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

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

For the first time, physicists have calculated exactly what kind of singularity lies at the center of a realistic black hole.

Since the 1970s, physicists have described black holes using borrowed versions of the laws of thermodynamics. But are black holes really thermodynamic systems? Craig Callender worries that the analogy has been stretched too far.

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 have disproved the strong cosmic censorship conjecture. Their work answers one of the most important questions in the study of general relativity and changes the way we think about space-time.

Gravitational waves have opened up new ways to test the properties of black holes — and Einstein’s theory of gravity along with them.

By 1913, Albert Einstein had nearly completed general relativity. But a simple mistake set him on a tortured, two-year reconsideration of his theory. Today, mathematicians still grapple with the issues he confronted.

Two teams of researchers have made significant progress toward proving the black hole stability conjecture, a critical mathematical test of Einstein’s theory of general relativity.

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