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A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.

A founder of modern geometric analysis who produced “some of the most dramatic advances in mathematics in the last 40 years,” Uhlenbeck is the first woman to be awarded this top honor.

In mathematics, where proofs are everything, evidence is important too. But evidence is only as good as the model, and modeling can be dangerous business. So how much evidence is enough?

A pair of mathematicians has built on an obscure, 30-year-old mathematical theory to show that soap-filmlike minimal surfaces appear abundantly in a wide range of shapes.

A two-player game can reveal whether the universe has an infinite amount of complexity.

A new proof shows why an uncountably infinite number of Möbius strips will never fit into a three-dimensional space.

Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems.

A graduate student has helped illuminate a long-suspected connection between addition and multiplication.

Neural networks can be as unpredictable as they are powerful. Now mathematicians are beginning to reveal how a neural network’s form will influence its function.