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The Jungle of Mathematical Knowledge


Mathematics as a branch of human knowledge is several millenia old, and though each individual mathematician's historical contribution to this branch of knowledge may be small, the resulting edifice is grand indeed. It long ago ceased to be possible for a single mathematician to even know the basic definitions of every subfield of mathematical knowledge. We have reached the point of decay in some areas. Richard Askey has observed that Gregory Chudnovsky knows things about hypergeometric functions that no one has understood since Riemann and that, with Chudnovsky's eventual passing, no one is likely to understand again. The forest of mathematical knowledge, organized into specialties and sub-specialties and sub-sub-specialties, none of which even use the same notation for similar ideas, has become a vast jungle. The obvious success of mathematics makes this problem worse in a sense. New mathematical papers are being published every day, in journals almost too numerous to count, and certainly too numerous to read. New mathematical textbooks written at an undergraduate level arrive on the scene nearly as quickly. Moreover, even were no unfamiliar jargon and notation being used, no one could possibly look through all this material to find what they wanted.

This ever increasing morass of mathematical information poses a considerable challenge for today's young mathematicians. The emerging digital and network technologies may provide some of the means for answering that challenge.