Clippings

It was in July, I don’t remember the year. I was participating in a summer meeting on category theory at the Isles of Thorns, in Sussex. Somebody was actually giving a talk on the history of Eilenberg and Mac Lane’s collaboration in the forties, making clear what the exact contribution of the two authors was. At some point, somebody in the audience started to complain about the speaker giving credit to Eilenberg and Mac Lane for some basic aspect of their work which – he claimed – they borrowed from somebody else. A very sophisticated and animated discussion followed, which I was too ignorant to follow properly. The only things I can remember are the names of the two opponents: the speaker was Saunders Mac Lane and his opponent was Samuel Eilenberg. I was not born when they invented category theory. With my little story in mind, maybe you will forgive me for not having tried to give credit to anybody for the notions and results presented in this Handbook.

What, then, impels us to devise theory after theory? Why do we devise theories at all? The answer to the latter question is simply: because we enjoy “comprehending,” i.e., reducing phenomena by the process of logic to something already known or (apparently) evident. New theories are first of all necessary when we encounter new facts which cannot be “explained” by existing theories. But this moivation for setting up new theories is, so to speak, trivial, imposed from without. There is another, more subtle motive of no less importance. This is the striving toward unification and simplification of the premises of the theory as a whole…

…the world of mathematical truth has infinite complexity, even though any given [formal axiomatic system] only has finite complexity.

That is amazing said Rachel He doesn’t even care what cupboard he puts it in. Reprehensible said Fisher. I’m the only tidy person here said Rachel. And you have beautiful lustrous black hair thought Fisher But you have devised a system for using sponges which ranks with the most gruesome inventions of man.

Happiness is not, except in very rare cases, something that drops into the mouth, like a ripe fruit, by the mere operation of fortunate circumstances. … For in a world so full of avoidable and unavoidable misfortunes, of illness and psychological tangles, of struggle and poverty and ill-will, the man or woman who is to be happy must find ways of coping with the multitudinous causes of unhappiness by which each individual is assailed. In some rare cases no great effort may be required. … But such cases are exceptional. Most people are not rich; many people are not born good-natured; many people have uneasy passions which make a quiet and well-regulated life seem intolerably boring; health is a blessing which no one can be sure of preserving; marriage is not invariably a source of bliss. For all these reasons, happiness must be, for most men and women, an achievement rather than a gift of the gods…

If I had the power to organize higher education as I should wish it to be, I should seek to substitute for the old orthodox religions … something which is perhaps hardly to be called religion, since it is merely a focusing of attention upon well-ascertained facts. I should seek to make young people vividly aware of the past, vividly realizing that the future of man will in all likelihood be immeasurably longer than his past, profoundly conscious of the minuteness of the planet upon which we live and of the fact that life on this planet is only a temporary incident; and at the same time with these facts which tend to emphasize the insignificance of the individual, I should present quite another set of facts designed to impress upon the mind of the young the greatness of which the individual is capable, and the knowledge that throughout all the depths of stellar space nothing of equal value is known to us.

…a sense of proportion is very valuable and at times very consoling. We are all inclined to get unduly excited, unduly strained, unduly impressed with the importance of the little corner of the world in which we live, and of the little moment of time comprised between our birth and death. In this excitement and overestimation of our own importance there is nothing desirable. True, it may make us work harder, but it will not make us work better. A little work directed to a good end is better than a great deal of work directed to a bad end… Those who care much for their work are always in danger of falling into fanaticism, which consists essentially in remembering one or two desirable things while forgetting all the rest, and in supposing that in the pursuit of these one or two any incidental harm of other sorts is of little account. Against this fanatical temper there is no better prophylactic than a large conception of the life of man and his place in the universe.