The Kakeya conjecture predicts how much room you need to point a line in every direction. In one number system after another — with one important exception — mathematicians have been proving it true.

In this paper, we prove the decidability of the theory of ℚp in the language (+, −, ·, 0, 1, Pn(n ∈ ℕ)) expanded by a predicate for the multiplicative subgroup nℤ (where n is a fixed integer). There ...

The Journal of Symbolic Logic (JSL) was founded in 1936 and it has become the leading research journal in the field. It is issued quarterly. Volume 71, being published during 2006, will consist of ...

Catalan numbers, a distinguished sequence in combinatorial mathematics, consistently emerge in a wide range of counting problems—from enumerating binary trees and Dyck paths to counting possible ...

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.” In the run-up to the presentation of the Fields ...