3 papers
math.CO2026
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 ErdÅs unit distance conjecture, and a sequence of reflections on it. The…
math.NT2026
Beyond the square-root barrier: cubic forms of Perazzo type
Tim Browning, Ritabrata Munshi, Victor Y. Wang
We show how the circle method can be used to study rational points on a certain cubic fourfold, going beyond the square-root barrier.
math.NT2025
Pairs of commuting integer matrices
Tim Browning, Will Sawin, Victor Y. Wang
We prove upper and lower bounds on the number of pairs of commuting matrices with integer entries in , as . Our work uses Fourier analysis and lead…