History of Science and Mathematics Asked by user4281 on September 2, 2021
John von Neumann wrote the following in his essay The Mathematician:
As a mathematical discipline travels far from its empirical source,
or still more, if it is a second and third generation only indirectly
inspired by ideas coming from "reality" it is beset with very grave
dangers. It becomes more and more purely aestheticizing, more and more
purely I’art pour I’art. This need not be bad, if the field is
surrounded by correlated subjects, which still have closer empirical
connections, or if the discipline is under the influence of men with
an exceptionally well-developed taste. But there is a grave danger
that the subject will develop along the line of least resistance, that
the stream, so far from its source, will separate into a multitude of
insignificant branches, and that the discipline will become a
disorganized mass of details and complexities. In other words, at a
great distance from its empirical source, or after much "abstract"
inbreeding, a mathematical subject is in danger of degeneration. At
the inception the style is usually classical; when it shows signs of
becoming baroque, then the danger signal is up. It would be easy to
give examples, to trace specific evolutions into the baroque and the
very high baroque, but this, again, would be too technical. In any
event, whenever this stage is reached, the only remedy seems to me to
be the rejuvenating return to the source: the re-injection of more or
less directly empirical ideas. I am convinced that this was a
necessary condition to conserve the freshness and the vitality of the
subject and that this will remain equally true in the future.
So, did John von Neumann hate pure mathematics that became too abstract? In many ways, he seems to be the complete opposite of G.H Hardy.
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