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    a16z Shares Daniel Litt Quote on AI and Math

    a16z posts quotes from University of Toronto mathematician Daniel Litt on AI's current limits in proofs and verification.

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    14 Sources, 29d ago, first seen 29d ago

    TLDR

    a16z posted several clips in which Daniel Litt states that the goal of mathematics is understanding rather than papers, and that models remain bottlenecked on verifying long proofs. Litt notes models can grind computations and retrieve ideas from many papers yet struggle to produce complex correct proofs without external checking. Partner Lisha Li adds that human reluctance to perform tedious proofs motivates more compressive mathematics, and the same preference may affect AI outputs. The posts reference an interview on the topic.

    Combined views

    265.6K

    14 Sources, first seen 29d ago

    Combined views

    265.6K

    14 Sources, first seen 29d ago

    558 likes
    558 likes
    59 comments
    291 saves
    97 reposts

    Sentiment

    Positive52.2%47.8%Negative

    Based on 26 sentiment-bearing replies from 23 accounts across 5 conversations.

    59 comments
    291 saves
    97 reposts

    Sentiment

    Positive52.2%47.8%Negative

    Based on 26 sentiment-bearing replies from 23 accounts across 5 conversations.

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    14 Sources

    @a16zUniversity of Toronto mathematician Daniel Litt and a16z's Lisha Li on AI's impact on mathematics: The models are good at a narrower slice of math than the headlines suggest. They grind long computations, pull technical ideas from more papers than any human could read, and apply every known technique better than almost anyone. What they don't do is build theory, or hold a vague philosophy long enough to make it precise, which is most of what Daniel says he actually does for a living. In this conversation, he and Lisha get into how mathematicians raided an AI proof for parts and broke several other problems with them, why a thousand AI mathematicians might all turn out to be the same mathematician, and why the proof a model handed Daniel was correct but still worth nothing. 00:00 Intro 02:10 The Erdős problem AI disproved 06:20 AI's reasoning looks recognizably human 07:55 Why English beat formal proofs 10:00 Why models can't build theory 14:50 Open problems measure your ignorance 17:45 How a graph became a Millennium Prize problem 18:58 Where AI doesn't help Daniel 21:15 Why ugly proofs are worth doing 23:42 True conjectures are harder than false ones 29:32 10 pages of calculation, zero insight 34:55 The goal of math is not to produce papers 36:25 5 conjectures, 3 bad papers, 1 hour 38:05 One mathematician duplicated 1000x 40:48 Why humans matter even if models win 46:30 When cheaper and worse beats better 49:22 Why the newest AI result isn't a big deal 57:05 How mathematicians actually check a long proof 59:38 Daniel's 3-year-old is already doing math YouTube: https://www.youtube.com/watch?v=tQI35CSNB08 @littmath @lishali88
    @lishali88AI is now solving serious open problems in math. I talked to @littmath about what the models have actually mastered so far, what's still hard, and what that gap tells us about the frontier of reasoning capabilities. Measuring progress in math capabilities gives us a way to probe what higher level reasoning might still be missing. It’s also an opportunity to discuss what happens as the capabilities models have already mastered become abundant. Daniel and I get into which recent AI math results are the most impressive and why; whether increasingly difficult conjectures could themselves form a curriculum for better reasoning; whether AI math could mode collapse onto the same styles of thought; what mathematical taste is; and whether beauty is even something worth optimizing for. 👶♾️And, because we both have toddlers, how you teach kids math in a world with increasingly capable AI :) We recorded just before the recent S⁶ result, so maybe an illuminating version of its proof has dethroned the Erdős unit distance problem as the most impressive result so far? Our hour long chat here!
    @_chenglouRT @lishali88: AI is now solving serious open problems in math. I talked to @littmath about what the models have actually mastered so far,…
    @patrickshaftoRT @a16z: University of Toronto mathematician Daniel Litt on how AI has changed academic mathematics' reward incentives, and how easily he…
    @everyAI has given math a new problem: It has solved more problems than humans can verify. Normally, more solutions (aka “proofs” in the math world) mean more math problems have been solved. But AI has generated so many proof submissions—most likely correct, too—that the mathematicians are struggling to keep up. Recently, Terence Tao, one of the greatest living mathematicians, spent days translating a 90,000-line AI-generated math proof into 15,000 lines for other humans to understand. A new way of working in math may have to do with the division of labor. Machines can find results, and humans can translate them for other humans. More in this issue of Context Window: https://every.to/context-window/our-agents-ourselves?utm_source=x&utm_content=ouragentsourselves260830
    @danshipperRT @every: AI has given math a new problem: It has solved more problems than humans can verify. Normally, more solutions (aka “proofs” in…
    @ledwards@deliprao What are examples of how to correctly use AI to learn? Here is one. https://www.youtube.com/watch?v=Q8Fkpi18QXU

    14 Sources

    @a16zUniversity of Toronto mathematician Daniel Litt and a16z's Lisha Li on AI's impact on mathematics: The models are good at a narrower slice of math than the headlines suggest. They grind long computations, pull technical ideas from more papers than any human could read, and apply every known technique better than almost anyone. What they don't do is build theory, or hold a vague philosophy long enough to make it precise, which is most of what Daniel says he actually does for a living. In this conversation, he and Lisha get into how mathematicians raided an AI proof for parts and broke several other problems with them, why a thousand AI mathematicians might all turn out to be the same mathematician, and why the proof a model handed Daniel was correct but still worth nothing. 00:00 Intro 02:10 The Erdős problem AI disproved 06:20 AI's reasoning looks recognizably human 07:55 Why English beat formal proofs 10:00 Why models can't build theory 14:50 Open problems measure your ignorance 17:45 How a graph became a Millennium Prize problem 18:58 Where AI doesn't help Daniel 21:15 Why ugly proofs are worth doing 23:42 True conjectures are harder than false ones 29:32 10 pages of calculation, zero insight 34:55 The goal of math is not to produce papers 36:25 5 conjectures, 3 bad papers, 1 hour 38:05 One mathematician duplicated 1000x 40:48 Why humans matter even if models win 46:30 When cheaper and worse beats better 49:22 Why the newest AI result isn't a big deal 57:05 How mathematicians actually check a long proof 59:38 Daniel's 3-year-old is already doing math YouTube: https://www.youtube.com/watch?v=tQI35CSNB08 @littmath @lishali88
    @lishali88AI is now solving serious open problems in math. I talked to @littmath about what the models have actually mastered so far, what's still hard, and what that gap tells us about the frontier of reasoning capabilities. Measuring progress in math capabilities gives us a way to probe what higher level reasoning might still be missing. It’s also an opportunity to discuss what happens as the capabilities models have already mastered become abundant. Daniel and I get into which recent AI math results are the most impressive and why; whether increasingly difficult conjectures could themselves form a curriculum for better reasoning; whether AI math could mode collapse onto the same styles of thought; what mathematical taste is; and whether beauty is even something worth optimizing for. 👶♾️And, because we both have toddlers, how you teach kids math in a world with increasingly capable AI :) We recorded just before the recent S⁶ result, so maybe an illuminating version of its proof has dethroned the Erdős unit distance problem as the most impressive result so far? Our hour long chat here!
    @_chenglouRT @lishali88: AI is now solving serious open problems in math. I talked to @littmath about what the models have actually mastered so far,…
    @patrickshaftoRT @a16z: University of Toronto mathematician Daniel Litt on how AI has changed academic mathematics' reward incentives, and how easily he…
    @everyAI has given math a new problem: It has solved more problems than humans can verify. Normally, more solutions (aka “proofs” in the math world) mean more math problems have been solved. But AI has generated so many proof submissions—most likely correct, too—that the mathematicians are struggling to keep up. Recently, Terence Tao, one of the greatest living mathematicians, spent days translating a 90,000-line AI-generated math proof into 15,000 lines for other humans to understand. A new way of working in math may have to do with the division of labor. Machines can find results, and humans can translate them for other humans. More in this issue of Context Window: https://every.to/context-window/our-agents-ourselves?utm_source=x&utm_content=ouragentsourselves260830
    @danshipperRT @every: AI has given math a new problem: It has solved more problems than humans can verify. Normally, more solutions (aka “proofs” in…
    @ledwards@deliprao What are examples of how to correctly use AI to learn? Here is one. https://www.youtube.com/watch?v=Q8Fkpi18QXU