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Solutions to the simplest polynomial equations — called “roots of unity” — have an elegant structure that mathematicians still use to study some of math’s greatest open questions.

Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.

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.

Enter the world of perfect numbers and explore the mystery mathematicians have spent thousands of years trying to solve.

Imagine if we lived on a cube-shaped Earth. How would you find the shortest path around the world?

Struggling with math problems that can’t be solved helps us better understand the ones we can.

Despite recent progress on the notorious Collatz conjecture, we still don’t know whether a number can escape its infinite loop.

How to safely reopen offices, schools and other public spaces while keeping people six feet apart comes down to a question mathematicians have been studying for centuries.

Sizing up patternless sets is hard, so mathematicians rely on simple bounds to help answer their questions.