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Renormalization has become perhaps the single most important advance in theoretical physics in 50 years.

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.

Cosmologists have concluded that the universe doesn’t appear to clump as much as it should. Could both of cosmology’s big puzzles share a single fix?

Three mathematicians have resolved a fundamental question about straight paths on the 12-sided Platonic solid.

A powerful technique called SAT solving could work on the notorious Collatz conjecture. But it’s a long shot.

Studies suggest that self-disseminating vaccines could prevent the “spillover” of animal viruses into humans as pandemic diseases.

Physicists have identified an algebraic structure underlying the messy mathematics of particle collisions. Some hope it will lead to a more elegant theory of the natural world.

Emperor penguins display rigorously geometric spacing and mathematical efficiency when they huddle together for warmth, which may reveal secrets to their overall health.

An 18th-century physicist first predicted the existence of a chorus of atmospheric waves that swoop around Earth. Scientists have finally found them.

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