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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
with Chudnovsky's eventual passing, no one is likely to understand
again. The body 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 if no unfamiliar
jargon and notation were 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.