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Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works.

To avoid garbled messages, mathematicians might translate them into geometric form.

Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.

Powerful new quantitative tools are now available to combat partisan bias in the drawing of voting districts.

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.

The French mathematician was cited “for his pivotal role in the development of the mathematical theory of wavelets.”

Top women in mathematics and physics discuss how they got to where they are — and why there aren’t more of them.

19th-century mathematicians thought the “roots of unity” were the key to solving Fermat’s Last Theorem. Then they discovered a fatal flaw.