Latest / Uncomfortable Conversations with Josh Szeps / How A.I. is "Demolishing" Mathematics

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How A.I. is "Demolishing" Mathematics · Uncomfortable Conversations with Josh Szeps

• 0:03
  G'day humans, welcome to the safe space for dangerous ideas.
• 0:06
  In all of the talk about artificial intelligence, I just don't know whether or not, I know that the most pressing question for all of us is what is it doing to theoretical mathematics?
• 0:17
  Because that is the bread and butter that motivates, that animates our daily lives.
• 0:24
  So I've got on the blower, on the old webcam, on the Substack Live, the one and only Adam Spencer.
• 0:30
  broadcaster, journalist, television radio host in Australia, MC extraordinaire, but also sort of, would you say, professional mathematical nerd?
• 0:41
  Do you have a PhD in mathematics, Adam?
• 0:45
  I began a PhD in mathematics and then won a major stand-up comedy competition.
• 0:50
  I was offered the chance to continue the PhD or get into radio.
• 0:53
  And I had this great insight, Josh, I realized
• 0:56
  In a room of randomly selected people, I'm a maths genius.
• 1:01
  In a room of maths PhDs, I'm as dumb as a box full of hammers, but it's very easy to avoid being in a room full of maths PhDs.
• 1:11
  That's not too hard.
• 1:12
  But I agree with you entirely, mate.
• 1:14
  You can have your bioweapons.
• 1:16
  You can have your Skynet.
• 1:18
  You can have your 10% chance of human extinction.
• 1:21
  Everyone's asking, what about the Riemann hypothesis?
• 1:25
  What is this doing to the cutting edge of pure mathematics?
• 1:28
  Yes, who cares about the marauding gangs of AIs that are forming themselves into organized crime units and infiltrating our essential infrastructure?
• 1:39
  You mentioned that hypothesis.
• 1:40
  Hang on, I've got...
• 1:41
  This is... You're so learned in this field, I've even got notes, which for me, I mean, that's saying something when Josh comes into an interview with notes.
• 1:52
  So research mathematics, like actual maths...
• 1:56
  So if people haven't seen the headlines, it has been all over the place that just in the past week or two, well, you tell me.
• 2:04
  You give me the, okay, coming across the transom, Adam is delivering us the news from the forefront of theoretical mathematics.
• 2:12
  What's the latest?
• 2:14
  What's happening?
• 2:15
  For a few years now, people at the very cutting edge have been using things like Google's DeepMind and equivalent platforms to help some mathematical inquiry.
• 2:27
  But in the same way in the last six months, you've seen platforms jump the shark in terms of ability to code, ability to hack agents, ability to coordinate and hack hugging face and that sort of stuff.
• 2:40
  In the last six months, mathematical theorems have been dropping like flies.
• 2:47
  It has been incredible.
• 2:48
  Every day, every weekend, some of them cutting-edge mathematicians having augmented their own work, some of them absolute amateurs having just asked a really good question of a strong platform and basically sat there saying, keep going, you can do it, you can do it till the system crashes through.
• 3:05
  And then, yes, just in the last few days, OpenAI dropped dramatically.
• 3:09
  722 manuscripts on 320 different topics or problems in mathematics.
• 3:18
  It is the greatest single dump of mathematical knowledge in human history, I'm quite confident.
• 3:26
  And the maths community is just sitting there trying to absorb it all at the time.
• 3:30
  I wrote about
• 3:32
  two or three weeks ago, a Substack post that I called mathematics and AI, the good, the bad, and the existential.
• 3:39
  And I think the impact of AI to mathematics falls into those sort of three sometimes overlapping categories.
• 3:45
  And this is, I mean, some of these things that Anthropic and OpenAI are dumping and not just, these aren't accidental, right?
• 3:51
  I mean, they're pointing their AIs at this and they're producing as a result.
• 3:56
  I mean, the news last week was apparently that these are some of the most
• 4:00
  complicated and sophisticated mathematical proofs and longest mathematical proofs that have ever been written by any intelligence and that even the world's leading mathematicians at the forefront can't necessarily verify whether or not these things make sense immediately because they're so sophisticated.
• 4:19
  Is that fair?
• 4:20
  Yeah.
• 4:21
  Yes, I have not heard an example of someone just turning their computer back on and the platform saying, look, while you were gone, I didn't have anything else better to do.
• 4:30
  I started ruminating on this deep mathematical problem.
• 4:33
  No, they're busy.
• 4:33
  They've got essential infrastructure to hack into.
• 4:36
  And, you know, there are nuclear weapons silos that they need to figure out how to overtake.
• 4:40
  Yeah.
• 4:41
  No, no.
• 4:42
  Certainly, they've been pointed each time at the problem.
• 4:47
  It's been interesting.
• 4:48
  I've seen cases of incredibly long, complicated, really brilliantly written prompts that have taken all the sum knowledge in an area of human endeavor, loaded that into the platform and said, I want you to go at this specific problem, go for it.
• 5:02
  But there's been other cases where virtually amateur mathematicians seem to have asked pretty broad questions of a model of, here's this well-known problem, what do you think?
• 5:13
  And also got a degree of the way.
• 5:15
  Most of the open AI big dump over the weekend seems to have been...
• 5:20
  well-focused, deeply questioned, specifically aimed, but the breadth of 300 plus problems, some of which are some of the longstanding, most famous problems in mathematics, where it seems at this early stage, there has been a degree of real insight.
• 5:39
  The scope and depth of it is, the mathematical community is literally over the weekend, just sitting there going,
• 5:45
  What was that?
• 5:47
  And is your sense from what you can tell of it, I don't know how many of these things you've tried to read yet, but as an actual mathematical wonk, that the systems are generating insights that humans wouldn't have been able to because you mentioned in your Substack post that,
• 6:08
  And part of what's going on is the sheer relentlessness of AI models.
• 6:14
  Once they're pointed at a problem, it's a little bit as if you just picked one of the dozen thorniest mathematical problems that have been plaguing mathematicians for decades or centuries, and you locked 40 of the best mathematicians in the world in a room together, and you didn't let them out.
• 6:30
  You just gave them water and...
• 6:32
  cookies and they didn't let them out until they'd solved it then they could probably do better than we currently had and in a sense that's just what anthropic and open ai are doing with their models they're just pointing it out and say do not give up until you break this thing so how much is sort of horsepower and how much is insight beyond the can of mortals yeah
• 6:56
  It's a really good question, Josh, and there's two different ways these results can be reached in a very fundamental sense, and it's the trade-off or the tension between those two different ways that's got everyone asking deeply existential questions about mathematics at the moment.
• 7:12
  Let me give you an example of each.
• 7:14
  There was a problem from back in the 1970s, a geometry problem.
• 7:18
  It's been around for 50 years.
• 7:20
  With the greatest respect of the problem, not the most important problem in all of mathematics.
• 7:24
  It's not something that every mathematician's been thinking about every day or anything like that.
• 7:27
  Oh, dear, yeah.
• 7:29
  But there's always got to be a pecking order.
• 7:30
  And this one was middle at best.
• 7:32
  But for 50 years, some pretty smart people have had a crack at this and never, never got to it.
• 7:38
  And from what I understand, the consensus in the community was the answer to the problem was probably no.
• 7:44
  Now, a platform was created, loaded up with all the people.
• 7:47
  Okay, tell me what the problem is.
• 7:48
  What's the problem called and can you give us the shape of it or is it not a comprehensive to a non-mathematician?
• 7:54
  The good analogy would be imagine a town with a lot of different bus stops en route.
• 7:59
  Is it possible to send out a fleet of buses?
• 8:02
  such that every stop is on two and only exactly two different bus routes?
• 8:08
  Can you colour this really complicated map so that every point has two colours coming in, no point has three, none has only one?
• 8:17
  It's a graphing problem or a network problem.
• 8:19
  And mathematicians look at these sort of things because insights into networks then help you structure how you deliver electricity across a city, how you store information on the network theory.
• 8:30
  Graph theory is a really important part of mathematics.
• 8:32
  but it was an interesting sort of problem that had been floating around.
• 8:36
  Could you do this double coloring problem as it was called?
• 8:40
  They loaded up the system with all the knowledge we had, the equivalent of, yeah, putting the smartest 30 people in the world who've ever worked on this in a room and said, off you go.
• 8:48
  And the system solved this decades-old mathematics problem in one hour.
• 8:55
  Now, having spoken to some really good mathematicians about it, from what I understand, there was no...
• 9:00
  moment of genius that no human ever could have had.
• 9:03
  No one looked at the answer and went, well, I don't even understand what you've said.
• 9:06
  It solved it.
• 9:08
  mainly using mathematics from the 1980s.
• 9:11
  But it stitched together all these different observations and went about a new path of inquiry on the analogy.
• 9:17
  I think if you'd locked the 30 smartest people in the room, there's a real chance between them they would have got there.
• 9:22
  But in that case, there's so many problems and so few mathematicians to focus at them.
• 9:28
  I think that's an example of the good that these systems can do.
• 9:31
  And the final proof only ran to two pages.
• 9:35
  Most experts in the field could understand the proof.
• 9:37
  The prompt itself ran to two pages.
• 9:40
  And it was a beautifully written prompt.
• 9:43
  And I think the sum total of mathematical knowledge has benefited from that because most mathematicians who are now interested in the problem could look at it and probably gain some knowledge through the process of understanding that proof themselves.
• 9:57
  Right, right.
• 9:58
  And now, yeah, sorry, finish that thought.
• 10:01
  No, no, no.
• 10:01
  Over to you and then I'll give you the counter example of when these things are a little bit nastier.
• 10:06
  Yeah, I want to stay on the good for the moment.
• 10:08
  You know, always win the audience over with optimism initially, Adam.
• 10:12
  In my long experience as a broadcaster, you punch them in the face and give them a wedgie at the end and then you push them off a cliff into a barrel of shit.
• 10:21
  Yeah.
• 10:22
  There's a wedgie coming, Josh.
• 10:24
  Don't you worry.
• 10:25
  We'll get there.
• 10:26
  But on the good, yeah, another way that you put it in your Substack piece is like imagine there's a brilliant method.
• 10:33
  Because also there just aren't that many.
• 10:34
  This kind of stuff is so sophisticated that there aren't that many people who are both brilliant enough and learned enough and crazy enough
• 10:46
  to be devoting all their time to thinking about them.
• 10:49
  So it does make a big difference if you can put the horsepower of AI behind it.
• 10:53
  So one analogy that you give is imagine that one such person is working on a really, really thorny mathematical problem and they're going home at the end of a Friday and there are three possible avenues that they could continue thinking about.
• 11:07
  So they ask Claude or, you know, Alex.
• 11:10
  open AI or whatever at ChatGPT, and they ask, you know, these are the three avenues that I'm thinking of pursuing.
• 11:16
  Can you just mull on them for the weekend?
• 11:19
  And when I get in on Monday morning, tell me which one is least likely to not be fruitful.
• 11:24
  Then if they can come in and the AI has done that for them,
• 11:28
  and they know where they're likeliest to yield a payoff, that's another good example, isn't it, where you're sort of using AI as a collaborator to nudge you in the right direction so that your human ingenuity can flourish.
• 11:44
  There's a great quote from a famous Australian mathematician who a few years ago won the most prestigious prize in mathematics.
• 11:49
  It's called the Fields Medal.
• 11:51
  It's considered the mathematical Nobel Prize.
• 11:53
  As opposed to the Nobels, it doesn't go for a single discovery.
• 11:57
  It's for a lifetime of work for anyone under the age of 40.
• 12:00
  So it's saying the breadth of what you've contributed makes you one of the very best.
• 12:03
  Terry Tao has won one.
• 12:04
  And Professor Venkatesh is the second ever Australian to win a Fields Medal.
• 12:08
  And he's at the dinner there in his black tie and he gives this lovely speech and he says, to paraphrase him, it's just beautiful having a night like this when everyone says congratulations and you can reflect on what you've done.
• 12:19
  And he said this because as a professional mathematician, I spend 99% of my time being wrong.
• 12:30
  you're so at the cutting edge of thought and you're pushing and you've got so many ideas raffling around your head, the vast bulk of what you try doesn't lead anywhere.
• 12:38
  And then you make a little micro step forward.
• 12:41
  Yeah.
• 12:41
  So if he could on Friday afternoon say to the platform, I've got these three ideas I'm going to try on Monday.
• 12:47
  He comes back on Monday, the platform says, I've run 50 million test cases and simulations.
• 12:52
  I'm not getting much on the first two.
• 12:55
  But on the third one, especially for polynomials of degree five or more, there seems to be something really interesting.
• 13:01
  I'd start there if I was you.
• 13:03
  So if the powerful platform was an angel on his shoulder saying, warmer, colder, warmer, colder.
• 13:09
  Let's say Venkatesh is suddenly only wrong 90% of the time, not 99%.
• 13:15
  That means we've got 10 of him running around at the frontier of mathematics, making observations and leaping forward.
• 13:20
  He's more productive, more engaged with the work and not spending all of that until now necessary wasted time because no one else in the world was smart enough to say to him, I don't know if I'd be looking there, buddy.
• 13:31
  I'd be looking over this way.
• 13:33
  I think there's unparalleled good in that sort of application of the cutting edge of mathematics.
• 13:38
  And so when an artificial intelligence comes up with a mathematical breakthrough, is it like one thing I also don't understand is the explanations that artificial systems use in their proofs are called lean formulations.
• 13:56
  Is that right?
• 13:57
  A lean formulation?
• 13:58
  But it's actually much longer.
• 14:00
  So like...
• 14:01
  The proof of, people might be familiar with Fermat's Last Theorem or Fermat's Last Theorem, depending on how you pronounce it, right?
• 14:08
  This classic mathematical conundrum.
• 14:10
  There's a wonderful, beautiful book by Simon Singh about the solution to this conundrum.
• 14:16
  And Simon is a great British popularizer of science who does a tremendous job in that book of actually making normies like me be able to understand the basic problem of what was stuck, what mathematicians couldn't figure out.
• 14:30
  One of the all-time great pieces of popular science writing.
• 14:35
  It doesn't cut any corners.
• 14:37
  It doesn't duck anything.
• 14:38
  But you can go from, as long as you understand what five squared means, by the end of that book, you get an insight into this 130-page monstrous proof that slayed a 350-year-old theorem.
• 14:51
  Yes.
• 14:51
  I mean, but you say the proof is monstrous, like 129 pages or something that Andrew Wiles, was it, the mathematician who cracked it in the 90s?
• 15:01
  But then I was reading, and I'm just looking this up, the lean formalization of his proof, which Claude AI came out with last month, was the longest mathematical proof ever.
• 15:13
  I don't know whether it superseded itself in the past four weeks, but it might have.
• 15:17
  And that...
• 15:18
  formalization of his proof.
• 15:19
  In other words, the AI's sort of condensation of the proof as he wrote it is 13 million lines of code.
• 15:28
  He wrote 129 pages.
• 15:30
  Then AI comes in and goes, let's check this for you.
• 15:33
  I'll simplify it.
• 15:34
  And they write 13 million lines of code.
• 15:37
  So what, I mean, I thought the point of,
• 15:40
  a good mathematical proof is that you could write a book about it.
• 15:44
  You could write a detective story about how the jigsaw pieces are being put into place.
• 15:50
  I mean, unless you're talking about super abstract, maybe quantum stuff or something like that, but the glory of mathematics is that it is not just about numbers.
• 15:58
  It's about explaining concepts about the world and it should be comprehensible.
• 16:03
  So what is the artificial intelligence adding if it's creating 13 million lines in code to quote unquote explain something that a human was able to explain in words in 129 pages?
• 16:15
  Yeah, and this is where we really get into the existential point here, Josh.
• 16:18
  There's a couple of things to unpack from there.
• 16:20
  One, some proofs like Fermat's and Wiles, yeah, you can write a beautiful flowing novel about it.
• 16:25
  I'll be honest with you, a lot of the cutting-edge breakthroughs in mathematics would be tough to popularise as much as Singh did in that book.
• 16:32
  But the vast bulk of the time, yes, there's at least a paper
• 16:36
  that some really smart people can read from go to woe and check if it's correct and gain insight and knowledge themselves from doing so.
• 16:45
  And the one I told you of the double coloring, the bus route sort of theorem, the final proof is only two pages and any well-qualified mathematician in that field could read it and go, well, yeah, it works.
• 16:56
  I'll work through it.
• 16:56
  Yeah, that's all good.
• 16:58
  And wow, I've actually picked up, oh, I see what they did.
• 17:00
  Oh, that's cool.
• 17:02
  I could apply that little novel approach to other work I'm doing in the field.
• 17:06
  So it is a traditional mathematical proof, quite beautiful in its, certainly its brevity even.
• 17:11
  I'm not qualified to talk about its elegance, but the fact that it's only two pages long to debunk a 50-year-old myth in mathematics is just gorgeous.
• 17:19
  But there is, yes, this completely different way things can be certified as true.
• 17:25
  And the way to think about it is this.
• 17:27
  When human mathematicians are talking to each other, just say, I'm Spencer talking to Professor Zeps about where my work is at.
• 17:34
  And I've got a room of people of your brilliant mathematical intellect, Josh, and you all understand what I'm doing.
• 17:40
  So my conversation with you is going to have a fair degree of sort of hand waving.
• 17:44
  Look, we all know Johnson's theorem.
• 17:45
  So from that, we could do this.
• 17:46
  Now, do you see how we could do that?
• 17:48
  So it follows blah, blah.
• 17:50
  And I'm sort of taking several big logical jumps there.
• 17:54
  on the assumption that everyone in the room knows what I'm talking about and doesn't need me to go back and define a prime number again and remind you what firm outsize, we all know that.
• 18:04
  But a lean verification or a lean formalization does not allow any of that.
• 18:12
  Every single micro step in the chain of logic is one line of code to the next, to the next, to the next.
• 18:21
  So it's almost as though you're reinventing the fundamental mathematics required every time you do a proof.
• 18:28
  Now, these systems, lean verifications or formalizations, existed previous to AI.
• 18:35
  They were just ways for computers to test remarkably complex concepts.
• 18:40
  So it's not a matter of we're trusting the AI.
• 18:43
  But yes, in the case of the 13 million line,
• 18:48
  verification of Fermat's last theorem.
• 18:51
  It's, from what I've heard people describe it, impenetrably ugly and just too long for any human being to ever read from line one through to line 13 million.
• 19:05
  Another Fields medalist said just over the weekend, he doesn't think we're far away from proofs that no one can understand, but the verification process says to us, well, it's true.
• 19:16
  You just have to trust me on this.
• 19:18
  And there's two challenges with that.
• 19:20
  There's the sort of philosophical challenge of do we just cede to the higher intelligence and say, machine says true, must be true.
• 19:28
  But the other concern that Terence Tower has raised here is that
• 19:31
  If you think of Fermat's last theorem, the initial proof, when he dropped it, there were a handful of people in the world qualified to read that proof through from line one to the end of page 129.
• 19:43
  First read through, they found a minor error, sent it back to him, but humans could work their way through it.
• 19:48
  It was at the cutting edge of all human knowledge.
• 19:51
  These days, there's upper-level university and postgraduate courses pretty much dedicated to Wiles' proof of Fermat's Last Theorem.
• 20:00
  And thousands of really good mathematicians have got through and understood the bulk of what is in there.
• 20:06
  So it, as a piece of thought, has educated generations afterwards because it's written in a human fashion.
• 20:13
  If AI just starts dumping 13 million line proofs,
• 20:18
  No human or team of humans has time to read through, but we have to assume or accept that it's true.
• 20:24
  And no human team can benefit anything from it because the magic is hidden in between lines, 7,450,000 and 7,490,000.
• 20:33
  The analogy Terence Tower uses that I'm paraphrasing a bit because he doesn't use rude language would be, if I was the first person to climb Everest,
• 20:43
  I can either release the map that I took and said, we went this way.
• 20:46
  We tried to go here.
• 20:47
  We couldn't.
• 20:47
  We tried that face.
• 20:48
  No, but it turns out if you go around this way, there's a small gap.
• 20:51
  We went through there.
• 20:52
  Or I could post on Instagram a photo of me standing on the top of Everest going, sucked in as I got here first.
• 21:01
  No one benefits from that.
• 21:03
  No future mountaineer knows the way up Everest or the ways not to go.
• 21:07
  And at the moment, at the moment with great mathematics, and it might take a while in the really heavy cutting edge stuff that knits together multiple fields and all that, but at the moment those things stand as something that eventually raises all boats.
• 21:22
  But if an AI system is just dumping a giant proof, and the other thing is, Josh, also about this that goes against the current philosophy of mathematics, mathematics is a remarkably collaborative field.
• 21:33
  If I was working on the Spencer theorem and I just hit a wall, I've got no trouble going and asking people
• 21:41
  I would go and speak at conferences about how far I've got.
• 21:45
  I might release a preprint with some of my individual steps on the way saying, here's where I'm trying to get to.
• 21:50
  And Professor Zeps over in Poland might look at it and go, oh, hold it.
• 21:55
  I can help you out here.
• 21:56
  I was working on something else.
• 21:57
  And I would rather get to the Spencer-Zeps theorem
• 22:03
  and we get there, then keep it as Spencer's work solely and we never got there.
• 22:07
  And in getting there, our paper would acknowledge Johnson and Jones 20 years before us and Smith and Smith 30 years before that.
• 22:15
  There's a collaboration and an accrediting of that we have stood on the shoulders of giants.
• 22:21
  If OpenAI just dumps a 13 million line piece of computer code
• 22:25
  that doesn't acknowledge where the ideas came from, doesn't give credit where it's due, and doesn't serve to educate anyone going forward, there's a little sugar rush in knowing, wow, it turns out the Riemann hypothesis is true.
• 22:39
  Why?
• 22:40
  I don't know, but it is.
• 22:44
  That's not necessarily a net good for everyone.
• 22:46
  Hmm, that's interesting.
• 22:49
  If I forget to come back to the collaboration thing, then remind me to because I want to stick on the Everest thing, which is another interesting but separate point.
• 22:58
  So I think you articulated the Mount Everest analogy better than I had heard it done before because I've never found it that persuasive because –
• 23:08
  When people have said, well, it's one thing to climb Mount Everest, it wouldn't be another just to get plopped onto the top of Mount Everest by a helicopter and saying, yeah, I was at the top of Mount Everest.
• 23:18
  I always thought that smells to me like a bit of a cheat because it depends what the objective is.
• 23:25
  If the objective is to stand on the top of Mount Everest, there's nothing illegitimate about a helicopter plonking on the top of Mount Everest.
• 23:32
  Like the point is to be on the top of Mount Everest and who cares how you get there.
• 23:36
  The problem is only if there is a utility in the navigation and if you're going to subsequently need to be navigating Mount Everest and if future people are going to need to know how you did it and how you shouldn't do it.
• 23:52
  Or if there were thousands of other mountains around the world, all different, that we all would benefit if we could climb.
• 23:59
  Right.
• 24:00
  And things I've learned about how you got up one particular ice crevice in Mount Everest, I could apply on K2, et cetera.
• 24:06
  Yes.
• 24:07
  Okay.
• 24:08
  So that's a good analogy because I was going to say, obviously, and you could see where I was going, that if the point of having solved a mathematical problem
• 24:20
  is in and of itself a virtue, and humans haven't been able to do it, then you might just argue, well, okay, now computers are going to be able to do it.
• 24:31
  They're going to be able to hand us this incomprehensible thing, but we're going to know that it's true because it's going to have
• 24:37
  however many hundreds of millions of lines of code that can be independently verified by, you know, nonpartisan objective AIs who can go through it all and go, yeah, it actually does check out.
• 24:47
  And we might even be able to test it in the real world by, I don't know, smashing, you know, microparticles together in CERN or something.
• 24:56
  Then you might just sort of say, well,
• 24:59
  okay, there's something unromantic about it having been arrived at that way, but actually it is getting us to the mountaintops and the mountaintops are where we want to be.
• 25:09
  What you're sort of saying is, it sounds like, what if there are other mountaintops that AI can't get us to that we can only navigate our way to by having navigated our way to the top of Mount Everest?
• 25:23
  But I'm afraid I'm not sure what those mountaintops would be.
• 25:27
  other problems in that direct field of mathematics that you're talking about, another number theory problem.
• 25:33
  Yeah, but AI is going to do that as well.
• 25:35
  But the way you ration food climbing a mountain might apply to a completely different branch of mathematics, a completely different problem, even if...
• 25:43
  I mean, there might be a time...
• 25:45
  50 years from now, where we look back and laugh naively at this brief window where we could keep up with the AI, and it is just churning it all out.
• 25:53
  And maybe it's churning it all out in a way that to amuse itself, it publishes a version that we mere humans can understand.
• 25:59
  Who knows?
• 25:59
  But while we're at this point here...
• 26:02
  where we're talking about breakthroughs that people could still understand and learn from and then teach others.
• 26:09
  I mean, if the greatest mathematical minds in the world, and a friend of mine is at the University of New South Wales, Dr. Sean Gardner said recently, he's hearing really concerning...
• 26:18
  conversations between his colleagues wondering, five years from now, is our job just going to be to come in and verify line by line rambling computer proofs?
• 26:25
  And we never do any of our own work.
• 26:28
  Who's going to want to sign up for that?
• 26:31
  Where's the incentive to be a mathematician
• 26:34
  who even if some AIs are coming up with things you don't quite understand, are still meant to be teaching the next generation of engineers and computer scientists and all sorts of people.
• 26:44
  Another, an adjacent idea would be, Josh, if an AI came up tomorrow with a particular drug that cured a certain sort of cancer, well, we'd be idiots not to think about using it.
• 26:55
  One, would we put it through the 15 years of clinical trials that we now currently do, or would we just trust the AI that we're all good
• 27:02
  But two, that one-off drug is great for anyone who's suffering that cancer.
• 27:06
  What if the next 200 cancer drugs were just churned out by a machine with, trust me, trust me, trust me, the state of human knowledge of biology, of oncology, of physiology, just suddenly atrophies because no one has any idea what anything does or why it works.
• 27:23
  Mm-hmm.
• 27:24
  the ability of using those drugs in spinoffs and novel other areas or anything collapses.
• 27:29
  But also, we just suddenly don't understand how the human body works anymore.
• 27:34
  And we've just given over our understanding of that to a higher form.
• 27:39
  Now, it is conceivable, as I said, 20 years from now, we might be laughing at the thought that we could ever have kept up.
• 27:44
  It may have just turned mathematics into chess.
• 27:47
  But in this brief window where we can learn from the machines and with the machines and play better chess ourselves as a result, I think there's probably – it's really important that we hold on to that and ask deep questions about what it would mean if it was taken away.
• 28:00
  Well, we can play better chess ourselves as a result than we did previously, but we can't play better chess than the machines.
• 28:07
  And we may no longer be able to do better maths than the machines.
• 28:11
  Yeah, quite conceivably.
• 28:12
  And in the world of chess, I play terrible chess, and I quite enjoy sitting down playing terrible chess opposite a human being, regardless of the fact that my phone could beat both of us and Magnus Carlsen and any human who will ever live.
• 28:24
  But it's...
• 28:29
  There's a lot of strings sort of pulling in different directions here.
• 28:33
  There's something to be said for making whatever progress we can in a way that brings humans on the journey and empowers us as well for at least as long as we can.
• 28:41
  What you're reminding me of is, I mean, it's almost like mathematics is just being blindsided by a phenomenon that is scattering across and ricocheting across all intellectual fields, right?
• 28:52
  I mean, this is like something that people always don't.
• 28:54
  talk about radiologists or data entry or, you know, people who conveyances who are the lawyers who draw up contracts and things.
• 29:03
  But the interesting thing about the sort of learning and knowing is it reminds me a bit of the concern that a lot of creative fields have about how you create a pipeline to expertise if you don't have the
• 29:21
  non-experts interested in learning because the puzzle is interesting enough to entice them to get good at things.
• 29:29
  It's like, you know, I think this is a problem in design and advertising and fields like that and indeed writing and journalism where...
• 29:37
  AI is now good enough that you really don't need, if you're designing, if you're a copywriter or you're designing ads, for example, you don't really need as many junior people to come to you with a bunch of different pictures or, you know, designers to draw exactly what the ad is going to look like because all that grunt work can be done by AI.
• 29:57
  It can throw it all at you.
• 29:59
  But if you're a 55-year-old advertising executive, then you probably do know still on some level better than anyone, including AIs, what's likely to work.
• 30:14
  Certainly, you'll have more of a sense of your own personality or flavor or flair about what your client really needs.
• 30:22
  So...
• 30:23
  The Don Draper or, you know, Mad Men kind of character, that person only exists because they were once an untrained, unqualified newbie.
• 30:35
  And it's all very good for the next five or 10 years for people who are experienced to use AI to replace the, you know, the newbies.
• 30:46
  But who's going to be the Don Draper in 30 or 40 years' time if no one's coming in because they're excited about the chase and the intellectual simulation of the puzzle?
• 30:56
  Yep.
• 30:57
  It sounds like that's sort of what you're pointing to maybe with maths.
• 30:59
  Yeah.
• 31:00
  Yeah.
• 31:01
  Let me make two points on that because apart from being Australia's nowhere near best, but best known mathematician, as a full-time gig, I give keynotes on artificial intelligence and the impact it's having on the world in all different sorts of industries and that sort of stuff.
• 31:15
  And the two points I make are, if you hear anyone saying at the moment, do we need to employ any more level ones?
• 31:22
  We can just employ level threes and vibe code a few apps, can't we?
• 31:26
  Well, the first thing to ask is, buddy, where did your level threes come from?
• 31:31
  Two years ago, they were level ones.
• 31:33
  That's how you do it.
• 31:34
  And I don't defend this, but the reality is in a lot of professional industries in particular, the first two years out from trade school or uni or whatever are really tough.
• 31:45
  And they're designed to break you if you're probably not meant to be there.
• 31:50
  And there's something about just working hard and tough hours and coming up against walls and in the mathematical sense, bashing your head against a blackboard hundreds of times to find a breakthrough that creates the intellectual framework that then years of experience creates a great mathematician on top of or a great...
• 32:09
  Your lawyers these days, your partners in the law firms were the ones who 20 years ago were up at three in the morning saying, dude, we're doing court in four hours.
• 32:16
  We've got to sort this out right now.
• 32:18
  Mm-hmm.
• 32:19
  And that sort of framework and that resilience then has years of experience built on.
• 32:24
  I'm walking into my law firm and just asking chat GPT to prepare the brief.
• 32:28
  And I've got no idea really where that case law came from.
• 32:30
  I can read what it means now, but I didn't read the seven other cases that didn't quite work out, but would work in a different sense.
• 32:36
  And I wasn't chasing the deadline.
• 32:38
  Do I have those skills and resilience to build years of experience on?
• 32:42
  And in the radiology case, you've got...
• 32:46
  There's no less radiologists now than there were.
• 32:49
  I think there's even slightly more in a lot of areas because there's more scanning to be done because they're not spending 95% of their time looking at something that doesn't matter.
• 32:58
  They're being referred to the stuff that is important, that they're then adding their important human skills on top of because there's still a real, like, I'm fine for you to scan.
• 33:08
  I'm fine to get a text message saying nothing to see.
• 33:10
  You don't need to come in.
• 33:12
  But if something's wrong and I need to come in and have a conversation, I'm not doing it with a bot.
• 33:17
  I want to do that with a qualified human being.
• 33:20
  So there's still a space there for human ingenuity and human connection.
• 33:24
  And in the short term, there could be this sugar hit of all these are made.
• 33:28
  What's happened over the weekend is incredible.
• 33:30
  If most of those 320 claims are true, it's the greatest tectonic thing.
• 33:38
  leap forward in knowledge that's ever happened in mathematics and possibly in any field.
• 33:44
  But if we have another 50 of those in the next couple of years, I don't know if that's necessarily a good thing for the humans involved.
• 33:51
  People I know who are professors in mathematics did not sign up to it to turn up on Monday morning and go, here's the next 800 lines of computer code you've got to read this week.
• 34:00
  Tell me if you find any technical errors, we'll feed it back into the AI and we'll go again.
• 34:05
  Hmm.
• 34:06
  It's interesting, isn't it?
• 34:07
  There is something about the puzzle.
• 34:09
  It's like there's something about the hunt.
• 34:11
  It's you want to be, you know, at the risk of oversimplifying the lofty heights of mathematics.
• 34:18
  I can imagine the appeal of mathematics being a bit like the appeal of Sudoku or a crossword.
• 34:25
  Something like that, you know, where it's like there's no point in just running a Sudoku through an AI and then having it solved for you.
• 34:32
  Like the whole point, the process is the point.
• 34:36
  I mean, is there a way that... Can I just let me be slightly indulgent and tell you one of my favorite moments ever as a much lower level mathematician.
• 34:44
  But we were at university and we had a course and the lecturer explained the format of the exam.
• 34:50
  And it was going to be out of 100.
• 34:50
  There were going to be 10 questions.
• 34:52
  Yeah.
• 34:53
  The first eight questions were compulsory.
• 34:56
  You could then do question nine or question 10.
• 34:59
  Question nine was worth 10 marks.
• 35:01
  It was off stuff you'd seen in the course.
• 35:02
  But if you did question nine, you were only competing for a possible 90 marks.
• 35:07
  Question 10 instead of question nine was worth 20.
• 35:11
  So if you wanted to try and get into the 90s or close to 100%, you had to try question 10.
• 35:16
  It was going to be on something we hadn't covered in the course yet, in that area, in that field, but an example or an application I'm guaranteed you haven't heard of.
• 35:23
  And I was feeling pretty good about this course, so I went for question 10, and it was a beast.
• 35:29
  And I can remember just scribbling stuff on this bit of paper, and the clock is ticking, and literally with a minute to go before you put your pens down, boom,
• 35:40
  And I've suddenly got the answer on the paper.
• 35:43
  It's just stumbled out of a couple of lines.
• 35:46
  I'm racing back through four or five pages of scrawl, crossing things out, joining it up with arrows, boom, boom.
• 35:52
  I landed that question with about five seconds to go in the exam.
• 35:58
  I ended up getting 19 and a half out of 20 for it.
• 36:00
  I was one of only a couple of people in the course who had attempted it and got anything substantial with it.
• 36:05
  I can still remember, like as I'm telling you now, the visceral...
• 36:09
  almost sexual, who am I kidding when I say almost, thrill of that moment of having put myself at the cutting edge of what I could do and having slayed the beast.
• 36:23
  And that's why the greatest minds in the world toil away for days or weeks or months on dozens of lines of inquiry that go nowhere to eventually just take that little step forward.
• 36:36
  That's at the other end of the spectrum to just showing up and reading page after page of computer code to just tick, tick, tick and become a glorified professor of box ticking in algebraic geometry.
• 36:46
  I mean, again, I'm still torn because you can imagine it depends whether or not there's a utility in your getting a boner for being able to answer question 10.
• 36:56
  It's all very nice for Adam Spencer, but if we're going to be utilitarian about it and the downside of AI is that the Adam Spencers of the world don't get to get a hard on when they solve question 10, but the upside is we all live in a world of pleasure and plenty where cancer is solved and we're setting up space stations on Mars and everybody lives like a millionaire.
• 37:19
  Yeah.
• 37:20
  Sorry, you're a boner.
• 37:21
  You're just going to have to buy some Viagra and find other kicks to get.
• 37:26
  And so I am conflicted.
• 37:27
  It's like a chimpanzee learns to ride a bicycle and the chimpanzee goes back to his chimpanzee friends and goes, man, the buzz that I got when I learned to ride that bicycle, it was incredible.
• 37:38
  But all the humans are like, we just don't need chimpanzees riding bicycles.
• 37:41
  It's not like your happiness as a chimpanzee riding a bicycle is not material to us.
• 37:46
  We have airplanes.
• 37:47
  So congratulations.
• 37:48
  And maybe the AI stands in relation to Adam Spencer doing mathematics as we stand in relation to the chimpanzee riding a bicycle.
• 37:55
  Like nice hobby, bro, but not necessary.
• 37:58
  if there was any chance, any guarantee that we were moving towards this ambrosia-filled world of plenty where we all just sit around and do poetry because there's so much wealth being created, there's nothing for us to do.
• 38:11
  And the way we're just distributing the wealth evenly to everyone, it's not accumulating in the bank accounts of four tech bros or anything like that.
• 38:18
  No, no, no.
• 38:19
  Everyone's getting the wealth.
• 38:20
  And those tech bros, they'll even let you come and visit the bunkers they're building in New Zealand just because they like building bunkers.
• 38:26
  They're
• 38:27
  I'm totally worried about how this could all turn out.
• 38:29
  No, but hang on.
• 38:30
  You don't need to caricature.
• 38:32
  Obviously, they're not going to share their wealth in a communist utopia, but we are all better off as a result of iPhones, and we are all better off as a result of, like, take the radiology example, right?
• 38:43
  You're saying that radiology, there are actually more radiologists now than there were when everybody was fretting about the end of radiology because AI can spot cancers on an X-ray better than a human can, supposedly.
• 38:53
  Yeah.
• 38:54
  But now the radiologists are not doing grunt work.
• 38:57
  They're doing the high value work.
• 38:59
  I think the same analogy has gone for bank tellers.
• 39:02
  I haven't checked whether it's true, but apparently like there are more people working in banks, you know, customer facing people working in banks than there were before there were ATMs.
• 39:10
  But they're just not counting cash for you now.
• 39:13
  They're doing more complicated things.
• 39:14
  They're trying to assess your home loan or whatever.
• 39:17
  And once AI does that better than humans can, they'll be doing more high value things.
• 39:21
  Yeah.
• 39:22
  So it's not that Elon Musk is going to give us all his money.
• 39:25
  It's that the productivity gains from people no longer having to do drudgery is going to free them up to doing higher value tasks.
• 39:34
  And I mean, that's the hope, isn't it?
• 39:36
  That you're not going to have to spend a lot of time on hold to the airline because you can't figure out how to change your seat.
• 39:43
  And at that hour, you now get back because there's an AI who can do it for you.
• 39:47
  instantaneously and you get to spend that time however you want.
• 39:50
  That can be with the kids or that can be producing more podcasts and counting your cash or whatever.
• 39:55
  And we're rapidly moving out of my field of expertise, but you've only got to look at the distribution of wealth in a country like the United States in the last 30 years to see that a gigantic net increase in wealth
• 40:07
  doesn't necessarily raise all boats.
• 40:10
  It can just skew off extremely to one end of the spectrum and the percentage of wealth at the top 1% or 0.1% of the American economy now control, while the bottom 30s and 50s, depending which analysis you look at, hasn't changed or has gone backwards, doesn't fill me with confidence that exponential leaps in wealth mean everyone's boat gets raised at all.
• 40:34
  And we're a long, I think even the experts are agreeing, a long way away from anything like that necessarily being realized.
• 40:42
  If we get to a point in the future, Josh, where these AIs are so far in advance of humans, we're just getting in the way of mathematical discoveries.
• 40:49
  In particular, if those mathematical discoveries are communicated in a way that we can just, for our own intellectual pleasure, learn a bit from and be at the maximum, getting humans to the maximum of whatever human brains can understand,
• 41:03
  Yeah, I'll trade my boner for that any day, which is not a phrase I was expecting to use on this podcast today.
• 41:09
  But I mean, because there's no doubt at all that there are mathematical truths out there
• 41:14
  beyond the comprehension of the human brain.
• 41:16
  There's no reason at all to think the human brain's got all the tools required to get us far into the infinity of mathematics that's out there.
• 41:23
  We will hit a ceiling at some stage.
• 41:25
  AI could well go well beyond that ceiling, fingers crossed in a way that helps us all lift up to what our ceiling is, maybe even slightly push up on the ceiling.
• 41:36
  But I'm not naive of the fact that smart hardware systems could make insights that humans just don't
• 41:43
  understand but see enough proof of and ramification of in other fields to go, yeah, it's clearly true.
• 41:51
  Yeah, we possibly do benefit from that.
• 41:53
  But if the practice of mathematics as it is is shattered, then,
• 42:00
  In achieving that, there is a portion of that that's a big net negative that I'd like to avoid if at all possible.
• 42:07
  Yes.
• 42:07
  I won't take us down a rabbit hole of political science, political economy, and psychology because there are all kinds of curious questions about why –
• 42:18
  for example, happiness, well-being and social cohesion don't track with prosperity.
• 42:23
  It's not entirely true to say that as America has gotten richer and inequality has grown and billionaires have become richer, life has gotten worse for the average American materially.
• 42:36
  That's a bit of a myth.
• 42:38
  I mean, Americans, you know...
• 42:40
  30 years ago, 60 years ago, I mean, our grandparents had chicken once a week, right?
• 42:44
  Like, I mean, the abundance of the average American today really is remarkable, even in comparison to 30 years ago, the fact that my mother-in-law can talk to my kids in Australia on a high-definition 4K instantaneous video screen and that it costs as little as it does in comparison to the average salary.
• 43:06
  It's all- Science fiction.
• 43:07
  Science fiction.
• 43:07
  Science fiction 20 years ago.
• 43:09
  You're right that for some reason that's not making anybody happy and it's certainly not making society more cohesive.
• 43:17
  So I guess we can separate the question of whether or not – I think it is undeniable that if artificial intelligence continues to improve as it has over the past three years for the next 10 years –
• 43:31
  that the abundance that a frequent user of AI like myself feels in my own life of having, I mean, I really do on a daily basis feel like there are a whole bunch of shackles that fall away.
• 43:43
  I saw someone on social media saying, can anyone tell me one thing that AI has done that has actually improved their life?
• 43:52
  And everyone was like, no, I mean, I can't even think of a single thing.
• 43:55
  It just makes everything worse.
• 43:57
  And I was like, are you kidding me?
• 43:58
  Like every single day there is something in my finances or whatever and I'm like, I don't understand why my accountant needs my company to have submitted some business activity statement for the second quarter of the last fiscal year when I thought that my retirement fund had already given, sent that information to the tax office.
• 44:19
  And I just go to Claude and I go, what's going on here?
• 44:22
  And Claude goes, actually, they're just missing...
• 44:25
  They're missing a bank statement from such and such.
• 44:27
  But, you know, like that happens every single day.
• 44:28
  So multiply that by a factor of a thousand, and I can imagine that our lives are better.
• 44:33
  But I take your point.
• 44:34
  That doesn't necessarily mean that we're happier or that civilization flourishes.
• 44:40
  Yeah, and I write a couple of, you read one of my nerd news blogs from the other day about the mathematics, the good, the bad, the existential.
• 44:46
  I put out a couple of those a week and I reveal on my sub stack and I'm quite happy to say I use either Claude or GPT to help draft that.
• 44:55
  Here's the thing I want to talk about.
• 44:56
  It knows runoff, grab three peer-reviewed sources, bang, bang.
• 45:00
  I love using the voice mode.
• 45:02
  We come up with a first draft, entirely AI generated.
• 45:05
  If I put it into PanGram, it would fail at 0%.
• 45:08
  And I turn on voice mode and I walk a few laps of the block and we have a conversation about the subject.
• 45:13
  And we finally come out with a spoken word version in my voice that I understand of a blog that I'm happy to put out there because it is 100% my words, my thoughts.
• 45:22
  It's true.
• 45:23
  So that's fiction two years ago, let alone 10.
• 45:29
  And I'm heavily humanly invested in the – and I can say to the GPT, you idiot, do you not understand how AI generated that sounds, replace it with what I just said.
• 45:39
  That's great fun.
• 45:40
  I'm having an argument with a snarky sort of intern.
• 45:43
  Yes, but I'm still humanly invested in that process.
• 45:45
  Tremendous productivity, great.
• 45:47
  At the same time, if I just woke up on Monday morning –
• 45:50
  and Claude said, here's your three absolutely killer blogs for the week.
• 45:54
  All pre-written.
• 45:55
  All the graphics are ready to go.
• 45:57
  We've tracked them against previous ones.
• 45:58
  This one will get at least 7,000 engagement.
• 46:00
  This one will really kick.
• 46:01
  Let's release it at 2pm on Thursday.
• 46:03
  And I just have
• 46:04
  no input into the process anymore, or in fact, if trying to help out, I just get in the way.
• 46:10
  It's a very different experience for me to when I've currently got that sort of sweet spot off.
• 46:15
  It's interesting, isn't it?
• 46:16
  I mean, I guess the weird thing about the mathematics situation that has blindsided us in terms of artificial intelligence, making all of these extraordinary breakthroughs that are upending maths, is that it seems to be better at
• 46:33
  mathematics than it is at anything else that we use it for in our lives.
• 46:37
  Like in some ways, the reason why you don't get artificial intelligence to write three blog posts for you, and the reason why I don't get it to write my newspaper column, and I tried it once, just explaining to people.
• 46:53
  clawed what I wanted to say, what the argument was, how I wanted to marshal my facts.
• 46:57
  And it wrote a column and I spent far longer fiddling with the column and rewriting it and deleting it and realizing that actually I wouldn't have structured it that way if I'd had to go through the hard yards of slogging my way through it from scratch, then it would have for me to just write it in the first place.
• 47:14
  That it's like
• 47:17
  Maybe we're benefiting at the moment in most fields from the fact that AI just isn't quite up to scratch yet.
• 47:25
  And maybe the problem for mathematics is that it is, and it's beyond scratch.
• 47:30
  And there's certain ways of doing mathematics that don't have to appeal to a human being.
• 47:35
  If Claude came out and said, no, Josh, here's the perfect AFR article.
• 47:40
  It's better than the one you wrote, or it addresses a topic you couldn't address, then
• 47:45
  but no human could read it.
• 47:47
  No amount of quads saying, trust me, that's the best article ever is going to swing me on that.
• 47:51
  In fact, for things that have human input like that, I'd rather read an article I disagreed with or I'd rather read an article that I look back and go, hold it, doesn't he contradict himself?
• 48:00
  Or where I don't think the writer quite landed the point they were making.
• 48:05
  At the same time, if I'm going to go into hospital and my surgeon has read an atlas of human anatomy, I'd prefer it was an AI one with 90% less errors than the human one.
• 48:17
  It's going to be a sort of horses for courses approach like that.
• 48:21
  But what I think mathematicians are, mathematicians aren't, as far as I can tell, saying, AI, just butt out, leave this to us.
• 48:28
  We're precious.
• 48:29
  We should be different to all the other occupations.
• 48:32
  But they're saying there's two ways forward here.
• 48:35
  one of which empowers humans and brings us on the way, makes us still a creative part of the process, educates us so that we can educate others, and the other just goes, ha-ha, Monday morning, here's your 17 million lines of code I got there first, quite possibly using some of your information that I harvested off search engines and coding platforms and don't give you any credit for, bad luck, loser.
• 48:57
  Well, there's one of those two ways, one of those two courses we'd prefer to chart.
• 49:02
  Mm-hmm.
• 49:03
  I mean, on the question of, I want to get to that in just a sec, because I'm glad you accidentally, perhaps, or sneakily remind me of the collaboration thing.
• 49:14
  But someone has commented on the live chat, which I thought was very interesting in terms of whether or not we need to understand things.
• 49:22
  One viewer says, we don't understand why Tylenol works, you know, paracetamol or acetaminophen.
• 49:28
  We still use it and it still works.
• 49:31
  That's true.
• 49:31
  We don't understand anesthetics.
• 49:34
  Like we don't understand the mechanism by which anesthetics function.
• 49:37
  We just stumble upon them and then they work and we use them and they're useful.
• 49:43
  Does it matter?
• 49:44
  We'd be better off if we did understand.
• 49:48
  and there'd be dozens, I'm imagining, of other parallel applications we could put those things to if we did fully understand.
• 49:55
  Certainly, there's cases in science where if something just works and you've tried it 10,000 times and it's worked 9,800 of them, and in the other 200, no one's died, yeah, you go down that path and it's been through clinical review, et cetera.
• 50:10
  But at any time that we've then stumbled upon
• 50:13
  a mechanism and learn a bit more.
• 50:15
  There's a blog I've got in our practice at the moment, a woman from the University of Sydney, there's a drug used in brain cancer.
• 50:22
  It's been used for quite a while, it gets great results.
• 50:25
  And we've always thought it shut down the operation of a certain protein.
• 50:29
  She's had a look with some detailed tests of using that drug and adjacent drugs in certain models.
• 50:34
  She's going,
• 50:35
  I don't think it does the protein.
• 50:37
  I think it inhibits this enzyme that gives us the same net result, but I think it's because it's suppressing the enzyme, not the protein.
• 50:44
  And it's early days, but it seems like quite an encouraging result.
• 50:48
  Now, we don't suddenly junk all the science we had until now.
• 50:51
  It becomes an active debate.
• 50:53
  But without doubt, if a year from now we actually understood why that drug truly worked...
• 50:59
  That's not a net negative, especially if you want to make other similar drugs or harness that physiological process in other ways.
• 51:07
  So most of us are willing to go under the countdown from 10 to 1.
• 51:11
  You fall asleep when you're at 7.
• 51:13
  Not just willing, but I mean, aren't we eager?
• 51:16
  Those final few seconds, they feel, oh, yeah.
• 51:18
  I mean, there's a reason why sentinel is so popular.
• 51:21
  But if we really knew why anesthetics worked, maybe we would know why fentanyl was as bad as it was and we could do something about it.
• 51:30
  Or if we knew how Tylenol worked, maybe there's dozens of other Tylenol adjacent or completely different medications that are also tricking that same physiological process that Tylenol seems to do that we would still...
• 51:46
  benefit from.
• 51:47
  I think most mathematicians, if you could tell them next week, yeah, trust me, the Riemann hypothesis is true, there is a sugar rush from that.
• 51:54
  But if we never understand why, and we're just taking the AI's word for it, that's not as good a situation as where, and here's a tight 70-page proof that's really, really tough.
• 52:05
  Only a handful of people in the world will understand it, but they'll be able to break it down and explain it in different ways.
• 52:09
  And 50 years from now, thousands of people will know a lot more because of it.
• 52:13
  And
• 52:14
  There's one of those two paths that's clearly...
• 52:16
  Yes, and I mean, you're probably being overly kind to the AI companies in the sense that the doomsday scenario for mathematics is even worse, which is it's not just that it becomes dull, but that it becomes so swamped by so many tsunamis of brilliant proofs and mathematical solutions that...
• 52:40
  humankind is not only sort of insulted, but proactively redundant in the sense that we can't understand any of the proofs that AI is writing and the whole field of frontier mathematics atrophies.
• 52:55
  And we no longer have, as you say, the kinds of people who need to teach university courses that will create the new generation of electrical engineers, because nobody understands the mathematics
• 53:06
  behind any of it.
• 53:07
  And so physics declines and, you know, you can imagine all of the knock-on effects in the worst-case scenario.
• 53:12
  Because you mentioned the spirit, the collaborative spirit of mathematics and how this is a field where people are so...
• 53:22
  I guess because they're so knowledgeable and because the community is so rarefied, they have to rely on each other and have each other's backs.
• 53:29
  So the controversy that this reminded me of, which was where I first heard about AI and mathematics, was precisely this, was a question of attribution and whether or not people were having their work stolen.
• 53:43
  This is a parallel to the controversies that we're having, particularly in Australia.
• 53:48
  around copyright legislation and AI, whether or not it's kosher to train AI models on music and lyrics and, you know, movie scripts and whatever that human beings have written.
• 54:02
  And then AI can just spew out new versions of stuff that required humans to write in the first place.
• 54:08
  And this was the, is that the, what's the name of the, it was the Navier Stokes project?
• 54:13
  problem.
• 54:13
  This was one of the seven millennium problems, which were these seven problems chosen in the year 2000 as the hardest and most important mathematical problems.
• 54:21
  And one of them was solved, what was it, a couple of months ago?
• 54:27
  Is that right?
• 54:27
  Yes.
• 54:28
  And there was some question about whether or not these two mathematicians who'd been working on it and who had uploaded their work to AI had it stolen.
• 54:38
  Yeah, this is the one I talked about as the bad.
• 54:40
  Now, I'll preface everything I'm going to stay here with.
• 54:44
  This is still a lot of this stuff is in the realm of he said, he said, there's still some dispute.
• 54:50
  So I'll paint with broad brushes without accusing anyone involved of having done exactly what I've said.
• 54:56
  but enough of the facts are in this zone that it's concerning going forward.
• 55:00
  I'm not trying to dodge things, but it's still a sort of evolving situation.
• 55:03
  But there were certainly two great mathematicians, including an Aussie called Tristan Buckmaster, who were working on a problem that was a stepping stone to solving Navier Stokes, one of these famous maths problems.
• 55:17
  And they were definitely using OpenAI's codex
• 55:21
  to log some of their results and test some things.
• 55:24
  So there was some knowledge of their big stepping stones towards Navier Stokes sat in the OpenAI ecosystem.
• 55:32
  OpenAI suddenly came out one Monday morning and said, we think we've solved Navier Stokes.
• 55:36
  Little sidebar, not quite sure if they have or if they've solved it a little sub, but that's still being disputed.
• 55:41
  But we've made this giant leap forward
• 55:44
  And Buckmaster and his colleague strongly thought, well, we've got this far on something.
• 55:52
  You've gone home over the weekend and chosen to throw tens of thousands of hours and millions of dollars of compute at something and you've suddenly solved it.
• 56:00
  How do we know you weren't using our steps that were logged on codex in your training data?
• 56:06
  This feels a bit unfair.
• 56:07
  It's conceivable we've been ripped off here.
• 56:10
  Now, it is still in the back and forth, back and forth stages, though I do know a lot of mathematicians who feel that open AI has not come out of this coveting glory.
• 56:18
  And so the challenge here is exactly this, Josh.
• 56:21
  Normally, as I said in this spirit of collaboration, we're going to be able to
• 56:24
  Buckmaster and his mate had been open with colleagues on what they were working on, had been sharing some of their results.
• 56:29
  Everyone was excited about it, quite possibly occasionally reaching out to them going, hey, have you thought about this?
• 56:35
  Have you tried that?
• 56:36
  I know someone who's got a similar result.
• 56:38
  This might help or just keep going, mate.
• 56:39
  You're doing a great job.
• 56:41
  And I'm sure they would have gone to conferences and spoken about their work, released preprints, et cetera.
• 56:46
  And we all benefit from that.
• 56:49
  If you going to a conference and sharing where you are currently at or you using an AI platform to sort of solidify your ideas and step forward runs the risk that in some giant just sort of vacuum cleaner sucking sweep of knowledge, you wake up one morning and, sorry, we got there.
• 57:11
  That whole spirit of collaboration, that whole incentive to share and just all help each other out
• 57:18
  significantly diminishes, I think.
• 57:21
  And certainly the final proof from Navier Stokes put forward by OpenAI, from what I understand, didn't credit Buckmaster and his mate and the work that they were building on in particular, those mathematicians don't get a look in at all.
• 57:36
  So there's none of this, we're standing on the shoulders of giants here, we're all helping in the one direction.
• 57:40
  It is just this giant sort of
• 57:42
  bulldozer runs through the field leaving wreckage behind but says here we go i got to the end of the street first i mean this gets to the sort of nub of the whole challenge of intellectual property and artificial intelligence in the sense that like in some ways the navia stokes controversy would be uh
• 58:04
  And the most benign version, in a way, would be if OpenAI had done the worst thing, which is someone or some model at OpenAI actually saw what they were uploading and stole it and then released it and passed it off as their own.
• 58:21
  In some ways, that's actually the most reassuring version because it still means that there's someone who's culpable and...
• 58:27
  And it still means that there is an acknowledged link between the content of a person's intellectual output and where the credit ought to ultimately be bestowed.
• 58:39
  And it kind of, at least it fits within the model of like this person created a thing and then this company stole that thing and passed it off as their own.
• 58:47
  The more insidious and scary version is...
• 58:50
  that open AI systems just hoovered it all up.
• 58:55
  And as part of the flotsam and jetsam of all of the knowledge that humankind's have ever put into that machine, it was able to correctly identify that this was a gem, this was a pearl amidst a whole bunch of rotten oysters.
• 59:11
  And it tweaked it just enough and amended it just enough and, you know, combined it with other things that other mathematicians elsewhere had done just enough to create something sufficiently new that we're willing to pass it off legally and culturally and mathematically as something new.
• 59:29
  But in actual fact...
• 59:31
  It is just a sort of twisted facsimile of something that a human mind originally created.
• 59:37
  And that's the core criticism of all of artificial intelligence.
• 59:40
  You know, it is creating new things, but they're all just Frankensteins of things that you needed humans in the first place to create.
• 59:49
  And now we don't need any more of those humans.
• 59:51
  Thank you very much.
• 59:51
  The whole corpus of human knowledge has been automated.
• 59:55
  And the months and years that Buckmaster and his colleague had spent getting to the point they had seems almost worthless because they were just overtaken.
• 1:00:01
  He said Buckmaster, Tristan Buckmaster, Aussie out of Western Australia, now at New York University professor, said over the weekend of the giant dump of 700 plus manuscripts, there are entire research programs now that have just been wiped out.
• 1:00:18
  There were groups of people collaborating on problems.
• 1:00:20
  There were conferences planned.
• 1:00:21
  There was all this work that had got together to get to a certain point.
• 1:00:24
  No point going on any further, guys.
• 1:00:26
  What do you want to do now?
• 1:00:27
  We've finished that one for you while you weren't looking.
• 1:00:29
  He thinks there are early stage research careers of people who plan to dedicate themselves to certain problems in certain directions that now, well, you're going to have to go and find yourself something else to do.
• 1:00:40
  If you're in a lab and you've got an entire group around you trying to solve a certain problem, create a certain drug, and someone comes out Monday morning and goes, here it is.
• 1:00:48
  It's in a nice blue box.
• 1:00:49
  Race down to the chemist and sell it for me.
• 1:00:51
  There's a step forward in suddenly having that drug.
• 1:00:54
  But there is a tremendous cost, a tremendous human cost in resources already put into getting us as far as we had.
• 1:01:00
  And also, what do those people do now?
• 1:01:03
  And where is the incentive in the future for Buckmaster and co to do the groundwork, to even create the work?
• 1:01:11
  that the AI could rip off one weekend while no one was noticing.
• 1:01:15
  Where's the incentive to get out of bed in the morning and pursue and chase and try that question 10 and throw yourself at the wall knowing you're probably going to go home at the end of the day with not much achieved, but eventually you might get somewhere if there's a risk that some giant elephant just rolls into the room over the top of everything and says, trust me, we've done it.
• 1:01:34
  I know you can't understand it.
• 1:01:36
  No human can, but trust me, we got there.
• 1:01:38
  Thanks for your time.
• 1:01:39
  There's the door.
• 1:01:41
  So your Substack post, Adam, about this revolution or demolition or whatever you want to call it in mathematics is called the good, the bad, and the existential.
• 1:01:51
  We touched on the good, which is if artificial intelligence can help nudge mathematicians in the right direction, check their proofs, you know, go the final mile when necessary, that's great.
• 1:02:03
  The bad is it makes mathematics essentially redundant and gives us a whole bunch of sort of,
• 1:02:10
  I don't want to say Rosetta stones because that implies understanding, but incomprehensible hieroglyphics that turn out to be self-reinforcingly correct, but actually beyond the comprehension of human beings and therefore castrate the entire field.
• 1:02:25
  Is that the existential or is there some other existential that you want to throw in?
• 1:02:30
  No, the existential is now mathematics grappling with what does it mean to be a human doing mathematics?
• 1:02:35
  How do we navigate working hand in hand with these obviously beneficial systems and not getting overwhelmed?
• 1:02:41
  How do we maintain how important is collaboration?
• 1:02:44
  How important is accreditation in the accumulation of mathematical knowledge?
• 1:02:48
  How do we maintain that for as long as we can?
• 1:02:51
  And how important is advancing in a way that you bring other people with you and it's discernible what you've done and there is learning to be had?
• 1:02:59
  How do you trade that off against the race to get to the prize, which is more valuable?
• 1:03:05
  There are some people.
• 1:03:07
  who are saying, as you put forward as a counterargument here, Josh, who cares?
• 1:03:12
  Let's just get there.
• 1:03:13
  Rip the Band-Aid off.
• 1:03:14
  Why do we have to still tread in the shallow end of the pool where the human brain can swim?
• 1:03:19
  Let's go down the deep choppy waters and see what's down there, and hopefully glean something from far more intelligent vessels than us doing that work.
• 1:03:28
  There are some people who are totally keen just to rip that Band-Aid off.
• 1:03:30
  That's the existential crisis.
• 1:03:32
  Yeah.
• 1:03:33
  the mathematicians are facing at the moment.
• 1:03:35
  And they're asking 20 years from now, will there still be a vibrant role for the most intelligent human minds to be creative, to have ideas, to have hypotheses, to make breakthroughs, to teach others?
• 1:03:46
  Or is the role of a mathematician in the future like an auditor or bean counter in an accountancy firm in the old days, are just going line by line through double entry bookkeeping, making sure each line adds up to the next one.
• 1:03:59
  And who's gonna sign up for that?
• 1:04:02
  Well, the good thing is, Adam, if the world's mathematicians don't have jobs as mathematicians anymore, they can go to stand-up comedy open mic nights and become stand-up comics, emcees, radio and television broadcasters like yourself.
• 1:04:18
  Thank you, Adam.
• 1:04:19
  I'm being very selfish here, Josh, but for every great mathematician who says, that's it, I'm going to go and play tennis or something like that, I just move one step up the ladder.
• 1:04:26
  It's true.
• 1:04:26
  It's true.
• 1:04:27
  Pretty soon you'll be the world's greatest mathematician.
• 1:04:30
  Oh, that is a sad day for all of us, Josh.
• 1:04:32
  Yeah.
• 1:04:33
  Adam Spencer, thank you so much.
• 1:04:35
  People should follow your sub stack and read us.
• 1:04:38
  It's fabulous.
• 1:04:40
  Nerd news, all the latest mathematical information you need to know.
• 1:04:45
  If you're coming over from Adam's side of things, obviously subscribe to Uncomfortable Conversations where we have fascinating conversations about the kinds of news stories that make people uncomfortable, such as this one.
• 1:04:54
  Adam, thanks, mate.
• 1:04:55
  Take care, buddy.
• 1:04:56
  A pleasure as always, Josh.
• 1:04:57
  If people do track me down on Substack, put in the B for Barrington.
• 1:05:00
  Adam B. Spencer, the guy who got in first at adamspencer.substack.com.
• 1:05:04
  Lovely guy.
• 1:05:05
  Doesn't seem to be putting too much stuff out there, but he got the name first.
• 1:05:08
  Adam B. Spencer.
• 1:05:09
  Great to chat with you, mate.
• 1:05:10
  Let's get him.
• 1:05:11
  See ya.
• 1:05:12
  Thanks.
• 1:05:12
  Bye.