David S. Richeson

The discovery earlier this year of the “hat” tile marked the culmination of hundreds of years of work into tiles and their symmetries.

Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.

The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

Far from being an abstract mathematical curiosity, knot theory has driven many findings in math and beyond.

The quest to solve cubic equations led to duels, betrayals — and modern mathematics.

Dynamical systems can be chaotic and impossible to predict, but mathematicians have discovered tools to help understand them.

The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.

The relationships among the properties of flexible shapes have fascinated mathematicians for centuries.

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