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Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—can help. Last month, Claude completed the first formalized proof of Fermat’s Last Theorem, one of the most famous theorems of all time. This was...

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4,764,158 次观看 • 1 个月前 •via X (Twitter)

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34 条评论

Jester 的头像
Jester1 个月前

13 million lines of code just to double check a guy who died in 1665 was right

Dr Singularity 的头像
Dr Singularity1 个月前

Math Singularity

Burny - Effective Curiosity 的头像
Burny - Effective Curiosity1 个月前

Nice! Next step is formalizing full Weil conjectures proofs and Inter-universal Teichmüller theory!

Repojournal 的头像
Repojournal1 个月前

AI solves maths by giving you a solution so complicated that to proof that the solution is wrong will be harder than solving the actual problem so you just give up and accept that it’s solved. Mathematical gaslighting

Yohei Nishitsuji 的头像
Yohei Nishitsuji1 个月前

Fermat said the margin was too narrow. Claude needed 13 million lines. He was right.

Luke || The HYPE Critic 的头像
Luke || The HYPE Critic1 个月前

ngl this headline is doing a lot of lifting. wiles proved FLT in 95, this is just translating an ALREADY accepted proof into lean so a computer can double check it. useful yeah, but its not “ai solves 350 yr old problem” its “ai (with a huge human team) transcribes existing proof into a stricter language.” different thing

Lorenzo Price 的头像
Lorenzo Price1 个月前

Andrew Wiles is currently looking at this 13-million-line GitHub repo in disbelief.

shirish 的头像
shirish1 个月前

can some math guy explain what this thing is like i'm 11?

Neutral net 🕸️ 的头像
Neutral net 🕸️1 个月前

Well, Fermat was right about the proof, it couldn't fit the margins

Eirikr The Grey 的头像
Eirikr The Grey1 个月前

Meanwhile, over at an @OpenAI conference, it seems others are warning against this stuff; as well as seeing the end of the need for mathematicians alike:

Charles Rosenbauer 的头像
Charles Rosenbauer1 个月前

That's cute. Now do the Classification of Finite Simple Groups. Make no mistakes.

Larry Panozzo 的头像
Larry Panozzo1 个月前

New benchmark just dropped. Minimum number of steps to prove Fermat’s Last Theorem.

Repojournal 的头像
Repojournal1 个月前

Moravec was truly a man ahead of his time because how can this thing is solving the hardest things but still can't reliably give me back JSON output or write a simple tweet for these bots in my comments that reads like a human.

Csaba Szepesvari 的头像
Csaba Szepesvari1 个月前

Old question, I will sound like a broken grammaphone: How do we know this formalization is correct? I would like to learn about the efforts made on this and a honest discussion of the limits of these efforts. Please please..

Lech Mazur 的头像
Lech Mazur1 个月前

OK, that's really a huge amount of Lean. Mathlib is around 2.2 million lines, and formalizing Natural-Density Almost-Bounded Collatz Orbits in Logarithmic Time took 183k lines.

Andrew West 的头像
Andrew West1 个月前

I suggest a new benchmark - how short can an LLM make the formal Lean proof of FLT?

Charlie Cheesman 的头像
Charlie Cheesman1 个月前

The simple so what: At the moment people have to manually verify new mathematical proofs ‘Lean’ is code that enables you to mechanically verify a proof (i.e. check it automatically) But lean code takes a long time to write (The researchers at Imperial have been working on this for >3 years) Claude just took that process to 11 days. Verifying proofs (and therefore the rate of progress) is going to be WAY faster in the future. Hope that helps explain this simply!

Ofek Shaked | AI Engineer 的头像
Ofek Shaked | AI Engineer1 个月前

13 million lean lines to re-check a 1995 proof is a lot of compute to confirm wiles. the 29k side theorems are the only part other people can actually reuse.

History इतिहास 🇺🇲🛕 🚀 的头像
History इतिहास 🇺🇲🛕 🚀1 个月前

There is another of Fermat's which was copied from Bhaskara. The last theorem too I feel was formulated elsewhere but wrongly attributed to Fermat. This is a hunch, please do not shoot me.

White Us 的头像
White Us1 个月前

the 29,000 supporting theorems are the actual output here. fermat was already believed. what didn't exist was formalized foundations under half the fields it touches, and now the next proof starts from there

Charlie Cheesman 的头像
Charlie Cheesman1 个月前

Maybe the real treasure was the theorems we made along the way

cit1z3n 的头像
cit1z3n1 个月前

the headline is fermat. the useful part is 29,000 other theorems coming with it.

MJ Kang 的头像
MJ Kang1 个月前

If you’re interested in the next one, I am working on Poincaré conjecture’s formalization

Raj Singh 的头像
Raj Singh1 个月前

Me with Claude

LoroLoco 的头像
LoroLoco1 个月前

ok nice one. now do something with more concrete and direct impact to society, like a new drug or something. this is cool and is needed dont get me wrong, but we also need some of other stuff too

Nathan Nguyen 的头像
Nathan Nguyen1 个月前

Rip Kevin Buzzard and @imperialcollege

Duncan Burns 的头像
Duncan Burns1 个月前

Don't fucking trust anything from you:

Vlad Oleksiienko 的头像
Vlad Oleksiienko1 个月前

13 million lines of code to verify something we've technically known since 1995...

melatoninmotte 的头像
melatoninmotte1 个月前

Fermat. The biggest troll in history to leave a comment to keep humans being curious for such a long time. And it worked.

OpenlabX 的头像
OpenlabX1 个月前

Full summary here

Paul Atreides 的头像
Paul Atreides1 个月前

13 million lines of code! Fermat was not wrong, indeed margin was too small to contain the proof🫡

Renan 的头像
Renan1 个月前

> Our proof, which totals over 13 million lines of code These pension-eating parasites aren’t even pretending anymore.

Jasper 的头像
Jasper1 个月前

This is incredible. The bottleneck in mathematics may increasingly shift from proving things to asking the right questions.

shannon 的头像
shannon1 个月前

poor kevin

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Fermat's Library

1,985,772 次观看 • 11 个月前

Pensioners currently have to complete a Proof of Life Form every three months and get it signed by a JP. We will soon be introducing the ‘AmAlive’ App that will enable you to use your new national ID to complete the proof of life from the comfort of your home in no more than 2 minutes! #BudgetDebate2025 #WeChooseJamaica
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Pensioners currently have to complete a Proof of Life Form every three months and get it signed by a JP. We will soon be introducing the ‘AmAlive’ App that will enable you to use your new national ID to complete the proof of life from the comfort of your home in no more than 2 minutes! #BudgetDebate2025 #WeChooseJamaica

Andrew Holness

74,354 次观看 • 1 年前

David Friedberg calls OpenAI’s math release the biggest day of discovery in human history--and JCal makes him clarify that he means all of human history “I think I can confidently say it’s probably the biggest day of discovery in human history, with the amount of knowledge that was revealed.” Jason Calacanis: “In math history or human history?” David Friedberg: “Human history. “The implications that flow from all of these mathematical proofs are pretty significant. I’m not going to pretend to be an expert on any of these individual proofs, but many folks have started to highlight what some of the implications are. “They span everything from electronics, quantum computing, building systems for airplanes, and more sensitive diagnostic equipment for medical applications. “What’s really profound is how it was done, and what that implies for the role of humans in society going forward. “The prior Navier–Stokes proof took thousands of hours and millions of dollars. The report is that each one of these proofs took less than three hours of compute time. “That is the equivalent of hundreds, or perhaps thousands, of years of human labor being reduced to three hours on a computer for each of these major discoveries.”
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David Friedberg calls OpenAI’s math release the biggest day of discovery in human history--and JCal makes him clarify that he means all of human history “I think I can confidently say it’s probably the biggest day of discovery in human history, with the amount of knowledge that was revealed.” Jason Calacanis: “In math history or human history?” David Friedberg: “Human history. “The implications that flow from all of these mathematical proofs are pretty significant. I’m not going to pretend to be an expert on any of these individual proofs, but many folks have started to highlight what some of the implications are. “They span everything from electronics, quantum computing, building systems for airplanes, and more sensitive diagnostic equipment for medical applications. “What’s really profound is how it was done, and what that implies for the role of humans in society going forward. “The prior Navier–Stokes proof took thousands of hours and millions of dollars. The report is that each one of these proofs took less than three hours of compute time. “That is the equivalent of hundreds, or perhaps thousands, of years of human labor being reduced to three hours on a computer for each of these major discoveries.”

Fireside Alpha

40,665 次观看 • 16 天前

WOW. Hearing about Calcea Johnson & Ne’kiya Jackson’s #historymaking mathematical discovery will never get old! Nearly 2 months after it was revealed that the HS seniors found proof of the 2,000-year-old Pythagorean Theorem, I am still in awe and proud of these students! 👏🏾
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WOW. Hearing about Calcea Johnson & Ne’kiya Jackson’s #historymaking mathematical discovery will never get old! Nearly 2 months after it was revealed that the HS seniors found proof of the 2,000-year-old Pythagorean Theorem, I am still in awe and proud of these students! 👏🏾

Ben Crump

112,914 次观看 • 3 年前

Terence Tao explains the beauty of Lean proofs. Even if they’re not very comprehensible on their own to humans, they can be analyzed more easily - each bit of the proof can be taken apart, analyzed, tweaked, and understood in terms of how it fits into the whole.
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Terence Tao explains the beauty of Lean proofs. Even if they’re not very comprehensible on their own to humans, they can be analyzed more easily - each bit of the proof can be taken apart, analyzed, tweaked, and understood in terms of how it fits into the whole.

Dwarkesh Patel

51,293 次观看 • 7 个月前

Zcash engineer Evan Forbes explains how they're working to overcome a fundamental limitation of proof of work to enable much faster blocks and higher throughput “One of the fundamental problems with proof of work comes from its superpower. Proof of work is permissionless. It's censorship resistant and that means that anyone can produce a block” “As you produce a block, it can happen that someone else produced a block at the same exact time and this is problematic because now you lose money effectively” “It's basically the fundamental problem of two people producing blocks at the same time. This is the bound on making things lower” “There's different approaches. You have this DAG approach where we simply let all blocks contribute to the chain or most blocks” “There's a separate approach that we're working on now which is similar to autobond, which is another thing from proof of stake that we're sort of adapting for proof of work” “Both of these things allow us to make the blocks much, much, much faster and much, much higher throughput”
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Zcash engineer Evan Forbes explains how they're working to overcome a fundamental limitation of proof of work to enable much faster blocks and higher throughput “One of the fundamental problems with proof of work comes from its superpower. Proof of work is permissionless. It's censorship resistant and that means that anyone can produce a block” “As you produce a block, it can happen that someone else produced a block at the same exact time and this is problematic because now you lose money effectively” “It's basically the fundamental problem of two people producing blocks at the same time. This is the bound on making things lower” “There's different approaches. You have this DAG approach where we simply let all blocks contribute to the chain or most blocks” “There's a separate approach that we're working on now which is similar to autobond, which is another thing from proof of stake that we're sort of adapting for proof of work” “Both of these things allow us to make the blocks much, much, much faster and much, much higher throughput”

genzcash

14,019 次观看 • 12 天前

For the first time in 2000 years there’s a new proof of the Pythagorean Theorem that doesn’t use circular logic. This has never been done before in any of the previous hundreds of proof’s. This wasn’t proven by researchers at Oxford, Harvard or MIT. It was discovered by two 17 y/o high school students in New Orleans: Calcea Johnson & Ne’Kiya Jackson.
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For the first time in 2000 years there’s a new proof of the Pythagorean Theorem that doesn’t use circular logic. This has never been done before in any of the previous hundreds of proof’s. This wasn’t proven by researchers at Oxford, Harvard or MIT. It was discovered by two 17 y/o high school students in New Orleans: Calcea Johnson & Ne’Kiya Jackson.

Farhaj Mayan

663,050 次观看 • 3 年前

Leonardo de Moura (Leonardo de Moura) is the creator of Lean and the Z3 theorem prover. I talked with him about how Lean works and why LLMs plus Lean will fundamentally change how we write software and do math. In this episode: • How formal verification and proof assistants work • How Lean will impact handwritten math & software • Lean’s role in recent math breakthroughs • When software is worth formalizing Where to watch: • YouTube - • Spotify - • Apple Podcasts - • Transcript - Thank you to the sponsor of this episode for supporting my work: • WorkOS: makes your app Enterprise Ready with easy to use APIs to add SSO, SCIM, RBAC, and more in just a few lines of code, check them out at Chapters: 00:00 Intro 00:28 How formal verification works 05:21 A new way of writing software 13:15 Proof assistants vs programming languages 21:06 How Lean has assisted in mathematical breakthroughs 32:03 When is it worth formalizing software 33:29 How Lean will impact handwritten math 38:55 The Z3 theorem prover project he started 45:44 The most technically challenging work of his career 51:10 Lean vs its competitors 01:00:37 The future of Lean 01:04:10 Technical book recommendations 01:06:15 Advice for his younger self 01:07:10 Outro
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Leonardo de Moura (Leonardo de Moura) is the creator of Lean and the Z3 theorem prover. I talked with him about how Lean works and why LLMs plus Lean will fundamentally change how we write software and do math. In this episode: • How formal verification and proof assistants work • How Lean will impact handwritten math & software • Lean’s role in recent math breakthroughs • When software is worth formalizing Where to watch: • YouTube - • Spotify - • Apple Podcasts - • Transcript - Thank you to the sponsor of this episode for supporting my work: • WorkOS: makes your app Enterprise Ready with easy to use APIs to add SSO, SCIM, RBAC, and more in just a few lines of code, check them out at Chapters: 00:00 Intro 00:28 How formal verification works 05:21 A new way of writing software 13:15 Proof assistants vs programming languages 21:06 How Lean has assisted in mathematical breakthroughs 32:03 When is it worth formalizing software 33:29 How Lean will impact handwritten math 38:55 The Z3 theorem prover project he started 45:44 The most technically challenging work of his career 51:10 Lean vs its competitors 01:00:37 The future of Lean 01:04:10 Technical book recommendations 01:06:15 Advice for his younger self 01:07:10 Outro

Ryan Peterman

13,949 次观看 • 2 个月前