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Ladies and Gentlemen:

Mathematics is the science which draws
necessary conclusions. Such was the definition
given first by my father as early as 1870. At that
day, when the new mathematics was in its infancy,
the novelty of this definition was disconcerting even
to the profoundest mathematicians; but today
nobody would propose a definition differing much
from that. The only doubt that should entertain is
whether we ought to recognize as part of
mathematics, what is certain a most important
part of the mathematicians business, the formation
of the assumptions on which his reasoning is to be based.

Some of the mathematicians who have