• 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.

• On 'applied institutes':

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."