Pavel

1. Yes, we can use Lean toautomatically verify some (though not all) math solutions 2. The complexity comes from the many layers of abstraction and concepts needed to understand these problems and proofs. The jump from 2+2=4 to linear algebra and calculus is smaller than the jump from linear algebra and calculus to this.

@baltabaev Can you explain, for someone who's bad at math, what makes verification so difficult? Like, can't you just write a deterministic algorithm that will just calculate whether it's true or false?

I’ve spent well over 10,000 hours studying math in my life, yet I can’t understand these proofs, at least not without weeks of digging deep into each topic. What’s more, none of my math PhD friends know much about these problems either, and they can’t verify most of them without working directly in the field (yes, math is VERY diverse). LLMs are getting smarter than the experts themselves, and I’m not sure we have enough bright human minds to verify everything that will come out of them in the coming years. Remember when we compared AI intelligence to PhD students? I think we’re past that.

@bigmrrobert In math some solutions can be expressed in a formal language (Lean) and automatically verified which helps to avoid the need of human verification but otherwise these problems level of expertise required is increasing dramatically

@bigmrrobert There are people who can validate it in reasonable time but these experts are very few. Probably hundreds globally for most of these problems. Random math PhD won’t be able to tell within 1-2 hours because they work in a different domain.

@SlavaOPs Don’t get me wrong, I don’t question these results. Lean is super helpful but my understanding that not all problems/solutions can be converted to Lean. And then how we do it beyond Math.

The irony: Astra's proofs are actually the easy case for verification — Lean certificates make them machine-checkable, binary pass/fail. Compare that to verifying an AI agent's actions in production: no formal certificate, no clean proof object, just logs and hope. If we can't keep up with verified math, we're nowhere close to verifying unverified agent behavior at scale. TRIGGER→DO→VERIFY→STOP isn't optional anymore, it's the only thing standing between you and finding out the hard way.

I asked Fable to rank each problem from 1 (high school) to 10 (Fields medal) level and it graded all of them between 9 and 10.

We had 2 quarters of financial markets penalizing companies for data center Capex and over indexing on short-term FCF. Based on MAG7 reports in the last 24 hours, I think it’s shifting.

@AndrewCurran_ Gpt-5.6 Sol was the best OAI release in the last year and it shows

In an internal meeting today, OpenAI CFO Sarah Friar told employees that OpenAI's ARR in July exceeded the entire second quarter of 2026.

@pitdesi Funny enough, we almost hit our friend’s Tesla at a very similar spot in SF using FSD. The worst part that it tried to park in a stranger’s garage vs. road.

found out the hard way that FSD is bad at parking

@Noahpinion This is satire / fake

When Israeli right-wingers say stuff like what this Russian oligarch is saying, progressives take it as evidence of Israeli genocide.

Remember OpenClaw?

@MollySOShea @friedberg @RoKhanna Can't agree more with David on the tax policy

David @friedberg explains the rise of socialism and the hypocrisy of @RoKhanna: "It's a lot easier to claim an enemy and get elected, than it is to fix a difficult policy problem." "Ro Khanna is the perfect example of this." "This is some dude who has a $300M net worth. His children have memberships at 3 country clubs." "The dude lives in a $10M house in Washington, DC." "And he used to be the moderate Silicon Valley guy who would go around to all the tech CEOs and founders and VCs and be like, 'Give me your money. I'm a moderate. We're going to make the Democratic Party work for you.'" "Then he saw the tides change, and he's like, 'Oh, this is yum, yum. I'm going to run for president in 2028.'" "Just to be clear on this, he is so unlikable, I think he'll likely end up being Secretary of Housing and Urban Development if AOC is elected president." "I do not disagree with him or Gavin or anyone else that tax policy in America is fucked up." "When billionaires borrow against their unrealized capital gains, they should pay capital gains tax. Capital gains tax should be 40%, not 15% or 18% or 20%. In fact, labor should pay less. Income tax should be much lower. Capital gains should be much higher. That would be a fair tax policy." "I don't know a lot of people who are wealthy who will look me in the eye and truly disagree with that." "It's a lot of bullshit when we all say, 'It incentivizes investment.' Great, it incentivizes investment. What are you going to do with your excess capital if the tax rate is 40% versus 20%? You're not gonna invest it now? Of course you're going to fucking invest it." "But instead of those practical solutions like I just laid out, they're all like, 'Let's go fire up the fucking socialist train because it's worked so well in fucking Cuba and Venezuela and the Soviet Union and all these other places.'" "What both parties are missing is a policy agenda that says: Here's the shit we have to do to keep America from going down the socialist death spiral. And they all should be fucking doing it, both sides."

@DmitryRybin1 The “think macrohard make no mistakes” meme went out of control with this one. Amazing.

Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years. The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60. Chat with GPT 5.6 Pro where this was found: chatgpt.com/share/6a60b2eb…

Good point from a locked account: Prepare for VCs to be increasingly loud about the importance of open source + right for US companies to distill models This is because a world where most AI value accrues to the frontier labs makes the VC job difficult, if not impossible

Regardless of what kind of prompt chain and tool usage led to this discovery, it’s very impressive for an LLM to discover such counterexample given it’s not something you can grid search. I feel like we’re experiencing another major Leap in AI intelligence with Fable / Sol 5.6 / Kimi K3 after Opus 4.5 release last year.

@TheLaikYobaz @nikitabier please stop people from uploading images as videos to farm likes

İspanya Başbakanı Pedro Sánchez ve ABD Başkanı Donald Trump final maçında bir araya geldi. Bunların arası kötü değil miydi?

@stevehou True! There are years of agentic build and adoption to come to reach true potential.

Unpopular opinion: AI basically became useful for enterprise use early this year with agentic AI acceleration. Everything before was basically consumer and hobbyist. 2026 is year 0 for AI enterprise use. So why would anyone have expected measurable productivity increase already.

@alex STEM PhD*

Insta green cards for any phd would be insanely powerful

@hollyoxcoburn @SenSanders Not saying it's solving anything, but this is the worst tax alternative out there, and here's my argument. A wealth tax is simply a populist move: the goal isn't to fund social programs, it's to make people feel "justice," fueled by jealousy.

@baltabaev @SenSanders How is confiscating others' earned income solving any issue? When is the arbitrary taxation enough? What has govt managed well? Please name just one sector, sir.

Sergey Brin is worth $276 billion. He could save healthcare for 3 million people. Instead, he’s spending $82 million against California’s 5% billionaire wealth tax. He’d rather see low-income Americans die & suffer than pay his fair share of taxes. That is a moral obscenity.