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Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

The laws of physics stay the same no matter one’s perspective. Now this idea is allowing computers to detect features in curved and higher-dimensional space.

By considering simple symmetries, physicists working on the “bootstrap” can rediscover the basic form of the known forces that shape the universe.

A close look at fundamental symmetries has exposed hidden patterns in the universe. Physicists think that those same symmetries may also reveal time’s original secret.

Although Einstein’s theory of space-time seems more complicated than Newtonian physics, it greatly simplified the mathematical description of the universe.

Lurking behind Einstein’s theory of gravity and our modern understanding of particle physics is the deceptively simple idea of symmetry. But physicists are beginning to question whether focusing on symmetry is still as productive as it once was.

Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.

In a world seemingly filled with chaos, physicists have discovered new forms of synchronization and are learning how to predict and control them.

In a major mathematical achievement, a small team of researchers has proven Zimmer’s conjecture.

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