so yestery
1:34:29year.
1:34:30>> But in fact they were kind of inventing
1:34:32>> Okay. Sorry I got distracted by the
1:34:35history of this example.
1:34:36>> Yeah. No, no. Like I love it. Getting
1:34:39near and dear to your your particular
1:34:41field. I mean, so I think
1:34:43>> the analogy I'm making is not as
1:34:45entirely apt thing because what I what I
1:34:47would want to say is whatever it is No,
1:34:49no, no. It's actually good because maybe
1:34:50we can shape it in. I think
1:34:52>> you know
1:34:53>> there's a thing that was unlocked by
1:34:54being able to do just millions of
1:34:56computations at a time. Yes. And here
1:34:59maybe it's um it is bringing to life
1:35:01what Ponare had already discovered. But
1:35:02it in so far as maybe there are some
1:35:04other observations that not just Loren
1:35:06but but others uh following in his
1:35:08footsteps made that would be much harder
1:35:10to make without the like
1:35:13>> well I mean certainly Mandelro and
1:35:14fractals a lot of the work on fractals
1:35:17>> you really and that that was the problem
1:35:19that Puanker had the thing that he
1:35:21discovered at the essence of chaos
1:35:23called a today in today's language would
1:35:25be a homo clinicic tangle he even says
1:35:27in his writing that I I struggle to even
1:35:31describe what
1:35:32what I'm picturing in my mind
1:35:34>> and I won't attempt to draw. He says
1:35:37something like an infinite grid, an
1:35:39infinite lattice or some kind of
1:35:41trellis. What word does he use? He's
1:35:43talking about something that's like this
1:35:45and like this.
1:35:46>> And if you ever draw a picture, maybe
1:35:48you could do it on three blue, one brown
1:35:50of a homoclinic tangle.
1:35:52It's a really nightmarish shape. And
1:35:54without a computer, there was no hope of
1:35:56drawing it properly. But Plankare was
1:35:58imagining it. Nobody else could
1:36:00understand it. and he didn't draw it. So
1:36:03for like I say for 60 or 70 years nobody
1:36:06really knew what he was talking about
1:36:08>> but now we can draw it and we could see
1:36:10he pictured it perfectly [laughter]
1:36:12>> but Mandelro you know when Mandlerro can
1:36:14draw fractals with his technology at IBM
1:36:18um that opened up a whole universe
1:36:20starting in 1985 then people had
1:36:23personal computers everybody was drawing
1:36:25a Mando broad set on their screen saver
1:36:28I mean the visualization should not be
1:36:30underestimated
1:36:32So broadly, whatever whatever people
1:36:34want the math PhD to be, there's not
1:36:36infinite freedom, but there's much more
1:36:38freedom than there ever has been.
1:36:39>> There actually is. Yep.
1:36:42If if if departments see it that way. I
1:36:45mean, we're all wrestling with this. I
1:36:46mean, every department is asking itself,
1:36:48what should be our requirements? What
1:36:50what does count as a PhD in this era?
1:36:53And we haven't really seriously had
1:36:56those discussions yet, but people are
1:36:57aware that we need to.
1:37:00And sometimes people just need good
1:37:02examples to even look to. And I think as
1:37:04a, you know, if I was a secondy year
1:37:06grad student or something, I might be
1:37:07thinking one of the things I can do
1:37:09right now is at the very least provide
1:37:11an example that can be an element of
1:37:13discussion happening here rather than
1:37:15waiting for others to speculate to tell
1:37:17me what to do. I'm just going to do a
1:37:19thing and then let them, you know, maybe
1:37:20they reject it. But you can guide a
1:37:23conversation through creation in a way
1:37:26that um is often underappreciated. I
1:37:29think just the person to actually make a
1:37:30thing or do something new ends up just
1:37:32guiding how people even talk
1:37:34>> rather than
1:37:35>> just put the facts on the ground. We
1:37:36don't have to talk about it. Look at
1:37:38this.
1:37:39>> Yeah, something like that. So, as a very
1:37:41last question, um all of this discussion
1:37:45around math and a certain spotlight from
1:37:47the broader world turning to it and
1:37:49whether you know people saying like, oh,
1:37:51isn't math solved and and things like
1:37:53that misconception or not?
1:37:55>> How does this influence the
1:37:56popularizations that you'll do? you
1:37:58know, the the you know, you just wrote a
1:37:59new book or or if you're giving talks to
1:38:01the public or if you're on podcasts.
1:38:03Does any of that surrounding
1:38:05conversation recolor anything that
1:38:08you're writing or that you're saying?
1:38:11[snorts]
1:38:12>> H I don't know why I can't feel I find
1:38:15it hard to engage with that question.
1:38:18Part of it, let me give the reason maybe
1:38:21that is uh doesn't want to be named,
1:38:25which is that the labor of writing this
1:38:27book and
1:38:30all books before it
1:38:32has been so problematic for my family
1:38:37[laughter]
1:38:39and and the time it takes and the um
1:38:43lack of presence I show in my house. I
1:38:46mean, I should be sitting in the room,
1:38:48but I'm not there.
1:38:49>> I shouldn't laugh. It's just too
1:38:51relatable, I think. But go ahead.
1:38:52>> Okay. Oh, wow. All right. That's why
1:38:54you're laughing. Good. Well, it's made
1:38:57me a bad partner. Um, my wife has
1:39:00enabled me to do this for so long. Uh,
1:39:04it's now getting to be I mean, I started
1:39:06doing math popularization in earnest.
1:39:11Say, let's say around the year 2000.
1:39:14So, it's now whatever that is. It's now
1:39:1726 years. And that's a big fraction of
1:39:20my life up till this point. And
1:39:24I don't think I'm going to do it
1:39:26anymore. Not much. I mean, I have other
1:39:29things in my life that I care about
1:39:31more. I really want to be with Carol. I
1:39:34want to
1:39:36live in the youth of my old age to
1:39:38travel with her and do crosswords with
1:39:40her and watch dumb TV and you know just
1:39:44hold hands and go out and what you know
1:39:46what we did actually it does have a
1:39:48connection to AI. We're walking in the
1:39:50Botanic Gardens at Cornell, which has
1:39:53marvelous specimens of every tree and
1:39:55shrub and flower you could imagine. And
1:39:58you could take a photograph of the, you
1:40:01know, uh, a Norway spruce. And I don't
1:40:05know a spruce from a hemlock,
1:40:08but Chachi PT does. [laughter]
1:40:11And I could get a guide, but I I like to
1:40:14just take a picture of the tree that's
1:40:15right in front of me and do a little
1:40:17quiz to the machine and tease it and it,
1:40:20you know, playfully joke around with it.
1:40:21But Carol's right there. It's not just
1:40:23me and the machine. We're having fun
1:40:25with the machine and we're looking at
1:40:26nature and we're outdoors
1:40:28>> and we're learning stuff and it's fun
1:40:30and we're doing it together. So,
1:40:33[laughter] it's not about math
1:40:35popularization, but it's about me being
1:40:37a perpetual student. I I think that's
1:40:39what's next.
1:40:41Well, you you mentioned everything
1:40:43circles back to the meaning of life. I
1:40:44feel like that that's a perfect note to
1:40:46end it on that uh actually brought some
1:40:50tears to my eyes. I think that's that's
1:40:52just incredibly [laughter] sweet as the
1:40:54>> that's what that's what matters to me
1:40:56the most right now.
1:40:57>> So, uh yeah, I've written some other
1:40:59books. You could read those, too, if you
1:41:01want more. I think as we all um yeah, as
1:41:06as I'm sitting in a drought of wishing
1:41:07that I had more of your stuff to read, a
1:41:09part of me will smile knowing the reason
1:41:11for it. And so
1:41:12>> that is the reason. Thank you. But yeah,
1:41:15I I um I've sort of promised to not
1:41:18write anymore
1:41:20because it's too
1:41:22takes too much ju I mean, it's both
1:41:24innervating and energizing. I'm as happy
1:41:27as I can be when I'm creating that
1:41:29stuff. And in this last book, so big
1:41:31math is written with my really dear
1:41:35friend Alex Townend. I mean, I have had
1:41:38such a good time. This is my first book
1:41:40with a co-author. He's much younger than
1:41:42me. He could be my son. He's 28 years
1:41:45younger. And um we had the best time
1:41:49thinking about this subject together for
1:41:51the past two years. That's a whole new
1:41:53deal. I never wrote a book with someone
1:41:55else. I've done papers with other people
1:41:57and that's been fun. But to spend that
1:41:59much time that intensely with with one
1:42:01person for years,
1:42:04Carol's not that happy about it because
1:42:07it's not her, it's me and Alex. And
1:42:09she's seeing me having so much fun
1:42:12>> making this thing with him, figuring
1:42:14stuff out. And it seems it never ends.
1:42:17There's writing it, there's publicizing
1:42:19it,
1:42:20>> there's talking about it.
1:42:22>> Tell you what, I [laughter] will Let's
1:42:24end it here, Stephen. This has been an
1:42:26utter delight. I could happily chat with
1:42:27you at night.
1:42:28>> I'm sorry. I didn't mean that to be a a
1:42:30shutdown, but okay.
1:42:31>> On the contrary, nothing would bring me
1:42:33more joy than to let you go into the
1:42:34botanical gardens with Carol now and not
1:42:36keep you on the mic for one second more.
1:42:38So, thank you so much for taking the
1:42:39time. This was
1:42:40>> You're a good man, Grant.

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