Mathematics

The solution to our puzzle about Euler’s number explains why e pops up in situations that involve optimality.

By carefully constructing a multidimensional and well-connected graph, a team of researchers has finally created a long-sought locally testable code that can immediately betray whether it’s been corrupted.

The Chinese remainder theorem is an ancient and powerful extension of the simple math of least common multiples.

Ana Caraiani seeks to unify mathematics through her work on the ambitious Langlands program.

In nonreciprocal systems, where Newton’s third law falls apart, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.

New work establishes a tighter connection between the rank of a polynomial and the extent to which it favors particular outputs.

Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits.

The transcendental number π is as familiar as it is ubiquitous, but how does Euler’s number e transcend the ordinary?

Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.