korrents

Terence Tao

@terence-tao · 18 positions · 0 changes of mind

Mathematician at UCLA, Fields Medal 2006. Writes at terrytao.wordpress.com.

Everything they publish, on ppll ↗

Terence Tao did not write this page.

We collected these quotes from things they published elsewhere, and every quote links to where it was said. They have no account here and have not endorsed this site. Quotes are word for word; the short line under each one is our own restatement, not their wording. Their own site. Is this you? Claim it or ask us to remove it. Or tell us what is wrong here.

  1. Our reading

    What 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.
    spoken · official transcript hear it at 0:07:56 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 1st of 18 in this recording

    Interesting

  3. Our reading

    He 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.
    spoken · official transcript hear it at 0:55:26 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 2nd of 18 in this recording

    Interesting

  5. Our reading

    Physics will be unified again as it has been before; the obstacle is that relativity and quantum mechanics already explain almost everything we can measure.

    Their wordsBut I have faith that we've been doing this for centuries and we've made progress before. There's no reason why we should stop.
    spoken · official transcript hear it at 1:07:19 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 3rd of 18 in this recording

    Interesting

  7. Our reading

    String theory, the leading candidate for decades, is slowly going out of fashion because it is not matching experiment.

    Their wordsYeah, that was a leading candidate for many decades. I think it's slowly pulling out of fashion. It's not matching experiment.
    spoken · official transcript hear it at 1:09:25 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 4th of 18 in this recording

    Interesting

  9. Our reading

    Formalising a proof in Lean currently takes about ten times the effort of writing it out: doable, but annoying.

    Their wordsSo right now I estimate that the time and effort taken to formalize it, proof is about 10 times the amount taken to write it out. So it's doable, but it's annoying.
    spoken · official transcript hear it at 1:25:23 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 5th of 18 in this recording

    Interesting

  11. Our reading

    Lean 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.
    spoken · official transcript hear it at 1:34:39 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 6th of 18 in this recording

    Interesting

  13. Our reading

    Solving one Olympiad problem with three days of Google's server time shows what is possible, but the approach does not scale.

    Their wordsYeah, these are great work that shows what's possible. The approach doesn't scale currently. Three days of Google's server time can solve one high school math format there. This is not a scalable prospect, especially with the exponential increase as the complexity increases.
    spoken · official transcript hear it at 1:45:31 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 7th of 18 in this recording

    Google

    Interesting

  15. Our reading

    AI 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.
    spoken · official transcript hear it at 1:51:05 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 8th of 18 in this recording

    Interesting

  17. Our reading

    When 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.
    spoken · official transcript hear it at 1:55:54 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 9th of 18 in this recording

    Interesting

  19. Our reading

    His 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.
    spoken · official transcript hear it at 1:59:04 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 10th of 18 in this recording

    Interesting

  21. Our reading

    This decade, AI could propose a conjecture connecting two things nobody thought were related, with a real chance of it being correct and meaningful.

    Their wordsYeah, this decade I can see it making a conjecture between two things that people would thought was unrelated.
    spoken · official transcript hear it at 2:02:33 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 11th of 18 in this recording

    Interesting

  23. Our reading

    Current AI struggles even to rediscover old laws of physics from data, and when it does, contamination from training is the first suspect.

    Their wordsThe dream is you just feed it all this data, and this is here is a new patent that we didn't see before, but it actually, even the current state of the art even struggles to discover old laws of physics from the data.
    spoken · official transcript hear it at 2:02:59 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 12th of 18 in this recording

    Interesting

  25. Our reading

    In 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.
    spoken · official transcript hear it at 2:30:19 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 13th of 18 in this recording

    Interesting

  27. Our reading

    The 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.
    spoken · official transcript hear it at 2:33:00 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 14th of 18 in this recording

    Interesting

  29. Our reading

    On 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.
    spoken · official transcript hear it at 2:43:20 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 15th of 18 in this recording

    Interesting

  31. Our reading

    The 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.
    spoken · official transcript hear it at 3:01:25 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 16th of 18 in this recording

    AI and jobs

    Interesting

  33. Our reading

    Faced with a problem none of your techniques fit, try anything, the stupider the better, because the way it fails is the clue.

    Their wordsSo the next step then is to try anything no matter how stupid and in fact almost the stupider, the better, which technically is almost guaranteed to fail, but the way it fails is going to be instructive.
    spoken · official transcript hear it at 3:07:19 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 17th of 18 in this recording

    Interesting

  35. Our reading

    The mathematical community as a whole is a superintelligent entity that no single mathematician comes close to replicating.

    Their wordsso the mathematical community plural is incredibly super intelligent entity that no single human mathematician can come closer to replicating.
    spoken · official transcript hear it at 3:10:20 · all korrents from this recording

    ↗Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472youtube.com 18th of 18 in this recording

    AI alignment

    Interesting