An OpenAI model proves that non-sofic groups exist

linzhangrun1 pts0 comments

Sebastien Bubeck on X: "yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model.

We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more.

More thoughts here: https://t.co/8SjXONeh38" / X<br>Post

Log inSign up

Post

Sebastien Bubeck

@SebastienBubeck

yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model.

We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more.

More thoughts here: openai.com/index/ten-adva…<br>Ten advances in mathematics and theoretical computer science

From openai.com

span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0">7:34 AM · Aug 1, 2026254.3KViews

52<br>278<br>1.6K<br>445

span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0 min-w-0 overflow-hidden">James

@Darpinian

1h

195<br>svg]:size-5 text-body hover:bg-mix-current hover:bg-mix-amount-10 active:bg-mix-current active:bg-mix-amount-15 focus-visible:bg-mix-current focus-visible:bg-mix-amount-10 outline-current -m-2 shrink-0 cursor-pointer border-transparent p-0 text-body size-9 [&>svg]:size-[1.25em] [&>[data-engagement-icon]]:size-[1.25em] group-hover:bg-mix-current group-hover:bg-mix-amount-10" aria-label="View count" type="button" data-state="closed" href="/Darpinian/status/2083471575895179549/quotes">6.3K

span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0 min-w-0 overflow-hidden">Ananjan Nandi

@AnanjanN

1h

Crazy how all of this was started by one guy bullying his Claude during the World Cup final.

GIF

48<br>svg]:size-5 text-body hover:bg-mix-current hover:bg-mix-amount-10 active:bg-mix-current active:bg-mix-amount-15 focus-visible:bg-mix-current focus-visible:bg-mix-amount-10 outline-current -m-2 shrink-0 cursor-pointer border-transparent p-0 text-body size-9 [&>svg]:size-[1.25em] [&>[data-engagement-icon]]:size-[1.25em] group-hover:bg-mix-current group-hover:bg-mix-amount-10" aria-label="View count" type="button" data-state="closed" href="/AnanjanN/status/2083469591733485746/quotes">4.8K

span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0 min-w-0 overflow-hidden">MΛX V꩜X (Max Vox)

@DukeZer0

2h

very excited to meet a model that is smart enough to explain to me what i am doing with this, because i have no idea

22<br>svg]:size-5 text-body hover:bg-mix-current hover:bg-mix-amount-10 active:bg-mix-current active:bg-mix-amount-15 focus-visible:bg-mix-current focus-visible:bg-mix-amount-10 outline-current -m-2 shrink-0 cursor-pointer border-transparent p-0 text-body size-9 [&>svg]:size-[1.25em] [&>[data-engagement-icon]]:size-[1.25em] group-hover:bg-mix-current group-hover:bg-mix-amount-10" aria-label="View count" type="button" data-state="closed" href="/DukeZer0/status/2083458248397795829/quotes">6.4K

Log in or sign up for X<br>See what’s happening and join the conversation<br>Continue with phoneContinue with AppleContinue with Google<br>or<br>Log in with username or email

Relevant people

Sebastien Bubeck@SebastienBubeckFollow<br>I work on AI at OpenAI. Former VP AI and Distinguished Scientist at Microsoft.

Trending now

span empty current before size hover

Related Articles