- "As a mathematical discipline travels far from its empirical
source, or still more, if it is a second and third generation only
indirectly inspired from ideas coming from 'reality', it is beset with
very grave dangers. It becomes more and more purely aestheticizing,
more and more purely l'art pour l'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 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 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
reinjection of more or less directly empirical ideas. I am convinced
that this is a necessary condition to conserve the freshness and the
vitality of the subject, and that this will remain so in the future."
- John von Neumann (from The Mathematician)
How to Make a Linguistic Theory
More on Theory
The Chomskybot