Thomas Bloom
Royal Society University Research Fellow, University of Manchester; runs erdosproblems.com · as of 2026-10-04 · source
Maintains erdosproblems.com, the reference for checking AI claims about Erdős problems.
News mentioning Thomas Bloom (5)
- OpenAI says an internal model resolved 100+ long-standing open problems in 24 days of training; no list released ★★★
On 21 Sep 2026 OpenAI said an unnamed internal model had resolved more than 100 long-standing open problems during about 24 days of training (28 Aug – 21 Sep). It released no list and no proofs, and did not define 'resolved'. It also formed a 9-member Advisory Group on Mathematics and AI at IAS…
- GPT-6 Astra proves the Erdős–Sós conjecture (1962) with a short counting argument; mathematicians race to simplify and extend it ★★★★★
In Epoch AI's FrontierMath Erdős runs, a pre-release GPT-6 Astra autonomously proved the Erdős–Sós conjecture (Erdős problem #548): every graph with average degree greater than k−2 contains every tree on k vertices. The proof is Lean-verified. Its short, elementary argument counts vertex…
- Pre-release GPT-6 Astra disproves Erdős's 'first serious problem' (1931, $500) and proves the rational-exponents conjecture, all Lean-verified, in Epoch's FrontierMath Erdős runs ★★★★★
In Epoch AI's FrontierMath Erdős runs (announced 3 Sep 2026), a pre-release GPT-6 Astra autonomously resolved five of 68 hand-picked open Erdős problems with Lean-checked proofs. They include a disproof of Erdős problem #1 on distinct subset sums, which Erdős dated to 1931 and called 'perhaps my…
- GPT-5.6 improves the Erdős–Rankin / Ford–Green–Konyagin–Maynard–Tao bound for large prime gaps ★★★★
On 26 Aug 2026 the user "DottedCalculator" posted to erdosproblems.com (problem #4) a proof, generated with GPT-5.6, that there are infinitely many prime gaps larger than C·log n·log log n / log log log log n. This removes a log log log n factor from the 2018 Ford–Green–Konyagin–Maynard–Tao bound…
- OpenAI researchers claim GPT-5 'solved' 10 Erdős problems; the solutions were already in the literature ★★★
In mid-October 2025 OpenAI's Kevin Weil tweeted that GPT-5 'found solutions to 10 (!) previously unsolved Erdős problems'. Thomas Bloom, who runs erdosproblems.com, called this 'a dramatic misrepresentation': GPT-5 had found existing papers solving problems listed as open only because he did not…
Posts (1)
- Thomas Bloom: A big day for AI and mathematics — FrontierMath Erdős original ↗ Thomas Bloom @thomasfbloom · x · 2026-09-03
The erdosproblems.com maintainer's thread on the FrontierMath Erdős benchmark he helped curate: 68 hard open Erdős problems, formalised in Lean.
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