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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?

As chemists tie the most complicated molecular knot yet, biophysicists create a “periodic table” that describes what kinds of knots are possible.

Odd enough to potentially model the strangeness of the physical world, complex numbers with “imaginary” components are rooted in the familiar.

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

Two dynamic, seemingly opposing forces likely played an important role in the evolution of reproduction and child rearing in social animals like bees and humans.

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