Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.

Equations, like numbers, cannot always be split into simpler elements.

Through exacting geometric calculations, Philip Gibbs has found the smallest known cover for any possible shape.

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.

A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

A visual prank exposes an Achilles’ heel of computer vision systems: Unlike humans, they can’t do a double take.

In math, sometimes the most common things are the hardest to find.

An upstart field that simplifies complex shapes is letting mathematicians understand how those shapes depend on the space in which you visualize them.

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