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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.

Tadashi Tokieda discovers new physical phenomena by looking at the everyday world with the eyes of a child.

On November 16, 2018, more than 200 readers joined writers and editors from *Quanta Magazine* for a wide-ranging panel discussion that examined the newest ideas in fundamental physics, biology and mathematics research.

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

Puzzle solvers explored how evolution may have used negative and positive control mechanisms to shape the conflicting parental functions of reproduction and child rearing.

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

A new proof from the Australian science fiction writer Greg Egan and a 2011 proof anonymously posted online are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.

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?