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cs.CL2026
FrontierMath Erdős
Tom Adamczewski, Thomas F. Bloom
We introduce FrontierMath Erdős (FME), a benchmark of 68 Erdős problems that are open as of August 2026. To solve a task in FME, AI systems must resolve (prove or disprove) one of…
math.NT2026★ 1 cited
The sum-product conjecture is false for real numbers
Thomas F Bloom, Will Sawin, Carl Schildkraut +1
We disprove the sum-product conjecture for real numbers by constructing arbitrarily large (whose elements are algebraic integers in a number field of degree $…
math.CO2026★ 1 cited
Remarks on the disproof of the unit distance conjecture
Noga Alon, Thomas F. Bloom, W. T. Gowers +6
We present a short, digested, human-verified version of the recent OpenAI-generated counterexample to the Erdős unit distance conjecture, and a sequence of reflections on it. The a…