Mathematics

Building an accurate model of Earth’s climate requires a lot of data. Photography reveals the extreme efforts scientists have undertaken to measure gases, glaciers, clouds and more.

Tipping points in our climate predictions are both wildly dramatic and wildly uncertain. Can mathematicians make them useful?

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.

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.

The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation.

For decades, mathematicians have struggled to understand matrices that reflect both order and randomness, like those that model semiconductors. A new method could change that.

After finding the homeschooling life confining, the teen petitioned her way into a graduate class at Berkeley, where she ended up disproving a 40-year-old conjecture.

Fan Chung, who has an Erdős number of 1, discusses the importance of connection — both human and mathematical.

A team of mathematicians based in Vienna is developing tools to extend the scope of general relativity.