Oct 9, 2026 · 1h 9m
AI forces mathematicians to rethink proof and discovery
How AI Is Upending the World of Mathematics
As AI takes on more routine mathematical work, humans may need to redefine expertise around questions, judgment, verification, and originality.
- 1AI can generate mathematical claims, but reliable proof checking still requires formal systems such as Lean.
- 2Mathematical significance depends on human choices about which problems matter, not merely on producing more results.
- 3Education may shift toward collaborative, open-ended work as AI makes isolated problem solving and routine proof writing less central.
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Justin Solomon argues that AI may produce more mathematical results without resolving the human question of which discoveries are genuinely significant.
The brief
Odd Lots examines what remains distinctly human as AI becomes better at mathematics, from generating possible proofs to deciding which problems are worth pursuing.
Justin Solomon separates calculation and proof verification from the harder work of choosing meaningful questions, developing insight, and judging whether a result matters.
The conversation uses fluid dynamics, Pixar’s visual effects, and Navier–Stokes to show how applied mathematics connects elegant theory with computational practice.
Lean offers a machine-checkable way to verify proofs, but AI-generated claims could still overwhelm researchers and peer review with results that are difficult to assess.
The episode’s broader argument is educational: as AI handles routine work, mathematicians may focus more on taste, explanation, collaboration, and proposing the next breakthrough.
What was said on this episode
37 statements · 11 positive · 16 negative · 2 mixed · 8 neutral
Mathematicians pursue applications, fundamental insight, intellectual enjoyment, or understanding the universe.
“some people go into math because they want to see it translated into applications or to bring fundamental insight into the kind of things we do every day, whether it's predicting markets or physics, what have you. Other people in areas of math, sometimes you'll call them pure math. I don't love that. terminology like pure versus applied. But in other areas of math, it's almost just for the joy of the game or understanding the universe around you. All of these are totally legitimate reasons.”
Listen at 9:25
Studying mathematics develops reasoning skills useful across many fields.
“But along the way, I think you develop a lot of really important reasoning skills and skills that support work in all kinds of different areas.”
Listen at 9:54
Advanced mathematicians frequently use calculators.
“Very often.”
Listen at 10:11
Mathematics involves selecting interesting problems and extracting broader insight, not merely verifying facts.
“But it's also all about figuring out what are the interesting problems to study and what insight they bring to the broader world, right?”
Listen at 10:57
Mathematical research is fundamentally collaborative and social.
“math is a really social exercise”
Listen at 12:45
Modern cryptography developed partly from formerly abstract mathematical fields.
“a lot of modern developments in cryptography came from areas of mathematics that we used to think of as extremely pure and abstract.”
Listen at 14:25
Movie effects such as smoke and cloth are governed by partial differential equations and simulation algorithms.
“All the dynamics of those are governed by things called partial differential equations and coming up with the right algorithms for simulating those.”
Listen at 15:03
Navier–Stokes equations model fluid motion over time.
“the Navier-Stokes equations were this model. They go back quite a long time that explain the motion of, for example, liquid in a cup.”
Listen at 18:21
Current AI models are poor at checking mathematical proofs.
“in fact, actually, they're quite bad at proof checking.”
Listen at 21:51
Reliable AI proof generation requires a separate proof-checking module.
“what you have to do is to provide your model, like your large language model, with a second module that can check the AI's proof.”
Listen at 21:59
Lean can provide substantial confidence that AI-generated proofs are correct.
“if you believe that Lean is good at checking proofs, then it provides a lot of certainty that the things that the AIs are writing down are actually correct.”
Listen at 24:38
Mathematical verification is essential for trusting engineering simulation software.
“that's absolutely critical because without that, you really can't trust what your software is producing.”
Listen at 25:34
Judging a proof’s mathematical interest remains a human judgment.
“Exactly how interesting, for example, a mathematical proof is a very human judgment”
Listen at 28:34
ICLR submissions rose from roughly 1,000–2,000 to about 60,000 over ten years.
“If you look at the number of submissions to the machine learning conferences, it is wild. So in the last 10 years, I think about 10 years ago, it was maybe 1,000 or 2,000. The deadline for ICLR, the International Conference on Learning Representations, one of the big ones, I think it had 60,000 submissions.”
Listen at 33:30
AI has shifted mathematics from proof scarcity toward proof abundance.
“The way that Terence Tao put it is that it used to be we were in this era of proof scarcity that mathematicians It was really hard and it was this very bespoke object that took a lot of craft work and training to produce. Now we're in this era of proof abundance.”
Listen at 34:21
Essay assignments are intended to develop broader skills beyond producing essays.
“writing a five-paragraph essay was never the goal. It was to teach you to do other stuff.”
Listen at 36:28
Jobs focused on programming are becoming less common.
“But jobs as an actual programmer are becoming more rare.”
Listen at 37:54
An AI-generated counterexample challenged the Navier–Stokes conjecture.
“The AI gave was a counterexample. It said this conjecture is not true, that there exists a particular configuration of your fluid that becomes infinitely turbulent in a finite amount of time.”
Listen at 39:56
Academia currently lacks a good system for assigning credit in human–AI mathematical work.
“Currently, poorly. And it's a really interesting and challenging discussion. I don't think we have a good answer right now.”
Listen at 41:17
The Navier–Stokes counterexample is unlikely to transform markets or software development.
“Does a counterexample to Navier Stokes, is that going to revolutionize the markets or change the way we write software? Almost certainly not, right?”
Listen at 42:08
The reported Navier–Stokes proof had not yet received official verification.
“their proof has not been officially verified and checked.”
Listen at 43:51
Unequal computational resources are a major concern for mathematicians.
“That, I think, is one of the major concerns in our community right now.”
Listen at 45:15
OpenAI used vastly greater computational resources than typical academics for its proof.
“it appears that OpenAI suddenly poured some ridiculous amount of tokens or money or whatever into writing their proof first. The typical academic can't do that.”
Listen at 45:39
AI access is currently concentrated in a few widely used tools.
“at least in the current moment, the AI system is very centralized, right? I mean, there's two or three tools that almost everybody is using.”
Listen at 46:39
The Navier–Stokes proof is probably correct but probably not elegant.
“Is it elegant? Probably not. Is it correct? Yes, probably.”
Listen at 48:58
AI has produced few examples of genuinely novel mathematical theories so far.
“I don't think we've seen a whole lot of examples of that so far.”
Listen at 52:34
Current AI mostly recombines known mathematics rather than generating entirely new theories.
“for the most part, it's in that first category of like, Maybe making really interesting and surprising connections between things that we already knew, but not necessarily generating something entirely new out of left field.”
Listen at 52:41
Current AI tools are poor at attributing mathematical data sources.
“the current tools are very bad at answering it”
Listen at 53:39
Students’ AI-assisted homework performance may not translate into exam learning.
“A lot of our students maybe perceive that they're learning when they use these different AI tools, but then they go and take the exam and the score would say otherwise.”
Listen at 54:48
MIT is increasing experiential, research, hands-on, and industry-based learning.
“we're designing all kinds of programs that, for example, in the School of Engineering, try to bring the students in for research experience, for hands-on learning, for going into industry and seeing what things look like there.”
Listen at 55:44
Course redesign should assess human understanding rather than Claude’s capabilities.
“we're educating the human, not just testing the capabilities of Claude”
Listen at 57:34
AI systems should be treated as tools rather than authorities.
“I think the right way to think about these AI systems is that they're tools.”
Listen at 59:03
Current AI tools do not select meaningful modeling questions or determine their broader insight.
“the really interesting part is on the modeling and figuring out which questions to ask and what insight they bring us to the universe. And the AI tools are not doing that.”
Listen at 1:00:27
As routine proof writing declines, question selection and idea generation are becoming more important.
“that skill is somehow becoming more important than ever.”
Listen at 1:01:15
Children should continue learning mathematics.
“I think so.”
Listen at 1:01:26
Whether AI can build a successor model remains an open question.
“Can a model build a successor model?”
Listen at 1:03:33
Current AI models remain weak at generating novel scientific ideas and experiments.
“my impression is that the models still aren't great at that particular aspect. of, I guess, the scientific method.”
Listen at 1:04:49
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