The aesthetic viewpoint in mathematics

Abstract

Compared with representatives of most other disciplines, mathematicians suffer from a serious handicap. Lawyers, linguists, biologists, chemists, phys ic ians all these people can discuss their professions with uninitiated laymen. Perhaps they cannot fully explain the deepe r p rob lems wi th w h i c h they themse lves are wrestling, but they can easily give a comprehensible account of what lies on the surface, and their listeners will be interested and grateful. Not so in mathematics! It really seems to be true that a special sixth sense is needed to unders tand mathematics. The few who possess this sense fling themselves passionately into the subject; the rest stay as far away from it as possible or consider it a necessary evil. Of course, this isolation gives mathematicians one advantage: unlike other professionals, they are seldom tempted to burden the uninit iated with shop-talk at social gatherings. But mathematicians do not always enjoy their isolation, and I feel it with particular pain today, because I am so eager to give you an idea of the special charms that captivate me in mathematics. I believe my only hope is to avoid any objective discussion of mathematics and just explain my personal feelings about the subject. I do not think it too presumptuous to offer such a personal confession of faith, because even those closely involved with mathematics can adop t seriously d i f ferent a t t i tudes toward it. I don ' t believe that my own point of view has been precisely stated anywhere , though I know that a number of my colleagues share it by and large. Outsiders usually think of mathematics as an especially d r y science. Those w h o k n o w n o t h i n g at all about it picture a mathematician as a kind of calculator. I even remember a famous novel--Friend Death, by Emil S t r auss -which openly presents the view that the essence of mathematics lies in knowing logarithm