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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.

To begin to understand what mathematicians and physicists see in the abstract structures of symmetries, let’s start with a familiar shape.

After her untimely death, Maryam Mirzakhani’s life is best remembered through her work.

In order to fully understand the quantum world, we may have to develop a new realm of mathematics.

A new class of quantum particle is about to emerge from the tangled considerations of quantum statistics.

The author shows how new mathematical techniques can be used to revitalize a 650-year-old work of art.

Richard Feynman’s famous diagrams weren’t just a way to do calculations. They represented a deep shift in thinking about how the universe is put together.

How quantum entanglement connects with the “many worlds” of quantum theory.

The Go-playing program teaches itself to replicate something very much like human intuition, an advance that promises far-reaching consequences.