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Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.

June Huh thought he had no talent for math until a chance meeting with a legendary mind. A decade later, his unorthodox approach to mathematical thinking has led to major breakthroughs.

Paul Erdős placed small bounties on hundreds of unsolved math problems. Over the past 20 years, only a handful have been claimed.

The three young friends who devised the “happy ending” problem would become some of the most influential mathematicians of the 20th century, but were never able to solve their own puzzle. Now it receives its first big breakthrough.

Juggling has advanced enormously in recent decades, thanks in part to the mathematical study of possible patterns.

Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works.

To avoid garbled messages, mathematicians might translate them into geometric form.

Equiangular lines are an elemental part of geometry. Mathematicians have discovered a tighter limit on the number of such lines that exist in every dimension.

Powerful new quantitative tools are now available to combat partisan bias in the drawing of voting districts.