This article records tradition as it has been passed down and reported. Its sources are not yet part of the atlas's verified catalogue.
Paul Erdos owned almost nothing and lived almost nowhere. He carried a suitcase between the homes of mathematicians around the world, arrived unannounced, said Let n be an integer, and started working. What he left behind was not a single great theorem but a way of doing an entire field: combinatorics, the mathematics of counting, arranging and finding order inside finite structures, had existed before him as a scattering of clever individual results. Erdos, working with whichever mathematician was in the room, turned it into a single connected conversation. He wrote more than 1,500 papers with more than 500 different coauthors, so many that mathematicians now compute their own Erdos number, the length of the shortest coauthorship chain back to him, half joke and half genuine record of how far his collaborative habit reached. Extremal graph theory, which asks how large or small a graph can be while still avoiding some structure, and the modern form of Ramsey theory, which asks how much order is forced on a large enough structure no matter how it is built, both took their working shape substantially through Erdos and the mathematicians he worked beside. He also pioneered the probabilistic method: to prove that a structure with some property must exist, show that a randomly built structure has that property with positive probability, so at least one example does, without ever constructing it by hand. It is now one of combinatorics' standard tools, used across the field for problems that resist direct construction entirely. Erdos never held a permanent academic position for long and gave away most of the money from the prizes he won, offering small cash rewards of his own for problems he could not solve himself, some of which still stand unclaimed.