Paul Erdős ( 1913 – 1996 )

Paul Erdős was a searcher, a searcher for mathematical truth. Paul’s place in the mathematical pantheon will be a matter of strong debate, for in that rarefied atmosphere he had a unique style. The late Ernst Straus said it best in a commemoration of Erdős’s seventieth birthday. In our century, in which mathematics is so strongly dominated by “theory constructors” he has remained the prince of problem solvers and the absolute monarch of problem posers. One of my friends—a great mathematician in his own right—complained to me that “Erdős only gives us corollaries of the great metatheorems which remain unformulated in the back of his mind.” I think there is much truth to that observation, but I don’t agree that it would have been either feasible or desirable for Erdős to stop producing corollaries and concentrate on the formulation of his metatheorems. In many ways Paul Erdős is the Euler of our times. Just as the “special” problems that Euler solved pointed the way to analytic and algebraic number theory, topology, combinatorics, function spaces, etc., so the methods and results of Erdős’s work already let us see the outline of great new disciplines, such as combinatorial and probabilistic number theory, combinatorial geometry, probabilistic and transfinite combinatorics and graph theory, as well as many more yet to arise from his ideas.