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Jared Duker Lichtman, 26, has proved a longstanding conjecture relating prime numbers to a broad class of “primitive” sets. To his adviser, it came as a “complete shock.”

Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions for old problems.

Four puzzle solutions reveal different ways to divine someone’s hidden number with impossibly little information.

A bit of information theory can help you analyze — and improve — your Wordle game.

“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.

Mathematical magic can seem like mind reading. Your job is to reveal the secret behind these four tricks.

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

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.