OpenAI's unreleased AI tackles unsolved math and physics problems

A few weeks ago, OpenAI dumped more than 700 raw math papers onto the internet, leaving many researchers wondering if it was just an exercise in AI paper-churning. On October 26, the lab returned with something completely different: targeted strikes against foundational dogmas in computing, math, and physics.

OpenAI announced that its unreleased frontier models solved three long-standing problems. Crucially, the core proofs were formally verified in the Lean proof assistant before the announcement, moving well beyond vague statistical hallucinations.

Dismantling a 30-year-old computing assumption

The biggest shockwave hit theoretical computer science, where OpenAI claims its system disproved the Exponential Time Hypothesis, or ETH.

For decades, computer scientists assumed that Boolean Satisfiability (SAT) problems hit an unavoidable exponential explosion as rules and variables multiply. Hundreds of modern papers relied on ETH as an anchor to prove conditional limits on how fast algorithms could possibly run.

OpenAI's model devised a deterministic algorithm that counts solutions in subexponential time using clever algebraic translations and grouped compression. In short: ETH is false.

To check the work, OpenAI recruited Russell Impagliazzo and Ramamohan Paturi—the very researchers who formulated the hypothesis in 1999—alongside MIT's Ryan Williams. The full natural language write-up and Lean code are already public on GitHub.

Wave mechanics and the million-dollar physics problem

In pure mathematics, the model cracked the 35-year-old local smoothing conjecture for wave equations across all dimensions, using an auxiliary partial differential equation. That breakthrough automatically resolves the famous Kakeya conjecture across every dimension as well.

Over in theoretical physics, the AI provided a rigorous existence proof for four-dimensional interacting quantum field theories, including Quantum Chromodynamics (QCD) and pure Yang-Mills theory.

The Yang-Mills existence proof targets one half of the famous Clay Millennium Prize problem. OpenAI was careful to clarify that the second half—the mass gap—remains unsolved. A team led by Nobel laureate David Gross is stewarding this work, keeping raw outputs under wraps while writing their own explanatory papers.

Why it matters

We think this is the clearest sign yet that AI is transforming from an autocomplete coding partner into a genuine engine for fundamental scientific discovery. Disproving a thirty-year-old hypothesis accepted by hundreds of researchers is not regurgitation; it is creative, high-level mathematical reasoning.

Relying on Lean formalization is the smartest move OpenAI made here. By letting an automated proof checker verify every single logical deduction step, the company largely neutralized the usual skepticism around AI hallucinations.

Still, the rollout has drawn sharp pushback. OpenAI's advisory panel, AGMAI, openly criticized the practice of assigning selected academic shepherds early access, warning that it borrows prestige, invites bias, and creates information asymmetry. Science usually works best when outputs land on public preprint servers for everyone at once.

If the ETH refutation withstands broader peer scrutiny, entire textbooks in computational complexity will need a rewrite. For the broader AI industry, it shifts the benchmark of frontier reasoning from synthetic test scores to real-world mathematical breakthroughs.