Two mathematicians have proven Patterson’s conjecture, which was designed to explain a strange pattern in sums involving prime numbers.

Self-supervised learning allows a neural network to figure out for itself what matters. The process might be what makes our own brains so successful.

Quantum field theory may be the most successful scientific theory of all time, but there’s reason to think it’s missing something. Steven Strogatz speaks with theoretical physicist David Tong about this enigmatic theory.

Ever since Archimedes, mathematicians have been fascinated by equations that involve a difference between squares. Now two mathematicians have proven how often these equations have solutions, concluding a decades-old quest.

The key to understanding the origin and fate of the universe may be a more complete understanding of the vacuum.

The biochemist Nick Lane thinks life first evolved in hydrothermal vents where precursors of metabolism appeared before genetic information. His ideas could lead us to think differently about aging and cancer.

The solutions to Einstein’s equations that describe a spinning black hole won’t blow up, even when poked or prodded.

Partnerships between engineers and biologists have begun to reveal how birds evolved their superb maneuverability.

Christopher Kanan is building algorithms that can continuously learn over time — the way we do.