Renormalization

Turbulence is a notoriously difficult phenomenon to study. Mathematicians are now starting to untangle it at its smallest scales.

Renormalization has become perhaps the single most important advance in theoretical physics in 50 years.

Reductionism breaks the world into elementary building blocks. Emergence finds the simple laws that arise out of complexity. These two complementary ways of viewing the universe come together in modern theories of quantum gravity.

Artur Avila’s solutions to ubiquitous problems in chaos theory have “changed the face of the field,” earning him Brazil’s first Fields Medal.

A conversation with the mathematical physicist Freeman Dyson on quantum electrodynamics, climate change and his latest pet project.