Will Sawin

most citedThe sum-product conjecture is false for real numbers

1 citations · 3 across the 4 of their papers we have counts for

collaborators

6 papers

math.NT2026

Sets of unit fractions without two members whose average is a unit fraction

Will Sawin

We show that there is a constant $c > 0$ such that, for all sufficiently large $N$ , there is a subset $A \subseteq {1, \dots, N}$ of size $> c N$ such that for any two distinct element…

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 $A \subset R$ (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 ErdÅs unit distance conjecture, and a sequence of reflections on it. The…

math.CO2026★ 1 cited

An explicit lower bound for the unit distance problem

Will Sawin

We show that there are sets of $n$ points in the plane with $n$ arbitrarily large that contain more than $n^{1.014}$ pairs of points separated by a distance exactly $1$ . This impro…

math.NT2025

Random Diophantine equations of large degree

Tim Browning, Will Sawin

Among the set of hypersurfaces of degree $d$ and dimension $ℓ$ defined by the vanishing of a homogeneous polynomial with coefficients $\pm 1$ , we investigate the probability tha…

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 $n \times n$ matrices with integer entries in $[- T, T]$ , as $T \to \infty$ . Our work uses Fourier analysis and lead…