mathematics
The most common word in any language is roughly twice as frequent as the second most common, three times as frequent as the third, and so on. The pattern holds across languages and centuries. Why it does is one of the deepest unsolved questions in linguistics.
mathematics
The 1990s discovery that origami is computationally hard — that determining whether a crease pattern can fold flat is NP-complete — turned a children's craft into a substrate for serious mathematics. The applications now include space telescopes, heart stents, and self-folding robots.
mathematics
Two children, one cake. The classic solution (one cuts, the other chooses) generalizes into a mathematical field with surprising depth: envy-free divisions, proportional shares, the sorrow of the indivisible item, and the 1995 Brams-Taylor algorithm that solved the four-person envy-free problem a...
mathematics
How many shuffles does it take to randomize a deck of cards? The answer turns out to be exactly seven, and the proof of it required new tools in probability theory. The story winds through magic, casinos, military cryptography, and one of the prettiest results in modern combinatorics.
mathematics
Folding a sheet of paper is, formally, a problem in computational geometry. Origami has quietly become a research mathematics subject, and its results have escaped into telescope mirrors, heart stent design, and theorems about what a single sheet of paper can be made to do.
language
Counting feels universal, but the words and grammars we count with are anything but. The shapes of number across languages reveal that arithmetic was invented many times, in many ways, by people who did not need most of it.
mathematics
When seats are allocated by population, mathematics steps in to decide who gets the leftover. The methods we choose carry hidden ideologies.
mathematics
In 1951, a young economist named Kenneth Arrow proved that no voting system can satisfy a short list of obvious-looking properties at the same time. Seven decades later, the implications are still unresolved — and they affect every group decision you participate in.
mathematics
In 1967, Benoit Mandelbrot published a paper with a strange title: 'How Long Is the Coast of Britain?' His answer was stranger still — the question has no answer, and that fact reshaped a branch of mathematics.