A great department of thought must have its own inner life, however transcendent may be the importance of its relations to the outside. No department of science, least of all one requiring so high a degree of mental concentration as Mathematics, can be developed entirely, or even mainly, with a view to applications outside its own range. The increased complexity and specialisation of all branches of knowledge makes it true in the present, however it may have been in former times, that important advances in such a department as Mathematics can be expected only from men who are interested in the subject for its own sake, and who, whilst keeping an open mind for suggestions from outside, allow their thought to range freely in those lines of advance which are indicated by the present state of their subject, untrammelled by any preoccupation as to applications to other departments of science. Even with a view to applications, if Mathematics is to be adequately equipped for the purpose of coping with the intricate problems which will be presented to it in the future by Physics, Chemistry and other branches of physical science, many of these problems probably of a character which we cannot at present forecast, it is essential that Mathematics should be allowed to develop freely on its own lines.

I have always played with the fancy that some contagion from outer space had been the seed of man. Our passionate preoccupation with the sky, the stars, and a God somewhere in outer space is a homing impulse. We are drawn back to where we came from.

If I had influence with the good fairy who is supposed to preside over the christening of all children, I should ask that her gift to each child in the world be a sense of wonder so indestructible that it would last throughout life, as an unfailing antidote against the boredom and disenchantment of later years, the sterile preoccupation with things that are artificial, the alienation from the sources of our strength.

In our preoccupations with sex, our submission to gods and leaders, our sometimes suicidal commitment to ideas, religions, and trivial details of cultural style, we become the unconscious creators of the social organism’s exploits.

It is not only by the questions we have answered that progress may be measured, but also by those we are still asking. The passionate controversies of one era are viewed as sterile preoccupations by another, for knowledge alters what we seek as well as what we find.

It is the individual only who is timeless. Societies, cultures, and civilizations - past and present - are often incomprehensible to outsiders, but the individual’s hunger, anxieties, dreams, and preoccupations have remained unchanged through the millennia. Thus, we are up against the paradox that the individual who is more complex, unpredictable, and mysterious than any communal entity is the one nearest to our understanding; so near that even the interval of millennia cannot weaken our feeling of kinshiIf in some manner the voice of an individual reaches us from the remotest distance of time, it is a timeless voice speaking about ourselves.

Under pressure from the computer, the question of mind in relation to machine is becoming a central cultural preoccupation. It is becoming for us what sex was to the Victorians—threat and obsession, taboo and fascination.