Mathematics

Researchers are discovering the shortest knots and fattest Möbius strips, among other “optimal shapes.”

Throughout her 60-year career, Lenore Blum has developed new perspectives on logic and computation while championing women in mathematics and computer science. Now consciousness is on her mind.

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

Just as ice melts to water, graphs undergo phase transitions. Two mathematicians showed that they can pinpoint such transitions by examining only local structure.

The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century.

A team of four prominent mathematicians, including two Fields medalists, proved a conjecture described as a “holy grail of additive combinatorics.”

Researchers prove that navigating certain systems of vectors is among the most complex computational problems.

Mathematicians prove a theorem that illuminates the geometry of universes with tiny amounts of mass.

How Fermat’s less famous "little theorem" got mathematicians young and old to play with prime-like Carmichael numbers.