25 citations · 27 across the 5 of their papers we have counts for
5 papers
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…
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 $…
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…
Odd moments and adding fractions
Thomas F. Bloom, Vivian Kuperberg
We prove near-optimal upper bounds for the odd moments of the distribution of coprime residues in short intervals, confirming a conjecture of Montgomery and Vaughan. As an applicat…
Translation invariant equations and the method of Sanders
Thomas Bloom
We extend the recent improvement of Roth's theorem on three term arithmetic progressions by Sanders to obtain similar results for the problem of locating non-trivial solutions to t…