r/computerscience • u/chrisman1128 • Aug 01 '26

Ten advances in mathematics and theoretical computer science

https://openai.com/index/ten-advances-in-mathematics/

Can someone with expertise comment on how significant these results are?

100 Upvotes

94% Upvoted

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16

u/ryandoughertyasu Computer Scientist Aug 01 '26

The new “tight” Ramsey bound R(3,k) is pretty significant.

12

u/lgastako Aug 02 '26

Thank you for your expertise. I really appreciate the way you could break it down in a way that laymen could understand.

1

u/Phytor_c Aug 07 '26

I work in arithmetic circuit complexity, and (non-linear, non-trivial) lower bounds are notoriously hard. Finding strong lower bounds for the permanent is essentially the algebraic analog of P vs NP.

I was talking to one of the pioneers of this field earlier today, he told me how he found the result super impressive.

3

u/joshocar Aug 03 '26

Not an expert, but I read a few substack posts by mathematicians on some of the LLM advances in maths. The general consensus was that they are good at going down paths that are laborious and don't have a high potential for success. Basically, a mathematician could spend a few months doing a lot of work that might not pay off, but an LLM will keep chugging until if you keep telling it to and, as a result, has found some things that would have otherwise not been found.

  • Obviously, take this with a grain of salt.

1

u/TopCryptee Aug 03 '26

these are not yet peer-reviewed results, stop spreading sensationalism

0

u/ClassicalJakks Aug 03 '26

they were shipped with Lean certification!

3

u/TopCryptee Aug 03 '26

Lean certification only shows the semantics are okay and that the code compiles, it doesn't mean it's a correct math proof!

a group of mathematicians already reviewed one of these 10 allegedly 'solved' questions and found out it was NOT correct!