Dan B

[Kenny Daniel @platypii]

New lowest bound proved in lean: κ = 2^-19.2693 thanks to huge improvement by @jdb1729

[Dan B @jdb1729]

@platypii Kenny and I also formalized the same log-exponent for DFT over prime-order finite fields. https://t.co/IPug3EYLZd

[Dan B @jdb1729]

@platypii Kenny and I also formalized the same log-exponent for DFT over prime-order finite fields. https://t.co/IPug3EYLZd

[Dan B @jdb1729]

@_mctrinh w

[Dan B @jdb1729]

@Iluvalar1 @platypii @OpenAI Yeah, it's a valid concern that it might cheat at Lean! At least, we can read the theorem and definitions to check that the right thing is being proved, and we can believe that the bugs in Lean will eventually be discovered and fixed (and buggy proofs will no longer verify).

[Dan B @jdb1729]

@Iluvalar1 @platypii @OpenAI You're conflating two different constants, there's the rapidly improving exponent of the logarithm, but also the effective multiplicative constant that the big-oh notation hides (what makes it impractical). The old Harvey van der Hoeven also has this issue.

[Dan B @jdb1729]

@Iluvalar1 @platypii @OpenAI Worse, the Russian peasant method would beat it on a whole universe full of bits. I won't say the actual numbers because they're ghastly. It makes one question the sanctity of multi-tape TMs as a standard model of computation. But, it's not a physically realistic model anyway!

[Dan B @jdb1729]

@Iluvalar1 @platypii @OpenAI It isn't quite the right question to ask since the asymptotic time remains the same when small cases are handled differently. Which is the case with the specific proved TM2 machine, it computes 2*3=6 in exactly 23 steps. However, the asymptotic constant is enormous!

[Kenny Daniel @platypii]

@jdb1729 @OpenAI @0xdoug This result immediately interested me because n log n just looks like it should be the limit.

Integer multiplication was first proven to be possible in O(n log n) time only recently in March 2019, by David Harvey and Joris van der Hoeven

[Kenny Daniel @platypii]

6 days later and with huge help from @jdb1729 it looks like we proved in Lean the integer multiplication sub-n log n result from @OpenAI!

[Dan B @jdb1729]

@BlokdAndDefrend @RohanArun @grok 100%! The lower-bound on integer multiplication is O(n) = O(n * log(n)^0), since at the very least we have to read the numbers being multiplied. So the lim inf of the log exponent is a well-defined quantity.

[Dan B @jdb1729]

@mathNTb Yesterday I also made a proof of the irrationality exponent of logarithms of rationals: https://t.co/RvmO0cKsw6 Lean-verified: https://t.co/vVfwJBWviR

[Dan B @jdb1729]

@PQBW I also made a proof of this yesterday: https://t.co/RvmO0cL0lE Lean-verified: https://t.co/vVfwJBX38p

[Dan B @jdb1729]

The reciprocal sum of the prime-prefix-free integers converges under the Riemann Hypothesis https://t.co/9ecL8dQB5s

[Dan B @jdb1729]

now formally verified in lean! https://t.co/EZnINIPeR1

[Dan B @jdb1729]

sup tweeters guess what carmichael numbers can be found in quasipolylogarithmic time https://t.co/Sg2wxRL1GT

[𝐃𝐦𝐢𝐭𝐫𝐲 - biofoundationalism.com @BackTheBunny]

you need to be bull maxxxing. the bear is over. the evil meth nerd has been defeated. patriots in control. you need to be celebrating this triumph by putting on leverage longs with size. big up-only energy. the polycule has been destroyed. you need to be bull maxxxing

[Dan B @jdb1729]

@Jason Liking this vibe, now when 1999