Arithmetic geometry is a vibrant field at the intersection of number theory and algebraic geometry, focussing on the study of polynomial equations and the distribution of their rational solutions.

One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

They made some progress, re-proving the conjecture in two dimensions using different techniques—ones they hoped would be applicable to the three-dimensional case. But then they hit a wall. “At some ...

Summer Haag and Clyde Kertzer made major news in the math world while working on a summer research project Prior to the end of the 2022-2023 academic year, graduate student Summer Haag and junior ...

This is a preview. Log in through your library . Abstract The present paper explores three interrelated topics in Popper's theory of science: (1) his view of conjecture, (2) the aim of science, and (3 ...

A mathematician has solved a 30-year-old problem at the boundary between mathematics and computer science. He used an innovative, elegant proof that has his colleagues marveling at its simplicity. Hao ...

Scientists recently announced progress on an elusive problem from 1960 known as the Sunflower Conjecture. While it doesn’t involve any plant biology, it does deal with objects called “mathematical ...