Fifty years ago Kurt Gödel... proved that the world of pure mathematics is inexhaustible. ... I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics. If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed, I would feel that the Creator had been uncharacteristically lacking in imagination.
Freeman DysonRelated topics
fifty final formal hope mathematics prove pure set should turn years LawsRelated quotes
In reality, the likelihood of reaching the pinnacle of capitalist society today is only marginally better than were the chances of being accepted into the French nobility four centuries ago, though at least an aristocratic age was franker, and therefore kinder, about the odds. It did not relentlessly play up the possibilities open to all, and so, in turn, did not cruelly equate an ordinary life with a failed one.
Alain de Botton
It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way... Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.
John von Neumann
Iconography becomes even more revealing when processes or concepts, rather than objects, must be depicted-for the constraint of a definite "thing” cedes directly to the imagination. How can we draw "evolution” or "social organization,” not to mention the more mundane "digestion” or "self-interest,” without portraying more of a mental structure than a physical reality? If we wish to trace the history of ideas, iconography becomes a candid camera trained upon the scholar's mind.
Stephen Jay Gould
I am obliged to interpolate some remarks on a very difficult subject: proof and its importance in mathematics. All physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.
G. H. Hardy
Often, when following the trail which meanders over the hills, I pull myself up in an effort to encompass the glory and the grandeur which envelops the whole horizon. Often, when the clouds pile up in the north and the sea is churned with white caps, I say to myself: "This is the California that men dreamed of years ago, this is the Pacific that Balboa looked out on from the Peak of Darien, this is the face of the earth as the Creator intended it to look."
Henry Miller