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A new proof establishes the boundary at which a shape becomes so corrugated, it can be crushed.

Playing with numbers can lead to deep mathematical and scientific insights.

Jordan Ellenberg enjoys studying — and writing about — the mathematics underlying everyday phenomena.

Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.

A mathematical shortcut for analyzing black hole collisions works even in cases where it shouldn’t. As astronomers use it to search for new classes of hidden black holes, others wonder: Why?

Originally devised as a rigorous means of counting holes, homology provides a scaffolding for mathematical ideas, allowing for a new way to analyze the shapes within data.

Math teachers have stymied students for hundreds of years by sticking goats in strangely shaped fields. Learn why one grazing goat problem has stumped mathematicians for more than a century.

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.