It is hard for you to appreciate that modern mathematics has become so extensive and so complex that it is essential, if mathematics is to stay as a whole and not become a pile of little bits of research, to provide a unification, which absorbs in some simple and general theories all the common substrata of the diverse branches if the science, suppressing what is not so useful and necessary, and leaving intact what is truly the specific detail of each big problem. This is the good one can achieve with axiomatics (and this is no small achievement). This is what Bourbaki is up to.
André WeilRelated topics
achievement big common complex detail essential general good hard leaving mathematics modern necessary pile problem research science simple small specific stay suppressing unification axiomatics bitsRelated quotes
It is often said that all the conditions for the first production of a living organism are now present, which could ever have been present. But if (and oh! what a big if!) we could conceive in some warm little pond, with all sorts of ammonia and phosphoric salts, light, heat, electricity, &c., present, that a proteine compound was chemically formed ready to undergo stillmore complex changes, at the present day such matter would be instantly devoured or absorbed, which would not have been the case before living creatures were formed.
Charles Darwin
Psychohistory, like psychoanalysis, is a science in which the researcher's feelings are as much or even more a part of his research equipment than his eyes or his hands. [...] Weighing of complex motives can only be accomplished by identification with human actors, the usual suppression of all feeling preached and followed by most "science" simply cripples a psychohistorian as badly as it would cripple a biologist to be forbidden the use of a microscope. The emotional development of a psychohistorian is therefore as much a topic for discussion as his or her intellectual development.
Lloyd deMause
A common habit of thought... is the idea that space is [a] simple receptacle in which bodies move around, with no two bodies present at the same point. ...In modern quantum physics generally, and in the standard model of fundamental physics in particular, physical space appears as a far more flexible framework. Many kinds of particles can be present at the same point in space at the same time. Indeed, the primary ingredients of the standard model are not particles at all, but an abundance of quantum fields, each a complex object in itself, and all omnipresent.
Frank Wilczek
In the original discovery of a proposition of practical utility, by deduction from general principles and from experimental data, a complex algebraical investigation is often not merely useful, but indispensable; but in expounding such a proposition as a part of practical science, and applying it to practical purposes, simplicity is of the importance:-and... the more thoroughly a scientific man has studied higher mathematics, the more fully does he become aware of this truth-and... the better qualified does he become to free the exposition and application of principles from mathematical intricacy.
William John Macquorn Rankine
Humans have a more complex motivational structure and more capability to solve social dilemmas than posited in earlier rational-choice theory. Designing institutions to force (or nudge) entirely self-interested individuals to achieve better outcomes has been the major goal posited by policy analysts for governments to accomplish for much of the past half century. Extensive empirical research leads me to argue that instead, a core goal of public policy should be to facilitate the development of institutions that bring out the best in humans.
Elinor Ostrom
