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Mathematics
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What Is a Manifold?
In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation for modern geometry and physics.
First Shape Found That Can’t Pass Through Itself
After more than three centuries, a geometry problem that originated with a royal bet has been solved.
The Hidden Math of Ocean Waves Crashes Into View
The math of even the simplest ocean waves is notoriously uncooperative. A team of Italian mathematicians has made major advances toward understanding it.
Origami Patterns Solve a Major Physics Riddle
The amplituhedron, a shape at the heart of particle physics, appears to be deeply connected to the mathematics of paper folding.
New Math Revives Geometry’s Oldest Problems
Using a relatively young theory, a team of mathematicians has started to answer questions whose roots lie at the very beginning of mathematics.
A Simple Way To Measure Knots Has Come Unraveled
Two mathematicians have proved that a straightforward question — how hard is it to untie a knot? — has a complicated answer.
The Math of Catastrophe
Tipping points in our climate predictions are both wildly dramatic and wildly uncertain. Can mathematicians make them useful?
What Is the Fourier Transform?
Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, decomposes any function into its parts.
‘Ten Martini’ Proof Uses Number Theory to Explain Quantum Fractals
The proof, known to be so hard that a mathematician once offered 10 martinis to whoever could figure it out, connects quantum mechanics to infinitely intricate mathematical structures.