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Mathematicians have long grappled with the reality that some problems just don’t have solutions.

For millennia, mathematicians have wondered whether odd perfect numbers exist, establishing an extraordinary list of restrictions for the hypothetical objects in the process. Insight on this question could come from studying the next best things.

Emily Riehl is rewriting the foundations of higher category theory while also working to make mathematics more inclusive.

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

AI tools are shaping next-generation theorem provers, and with them the relationship between math and machine.

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

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.

By translating Keller’s conjecture into a computer-friendly search for a type of graph, researchers have finally resolved a problem about covering spaces with tiles.

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