Mathematics8 Aug 2026What makes a proof explanatoryTwo proofs of the same theorem can differ enormously in how much they tell you. Mathematicians have argued about why for a century, and the answer turns out to matter for how we teach machines.Editorial11 min read
Mathematics18 Jul 2026Counting without listingCombinatorics is the art of knowing how many things there are without producing them. Four rules do almost all of the work, and the fourth is the one people get wrong.Editorial9 min read
Mathematics12 Jul 2026Induction is recursion, read backwardsEvery recursive function you have written is a proof by induction you did not know you were writing. Seeing the correspondence makes both halves easier.Editorial8 min read
Mathematics6 Jul 2026Graphs are the default shape of everythingTrees, orders, dependencies, state machines and schedules are all graphs wearing different vocabularies. Learning the general object once beats learning five special cases.Editorial10 min read