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Two young mathematicians have astonished their colleagues with a full proof of the Kahn-Kalai conjecture — a sweeping statement about how structure emerges in random sets and graphs.

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near.

Lillian Pierce wants to transform access to the world of mathematics, while making headway on problems that bridge the discrete and continuous.

The American mathematician invented entire new ways to understand shapes and spaces.

Biomechanical interactions, rather than neurons, control the movements of one of the simplest animals. The discovery offers a glimpse into how animal behavior worked before neurons evolved.

A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.

Researchers have mapped hundreds of semantic categories to the tiny bits of the cortex that represent them in our thoughts and perceptions. What they discovered might change our view of memory.

Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.

Scientists thought that the brain’s hearing centers might just process speech along with other sounds. But new work suggests that speech gets some special treatment very early on.

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