What podcasts say about Justin Solomon
Every statement, with the speaker, the exact quote and the moment it was said.
What Justin Solomon has said on podcasts
35 statements · 11 positive · 15 negative · 2 mixed · 7 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen at 9:54
Advanced mathematicians frequently use calculators.
“Very often.”
Open the episode · How AI Is Upending the World of MathematicsListen 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?”
Open the episode · How AI Is Upending the World of MathematicsListen at 10:57
Mathematical research is fundamentally collaborative and social.
“math is a really social exercise”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen at 18:21
Current AI models are poor at checking mathematical proofs.
“in fact, actually, they're quite bad at proof checking.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen at 36:28
Jobs focused on programming are becoming less common.
“But jobs as an actual programmer are becoming more rare.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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?”
Open the episode · How AI Is Upending the World of MathematicsListen at 42:08
The reported Navier–Stokes proof had not yet received official verification.
“their proof has not been officially verified and checked.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen at 46:39
The Navier–Stokes proof is probably correct but probably not elegant.
“Is it elegant? Probably not. Is it correct? Yes, probably.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen at 52:41
Current AI tools are poor at attributing mathematical data sources.
“the current tools are very bad at answering it”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen 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.”
Open the episode · How AI Is Upending the World of MathematicsListen at 55:44
Statements are attributed to the speaker as said on the episode and reflect their view at the time, not PodLume's. They are not advice.