Paul Erdős, born this day in 1913, was a prolific and eccentric Hungarian mathematician. He was known both for his social practice of mathematics (he engaged more than 500 collaborators) and for his eccentric lifestyle. He lived out of a suitcase, and traveled the world, staying with other mathematicians, talking shop long into the night, sleeping on the living room sofa. “Property is a nuisance.” He devoted his waking hours to mathematics, even into his later years—indeed, his death came only hours after he solved a geometry problem at a conference in Warsaw.
Erdős asked questions only a mathematician could love (or understand) and proposed problems for others in the most abstract and recondite areas of math, but also in practical questions of approximation, set theory, and probability. Much of his work centered around discrete mathematics, cracking many previously unsolved problems in the field. Overall, his work leaned towards solving previously open problems, rather than developing or exploring new areas of mathematics.
Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed. He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathematicians. Erdős’s prolific output with co-authors prompted the creation of the Erdős number, a point of pride for all mathematicians of a certain age. Your Erdős number is 1 if you co-authored a paper with Erdős, 2 if you have co-authored a paper with someone whose Erdős number is 1, 3 if you co-authored a paper with someone whose Erdős number is 2, etc.
[This text was edited from his Wikipedia entry.]