mathematics

8 Apr 2026

David Heinemeier Hansson quoted

Our readingAesthetics is truth: when something is beautiful it is likely to be correct, in code as in mathematics and physics.

Their wordsI mean, I think aesthetics is truth. When something is beautiful, it's likely to be correct. I think this is true in mathematics. This is true in physics. This is true in a lot of different domains that when you arrive at something that has the correct aesthetic quality.

↗DHH’s new way of writing codeyoutube.com 5th of 20 in this recording

physics

30 Sept 2025

Pavel Durov quoted

Our readingMaths is essential schooling: it trains you to split big problems into small ones and to think for yourself, the same skill programming, project management and founding a company need.

Their wordsYeah. I still think math is essential. It's something that shapes your brain, it teaches you to rely on your logical thinking to split big problems into smaller parts, put them in the right sequence, solve them patiently, trying again if it doesn't work.

↗Pavel Durov: Telegram, Freedom, Censorship, Money, Power & Human Nature | Lex Fridman Podcast #482youtube.com 17th of 28 in this recording

14 Jun 2025

Terence Tao quoted

Our readingWhat sets mathematicians apart is caring whether something holds in 100 percent of cases, when 99.99 percent is good enough for everyone else.

Their wordsIf something holds 99.99% of the time, that's good enough for most things. But mathematicians are one of the few people who really care about whether really 100% of all situations are covered by it.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 1st of 20 in this recording

14 Jun 2025

Terence Tao quoted

Our readingHe works as a fox, not a hedgehog: moving between fields, chasing analogies, and re-proving results he likes with the tools he favours.

Their wordsI'm much more comfortable with the fox paradigm. Yeah. So yeah, I like looking for analogies, narratives. I spend a lot of time… If there's a result, I see it in one field, and I like the result, it's a cool result, but I don't like the proof, it uses types of mathematics that I'm not super familiar with, I often try to re-prove it myself using the tools that I favor.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 2nd of 20 in this recording

14 Jun 2025

Lex Fridman quoted

Our readingAI in chess and mathematics does not explain anything; it says which position is better, and humans build the theory from that.

Their wordsI don’t believe it’s providing a kind of formal explanation of the different positions. It’s just saying which position is better or not that you can intuit as a human being, and then from that, we humans can construct a theory of the matter.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 2nd of 20 in this recording

14 Jun 2025

Terence Tao quoted

Our readingLean and tools like GitHub will let experimental mathematics scale far beyond what one mathematician's spaghetti code allows today.

Their wordsI think the platform that Lean and other software tools, so GitHub and things like that will allow experimental mathematics to scale up to a much greater degree than we can do now.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 6th of 20 in this recording

14 Jun 2025

Terence Tao quoted

Our readingAI could compete with human mathematicians once it acquires a mathematical sense of smell: knowing which way of splitting a problem makes it easier rather than harder.

Their wordsVery rarely do you transform into a simpler problem. So if they can pick up a sense of smell, then they could maybe start competing with a human level of mathematicians.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 8th of 20 in this recording

14 Jun 2025

Terence Tao quoted

Our readingWhen formalising a proof costs no more than writing it, mathematics will flip: papers written in Lean first, and journals refereeing only for significance because correctness is certified.

Their wordsAnd that's a phase shift, because suddenly it makes sense when you write a paper to write it in Lean first, or through a conversation with AI, which is generally on the fly with you, and it becomes natural for journals to accept.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 9th of 20 in this recording

formal proof

14 Jun 2025

Terence Tao quoted

Our readingHis prediction that research-level mathematics papers would be written in collaboration with AI by 2026 has already come true.

Their wordsThere are certainly math results which could only have been accomplished because there was a human authentication and an AI involved, but it's hard to disentangle credit. I mean, these tools, they do not replicate all the skills needed to do mathematics, but they can replicate some non-trivial percentage of them, 30, 40%, so they can fill in gaps.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 10th of 20 in this recording

14 Jun 2025

Terence Tao quoted

Our readingIn ten years there will be many results much closer to twin primes, perhaps not the whole thing; on the Riemann hypothesis he has no clue.

Their wordsSo I think in 10 years we will have many more much closer results, we may not have the whole thing. So twin primes is somewhat close. The Riemann hypothesis I have no clue.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 13th of 20 in this recording

14 Jun 2025

Terence Tao quoted

Our readingThe twin prime conjecture is certainly true, the random model gives overwhelming odds of it, and he just cannot prove it.

Their wordsI can tell you with complete certainty the twin prime conjecture is true. The random model gives overwhelming odds it is true, I just can't prove it.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 14th of 20 in this recording

14 Jun 2025

Terence Tao quoted

Our readingOn P versus NP, the evidence leans towards no, and the problem is unusual in how many approaches have been proven not to work.

Their wordsCertainly more on the no than on the yes. The funny thing about P equals NP is that we have also a lot more obstructions than we do for almost any other problem.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 15th of 20 in this recording

14 Jun 2025

Terence Tao quoted

Our readingThe stable one-profession career is becoming a thing of the past; what will still be needed alongside AI is reasoning with abstractions and problem-solving when things go wrong.

Their wordsIt's becoming much more a thing of the past. So I think you just have to be adaptable and flexible. I think people will have to get skills that are transferable, like learning one specific programing language or one specific subject of mathematics or something. That itself is not a super transferable skill, but sort of knowing how to reason with abstract concepts or how to problem solve when things go wrong.

↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 16th of 20 in this recording