What Anthropic’s IPO Filing Reveals

Nathaniel Whittemore (0:00)

Well, it just keeps getting more exciting. The Anthropic IPO is inching ever closer, and this week we got the full S1 prospectus. Everyone has spent the last 24 hours pouring over every detail of the 400-page document, looking to see if there were any surprises coming their way. Overall, what we got is a picture of a business that completely redefines how fast a company can scale. Although ultimately, what people think of it isn't just going to be about how it's doing now, but also the commitments it's made for the next few years. We're going to get into all that and more as we look at everything important in the Anthropic S1.

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After releasing more than 100 mathematical proofs last month, OpenAI has added three new significant discoveries across mathematics, computer science, and physics. In mathematics, AI models proved a local smoothing conjecture proposed in 1991 as a general case across all dimensions. This conjecture proposes that focusing waveforms results in a single short-lift peak. Guth, Wang, and Zhang proved the conjecture in two dimensions in 2019, while Wang and Kaal proved the associated Ka-Keya conjecture in three dimensions in 2025

OpenAI's results generalizes the proof to every dimension. In computer science, OpenAI disproved the exponential time hypothesis, known in the field of complexity theory as ETH. This hypothesis is deeply related to the more well-known P versus NP problem dealing with computational complexity. It suggests that for an algorithm called 3SAT, adding variables necessarily increases time to compute exponentially. That would mean that for certain classes of problems, no computational shortcut exists. This hypothesis was assumed to be true for decades, so disproving it breaks one of the core assumptions in computational science. Finally, in physics, OpenAI is partway to an existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions. This work aims to produce a simplified version of a unified standard model, which combines gravitational forces with electromagnetism and subatomic forces. It contains a proof of the existence of pure Yang-Mills theory, which is one of the seven millennium prize problems.

The results were each found by OpenAI's internal models. And for those of us for whom that was maybe the least understandable segment on the AI Daily Brief ever, all we can do is turn to the peanut gallery to get a sense from people who are actually in these fields, which of them matter most. The short is that while each of those results is incredibly important in their field, disproving ETH drew the strongest response on X, Mathematics Professor and Fields Medalist Timothy Gowers wrote, For those who don't know, ETH is the hypothesis that 3SAT needs exponential time, very surprising and consequential that it is false. A16Z's Martin Casado commented, Wow, ETH being is a stunning result. Many remembered learning about ETH in college as a rock solid assumption they could rely on, so to see it disproved is very impactful. Practically, this means that some cryptographic algorithms may have shortcuts that are faster than brute force guessing, and that calls into question some of the key assumptions in the field. As a fun aside, I was literally about to call it a load-bearing assumption, but given how overused load-bearing is in AI right now, I went instead for the much less impressive key assumption. Weird times we're living in.

In any case, Anthropic researcher Levendalpoje noted that Anthropic had independently come to the same conclusion about ETH about two weeks ago. Mathematician and founder Konsti Woelland considered the further implications, writing, The complexity theory result is actually huge. If it survives peer reviews, this could be one of the biggest computer science breakthroughs of decades. OpenAI's Greg Brockman urged everyone to take a breath, commenting, P still probably doesn't equal NP.