OpenAI's GPT-6 Astra Solves Two Genuinely Unsolved Erdős Problems

For over a year, Epoch AI's FrontierMath benchmark was the industry's hardest yardstick for AI mathematical reasoning. Its top tier, launched in mid-2025, was designed to resist solution for years. Instead, frontier models tore through it: AlphaSignal reported that GPT-6 Astra hit 98% on FrontierMath Tier 4 in September 2026, closing out the final holdout problem — one authored by combinatorialist Jay Pantone — in roughly fourteen months. Every problem on that tier had a known answer, which meant saturation was as much a statement about benchmark design as about intelligence: once a correct answer exists anywhere, a model only has to find it, not discover it.

Epoch's response, announced September 1, was to remove the safety net entirely. FrontierMath Erdős, built with mathematician Thomas Bloom, selects 68 problems from a pool of 652 still-open Erdős conjectures — problems with no known solution to leak into training data. Each is formalized in the Lean proof assistant, and a model gets a $300 compute budget and a 72-hour window per attempt to actually prove or disprove one, not just guess a number.

The results, as reported by Epoch AI and independently covered by the-decoder.com and AlphaSignal, were narrow. Of five models tested under the formal rules — GPT-6 Astra (pre-release), GPT-5.6 Sol, GPT-5.5, Claude Fable 5.1, and Claude Fable 5 — only Astra solved anything at all, closing 2 of 68 problems, a 3% clearance rate. In looser follow-up runs with bigger budgets, Epoch let Astra keep trying; it eventually reached 5 solved problems, but at a combined compute cost north of $220,000, an average approaching $50,000 per additional proof once the easy formal wins are set aside.

"No doubt every mathematician will see some problems on this list and think 'why on earth did they include that?'" — Thomas Bloom, mathematician and curator of FrontierMath Erdős

The two data points don't tell the same story on their own. The-decoder's reporting includes a quote from OpenAI chief scientist Jakub Pachocki explaining that the company isn't chasing math specifically: it is prioritizing recursive self-improvement and automated alignment research instead, treating Astra's math gains as a byproduct. That reading is reinforced by Astra's drop on Humanity's Last Exam, where AlphaSignal reported it scored 57.2% versus its predecessor's 65.0% — a model can get dramatically better at formal proof search while getting worse at general reasoning in the same release.

What FrontierMath Erdős actually demonstrates is narrower and more useful than "AI does new math": a frontier model, using enormous compute, can now nudge open problems that have resisted human mathematicians for decades, some of which it also had to formalize before attempting. That is a real result. But a 3% clearance rate at $300 a shot, ballooning past $200,000 for marginal extra solves, and zero success from four other frontier-class models is also a clear signal that the industry's next math benchmark bottleneck isn't reasoning depth — it's cost and reliability at the edge of genuine discovery, which is exactly the gap Epoch says it will spend the next round of evaluation tracking.