Dmitry Krachun

[Dmitry Krachun @dmitrykrachun]

@msvetov Может он и глупый человек, но слов, которые вы ему приписываете, он в твите не писал

[Dmitry Krachun @dmitrykrachun]

@SebastienBubeck @AlexKontorovich Could you please clarify what exactly Alex is not correct about? I struggle to see a contradiction between what you’re saying and the original take.

[Dmitry Krachun @dmitrykrachun]

I almost accidentally coauthored a paper in cryptography! Turned out to be a lot of fun with some interesting maths.

As it happens with most of my attempts to use maths outside pure mathematics the techniques are based on Fourier analysis.

[Ariel Gabizon @rel_zeta_tech]

A new paper with Dmitry Krachun!
https://t.co/bF92RbpWzP

The basic idea: To randomly combine pedersen/KZG commitments, we usually choose λ-bit scalars for each one, and do an MSM - requiring roughly λn adds. This can be a bit better with pippenger; but in this paper we completely eliminate the multiplicative dependence between the two parameters - getting n^2+λ adds.

How do we do it?
- First encode the commitments in a code requiring few adds for encoding. Here there is much room for improvement if someone can analyze codes like RAA with O(n) adds over a large prime field.
Currently we use an RS code, with evaluation domain 1,2,..2n rather than roots of unity. The cool thing is that for this domain the encoding can be computed in n^2 adds via "forward differencing".

-Second, do λ steps of "double and random add" - at each iteration we double the current point and add a random index of the codeword. We use Fourier analysis to show if we started with a non-zero vector, the result is non-zero with high probability.

[Dmitry Krachun @dmitrykrachun]

@littmath @afg9000 Whatever the goal is, isn’t waiting a couple of years and speeding the process up by a factor of 10 makes more sense than spending time now?

[Tony Feng @tonylfeng]

Proposal: Any AI company that is earnest about "helping mathematicians" (rather than parading the intelligence of its models) should work on making a high quality AI referee service available to journals. Current peer review in mathematics is laughably slow, and accelerating that with AI would be easier and more helpful than autonomously proving the kind of random results we've seen so far, with the notable exception of the Unit Distance Conjecture.

[Dmitry Krachun @dmitrykrachun]

@GrantStenger Can’t the same heuristics be applied to argue that we don’t have any local maxima at all? Which we typically do, at the global max (unless it’s not achieved).

[Dmitry Krachun @dmitrykrachun]

@scottnarmstrong Do you expect humans to be able to contribute meaningfully to the development of maths in, say, 3 years?

Feels to me that #2 can only win short-term, and if they do, everyone loses long-term. Which is what I think will happen.

[Dmitry Krachun @dmitrykrachun]

@MoonlitMonkey69 @konstmish Are you implying that solving Erdos problems does not require “actual thinking”?

Also, figuring out what problems need solving seems like another cognitive task, not clear why AI wouldn’t surpass humans in it eventually.

[Dmitry Krachun @dmitrykrachun]

@konstmish Hmm, good for them. Can’t share their optimism but maybe that’s because I’ve been talking to way too many AI-pilled people in the Bay just recently.

[Dmitry Krachun @dmitrykrachun]

@TrushinBV Задача со звездочкой: доказать, что число не является алгебраическим

[Dmitry Krachun @dmitrykrachun]

@whynotqat Here (https://t.co/LX15fUgchK) Will Sawin explains that people had thought about number fields but mostly fixed number field & ball growing to infinity which does not improve upon the classical Z[i] construction. Thinking of smaller ball & growing field seemed technically hard

[Dmitry Krachun @dmitrykrachun]

@konstmish @zeratizerata Not sure what counts as thoughts but if we were to write down all the thoughts about Poincaré that Perelman had (e.g. make him speak out loud whenever he worked on it, then transcribe) it would be more like 5000 pages of thoughts, I bet. Possibly much less is actually required

[Dmitry Krachun @dmitrykrachun]

@apxhard @slatestarcodex @souljagoyteller Well, following this analogy, we kind of know and have discovered all integers, without ever discovering “the largest”, of course. So maybe in the same way all theorems will be discovered. (To clarify, I don’t believe they will but also I don’t find this argument convincing)

[Dmitry Krachun @dmitrykrachun]

@GregHBurnham The question is right, it's just a relatively simple one. Also, I am sure Dehn-Sydler theorem (which I guess is what you're referring to in "reformulated version") would have been proved much earlier if people cared more (e.g. if it was on the list).

[Dmitry Krachun @dmitrykrachun]

I doubt @ESYudkowsky would care much for 1.5k but perhaps just for the fun of it?

[Oleg Eterevsky @eterevsky]

Anyone can help with setting this up?

@ESYudkowsky I’ll share half of the winnings (1.5k) if you are ok to try. No obligations on your part if you try in good faith, but fail.

[Dmitry Krachun @dmitrykrachun]

@johnfrduncan Being paid for what we do?

[Dmitry Krachun @dmitrykrachun]

@davidbessis And Tier 3 problems are just much more tedious. I don’t know how they were checked for correctness but I feel like it’s just very expensive to create a single problem for a good benchmark.

[Dmitry Krachun @dmitrykrachun]

@davidbessis I think part of the issue is that FrontierMath underestimated how much effort is required to carefully check a problem of this level. Say, at the International Math Olympiad maybe 2000 person-hours of work are used to select 30 problems for the shortlist (after they are proposed)

[Dmitry Krachun @dmitrykrachun]

@konstmish @Bayesprof The perceived importance of a solved problem seems to depend quite a bit on the way it has been solved. Currently AI tend to solve problems in a way that makes them unimportant. Same with being interesting. I guess it will change as AI start being more creative, let’s see