3 ms·

When high quality effort is applied to a tool, such as AES or the linux kernel, we intuit that it "hardens" the tool. That is, it makes the tool more correct, m

When high quality effort is applied to a tool, such as AES or the linux kernel, we intuit that it "hardens" the tool. That is, it makes the tool more correct, more resilient, less assailable, etc. Similarly, when effort is applied to an open problem, such as the Riemann hypothesis or P v NP, without progress, it "hardens" the problem: it makes the problem feel more daunting to whoever takes a stab at it next. Andrew Wiles, whose interview also hit the homepage today (https://news.ycombinator.com/item?id=49075264 https://news.ycombinator.com/item?id=49075264), couldn't just tackle Fermat's Last Theorem head on, he had to wait until a different, modern problem reduced to it, because FLT had gathered this mystique of unassailability through its 300 years of existence. A thing I worry about is that as AI transmutes tokens into effort, it'll split the world into two: some problems will yield, making human effort entirely unnecessary, and others will harden to the point where human effort will feel increasingly less worthwhile, because "even AI couldn't solve it". I don't like this. AI is spiky, so I suspect it'll continue having major blind spots, and yet its mere presence will probably have a chilling effect on what would have otherwise been useful human effort.

some_furry 2mo ago
I wouldn't worry about too many mathematicians adopting the "even AI couldn't solve it" attitude. Business folks riding the hype train? Maybe.
Eridrus 2mo ago
This is a problem that will solve itself, people will continue to work on the problems that AI fails at, likely by telling AI the approaches they want AI to take.
8note 2mo ago
i think id almost worry more that ai can solve problems in latent space that it cant translate back to tokens because decoding ruins it, and that we wont be able to come up with concepts that we can map to properly decode those solutions in a way people understand
- pas 2mo ago
  ... what is understanding of mathematics anyway? if some AI result helps a mathematician to solve more problems I would say then that it gave them some understanding, but just as there are proofs that span hundreds of pages it's likely that soon proofs will be long Lean programs and studying them will be part of mathematics, just as studying Go played by AI. (see the open (Lean) label for Erdos problems https://mathstodon.xyz/@tao/116987866420438091 https://mathstodon.xyz/@tao/116987866420438091)
  - QwenGlazer9000 2mo ago
    https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e... This blog post talks in depth about what you're talking about. It may interest you. It even talks about the future where math proofs are just Lean programs, and why that won't necessarily be a good thing. It's worth a read, even if it's long AF.
    - pas 2mo ago
      I have complicated feelings regarding academia, and in general IMHO it's way past due to start focusing on quality instead of hype. who was first to some kind of novelty? who cares. someone did something but no one can replicate it? intentionally wasting public money. fraud by any other name. "science" wouldn't move slower if we would build more robust data generating processes. of course, since usually it's hard to judge quality academia uses proxies. not to mention that the people who could usually are also live inside fancy glassware. and it would be a shame to rock the boat. ... but math is doubly special, because we accepted that it doesn't matter (until it does, but then it's called cryptography and logistics network optimization and high frequency trading, and machine learning), and how long a problem stays unsolved was quite a good proxy. still, if AI solves the easy ones we can finally have fun with the hard ones!
himata4113 2mo ago
AI is nowhere near the intelligence of a very educated person that has innate talent for problem solving. It does solve the problem of applying human intelligence on problems that truly need it. AI is also a great tool to see if there's something simple that we've missed or just haven't even attempted due to wrong assumptions.
- PandaRider 2mo ago
  > if there's something simple that we've missed That's exactly what current mathematicians are using AI for [1]. However, the same mathematicians also believe that pursuing a beautiful proof (even if none exists) is worth it. [1] https://spectrum.ieee.org/ai-in-mathematics https://spectrum.ieee.org/ai-in-mathematics
- pseudohadamard 2mo ago
  In this case it's not actually that big a result, it's an incremental improvement on a series of previous results. Cryptographer Orr Dunkelman describes it better than I ever could, he's one of the people who produced one of the previous results: The main result in this paper is improving the Derbez, Foque, Jean attack from EUROCRYPT 2013, which is an improvement of our attack from CRYPTO 2010, which is an improvement of the Demirci-Selcuk attack, which is the improvement of the Gilbert-Minier collision attack against 7-round attack [...] To save everybody's time, the [DFJ13] attack is on 7-round AES. The new result is also on 7-round AES, "eroding" the security margin of 7-round AES by about 8 bits of security [...] While this is the first improvement in attacking 7-round AES in the last decade, if you were not worried by the series of papers that reduced the security of 5-round AES from 2^32 to 2^16, or the somewhat improved attacks on 6-round AES, then you should not really worry now to start a procedure for changing 10-round AES (for 128-bit key) for something else, when there are no attacks on 8-round AES-128. So someone threw a clanker at a series of previous results and told it to find improvements. Since it's ingested every piece of crypto research ever and can draw on all of them instantly, it managed to tweak the previous work a bit to improve the attack slightly... on a version of AES deliberately weakened to make attacks easier, a standard procedure for any iterated crypto algorithm where you see how many rounds you can get into it before your attack stalls. So it's a bit like saying you knocked out Mike Tyson's brother's cousin's uncle's sister's nephew in four rounds instead of five.
cxseven 2mo ago
1. Some of the "AI" proofs applied existing human work from lesser-known papers. AI proofs could solve the long-standing problem in math of almost all attention concentrating on less than 1% of authors. Human effort from the other 99% would have otherwise been wasted, which AI can rescue and give credit to thanks to its superhuman ability to match patterns across reams of text. Humans may remain superior in spatial / non-verbal reasoning for a while longer yet, and, in the meanwhile, computers may aid us in collaborating to put that to use better. 2. AI-assisted, computer-verified proofs could further democratize mathematics by reducing the power of connections to get a reviewer to look at a journal submission. We can then also decouple the two tasks of a. Verifying a statement is true b. Explaining it 3. Searching for previous work and finding the edges of human knowledge are now easier. And we can leap across tedious terrain that the machine has the patience to plod through to find more interesting questions.

some_furry 2mo ago

I wouldn't worry about too many mathematicians adopting the "even AI couldn't solve it" attitude. Business folks riding the hype train? Maybe.

Eridrus 2mo ago

This is a problem that will solve itself, people will continue to work on the problems that AI fails at, likely by telling AI the approaches they want AI to take.

8note 2mo ago

i think id almost worry more that ai can solve problems in latent space that it cant translate back to tokens because decoding ruins it, and that we wont be able to come up with concepts that we can map to properly decode those solutions in a way people understand

pas 2mo ago
... what is understanding of mathematics anyway? if some AI result helps a mathematician to solve more problems I would say then that it gave them some understanding, but just as there are proofs that span hundreds of pages it's likely that soon proofs will be long Lean programs and studying them will be part of mathematics, just as studying Go played by AI. (see the open (Lean) label for Erdos problems https://mathstodon.xyz/@tao/116987866420438091 https://mathstodon.xyz/@tao/116987866420438091)
- QwenGlazer9000 2mo ago
  https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy https://davidbessis.substack.com/p/the-fall-of-the-theorem-e... This blog post talks in depth about what you're talking about. It may interest you. It even talks about the future where math proofs are just Lean programs, and why that won't necessarily be a good thing. It's worth a read, even if it's long AF.
  - pas 2mo ago
    I have complicated feelings regarding academia, and in general IMHO it's way past due to start focusing on quality instead of hype. who was first to some kind of novelty? who cares. someone did something but no one can replicate it? intentionally wasting public money. fraud by any other name. "science" wouldn't move slower if we would build more robust data generating processes. of course, since usually it's hard to judge quality academia uses proxies. not to mention that the people who could usually are also live inside fancy glassware. and it would be a shame to rock the boat. ... but math is doubly special, because we accepted that it doesn't matter (until it does, but then it's called cryptography and logistics network optimization and high frequency trading, and machine learning), and how long a problem stays unsolved was quite a good proxy. still, if AI solves the easy ones we can finally have fun with the hard ones!

himata4113 2mo ago

AI is nowhere near the intelligence of a very educated person that has innate talent for problem solving. It does solve the problem of applying human intelligence on problems that truly need it. AI is also a great tool to see if there's something simple that we've missed or just haven't even attempted due to wrong assumptions.

PandaRider 2mo ago
> if there's something simple that we've missed That's exactly what current mathematicians are using AI for [1]. However, the same mathematicians also believe that pursuing a beautiful proof (even if none exists) is worth it. [1] https://spectrum.ieee.org/ai-in-mathematics https://spectrum.ieee.org/ai-in-mathematics
pseudohadamard 2mo ago
In this case it's not actually that big a result, it's an incremental improvement on a series of previous results. Cryptographer Orr Dunkelman describes it better than I ever could, he's one of the people who produced one of the previous results: The main result in this paper is improving the Derbez, Foque, Jean attack from EUROCRYPT 2013, which is an improvement of our attack from CRYPTO 2010, which is an improvement of the Demirci-Selcuk attack, which is the improvement of the Gilbert-Minier collision attack against 7-round attack [...] To save everybody's time, the [DFJ13] attack is on 7-round AES. The new result is also on 7-round AES, "eroding" the security margin of 7-round AES by about 8 bits of security [...] While this is the first improvement in attacking 7-round AES in the last decade, if you were not worried by the series of papers that reduced the security of 5-round AES from 2^32 to 2^16, or the somewhat improved attacks on 6-round AES, then you should not really worry now to start a procedure for changing 10-round AES (for 128-bit key) for something else, when there are no attacks on 8-round AES-128. So someone threw a clanker at a series of previous results and told it to find improvements. Since it's ingested every piece of crypto research ever and can draw on all of them instantly, it managed to tweak the previous work a bit to improve the attack slightly... on a version of AES deliberately weakened to make attacks easier, a standard procedure for any iterated crypto algorithm where you see how many rounds you can get into it before your attack stalls. So it's a bit like saying you knocked out Mike Tyson's brother's cousin's uncle's sister's nephew in four rounds instead of five.

cxseven 2mo ago

1. Some of the "AI" proofs applied existing human work from lesser-known papers. AI proofs could solve the long-standing problem in math of almost all attention concentrating on less than 1% of authors. Human effort from the other 99% would have otherwise been wasted, which AI can rescue and give credit to thanks to its superhuman ability to match patterns across reams of text. Humans may remain superior in spatial / non-verbal reasoning for a while longer yet, and, in the meanwhile, computers may aid us in collaborating to put that to use better. 2. AI-assisted, computer-verified proofs could further democratize mathematics by reducing the power of connections to get a reviewer to look at a journal submission. We can then also decouple the two tasks of a. Verifying a statement is true b. Explaining it 3. Searching for previous work and finding the edges of human knowledge are now easier. And we can leap across tedious terrain that the machine has the patience to plod through to find more interesting questions.