§ Under the spell of Leibniz's dream
I found it very quotable. I'm posting some quotes below.
- On applied versus pure mathematics:
An important side-effect of the hard times was the creation of a spiritual
climate in which the distinction between pure and applied science had
vanished: of all the things you could do, you just did the most urgent one,
and the development of some urgently needed theory was often the most
practical thing to do.
The worst thing with institutes explicitly devoted to applied science is that
they tend to become institutes of second-rate theory.
- On the artificial divide between theory and applied sections of university:
These days there is so much obsession with application that, if the
University is not careful, external forces, which do make the distinction,
will drive a wedge between "theory" and "practice" and may try to banish the
"theorists" to a ghetto of separate departments and separate buildings. A
simple extrapolation will tell us that in due time the isolated practitioners
will have little to apply; this is well-known, but has never prevented the
financial mind from killing the goose that lays the golden eggs.
- On programming as typing:
Needless to say, this confusion between the score and the composition led to
an underestimation of the intellectual challenges programming presents
- On hilbert and axiomatics:
Hilbert's revolution was in any case to redefine "proof" to become a
completely rigorous notion, totally different from the psycho/sociological
"A proof is something that convinces other mathematicians."