The elegant universe

General relativity and quantum field theory are among physics’ greatest triumphs. One describes gravity as the geometry of spacetime; the other describes matter and the remaining three fundamental forces. Both are confirmed to many decimal places, and each fails where the other cannot be ignored. Reconciling them is the deepest open problem in physics.

The Standard Model, our quantum theory of these particles and forces, leaves some of nature’s most basic patterns unexplained. Why do quarks and leptons come in three families, and why do their masses differ so widely? What is dark matter? What explains the pattern of particles and charges that cancels otherwise fatal gauge anomalies? We explore these questions through connections with condensed-matter physics and the search for a deeper framework that unites matter and gravity in a single quantum description.

Gravity brings its own puzzles, from the singularities predicted by general relativity to the dark energy associated with the universe's accelerating expansion. Black holes need gravity and quantum theory at once, and neither suffices. Their predicted evaporation appears to destroy what quantum evolution must preserve. We study what black-hole thermodynamics reveals about spacetime, and the wider relationship between information and matter—from the physical cost of erasing information to the role of quantum entanglement in the emergence of spacetime itself.

String theory and its proposed extension, M-theory, offer a possible route to a single quantum description of matter and gravity and dualities are central to this picture — two theories that look nothing alike can describe the same world. These surprising equivalences can connect strong interactions to weak ones; holography even relates a world with gravity to a lower-dimensional one without it. They raise a deeper question: could spacetime itself emerge from quantum physics? We explore these connections within exactly solvable models, where special symmetries make exact answers possible—offering rare footholds for testing ideas about nature’s underlying laws.

The search for exact solutions and hidden symmetries also opens new paths in pure mathematics. Wigner noted the unreasonable effectiveness of mathematics in physics. The reverse now holds too, and the hunt for exact solutions and hidden symmetries is driving pure mathematics, to the point where ideas from quantum theory now furnish new proofs of classical theorems in geometry. We investigate that convergence and take it as a guide: our aim is a description of nature in which the mathematics is not merely adequate but inevitable.