Abstractions blog

Zeta values seem to connect distant geometric worlds. In a new proof, mathematicians finally explain why.

Two ways of measuring the universe’s expansion rate yield two conflicting answers. Many point to the possibility of new physics at work, but a new analysis argues that unseen errors could be to blame.

To date the branches on the evolutionary tree of life, researchers are looking at horizontal gene transfers among ancient microorganisms, which once seemed only to muddle the record.

A recent experiment shows how quantum mechanics can make heat flow from a cold body to a hot one, an apparent (though not real) violation of the second law of thermodynamics.

Paradoxically, a small galaxy that seems to contain none of the invisible stuff known as “dark matter” may help prove that it exists.

Using a brain-computer interface, scientists are beginning to learn why learning is hard.

A simple, step-by-step breakdown of two “perfect” math proofs.

For decades, researchers have commonly assumed that higher oxygen levels led to the sudden diversification of animal life 540 million years ago. But one iconoclast argues the opposite: that new animal behaviors raised oxygen levels and remade the environment.

Generations of researchers have pursued his “Langlands program,” which seeks to create a grand unified theory of mathematics.