Hilbert's fully-booked hotel always finds room for one more
David Hilbert's 1924 thought experiment of a hotel with infinite rooms shows how infinity breaks the ordinary rules of counting.
category archive
Mathematics.
Patterns, puzzles and the precision of a well-formed question.
The gap in Andrew Wiles's proof of Fermat's Last Theorem
Wiles worked in secret for seven years, then a reviewer found a flaw. Quanta and Nautilus trace how he got round a 350-year-old problem, and nearly lost it.
Madhava's circle value missed by two, and no one knows why
A paper tests the series credited to Madhava of Sangamagrama and cannot explain his circle value. Almost nothing about his life is certain.
Buffon showed that falling needles could estimate pi
Georges-Louis Leclerc, Comte de Buffon, worked out in 1777 that a needle tossed onto lined paper could estimate pi through chance alone.
Andrew Wiles proved Fermat's Last Theorem after 358 years
Andrew Wiles proved Fermat's Last Theorem in 1995, working in secret for years and closing a gap that turned up during peer review.
A Dublin team's computer search proved Sudoku's 17-clue floor
In 2012, a University College Dublin team's exhaustive computer search proved no 16-clue Sudoku grid has a single, unique solution.
The geometry lecture that waited 61 years for Einstein
Bernhard Riemann's 1854 lecture on curved space sat mostly ignored for decades before Albert Einstein built general relativity on its ideas in 1915.
Alonzo Church's lambda calculus: computation without a machine
In 1936, Alonzo Church tied effective calculation to his lambda calculus. Alan Turing's work reached the same result on a related problem.
Galton's ox: a crowd's average guess landed within one per cent
At a 1906 Plymouth livestock show, 787 people guessed an ox's weight. Most were wrong, yet their average landed within one per cent of the truth.
Goldbach's 1742 claim about primes still has no proof
In 1742, Christian Goldbach told Euler that every even number over 2 is the sum of two primes. Nobody has proved it since.
Four under-40 mathematicians took the 2026 Fields Medals
Yu Deng, John Pardon, Jacob Tsimerman and Hong Wang won the 2026 Fields Medals, a prize for work done and for the promise of more.