It is now known that the truth or falsity of the continuum hypothesis and other related conjectures cannot be determined by set theory as we know it today. This state of affairs regarding a classical and presumably well-posed problem must certainly appear rather unsatisfactory to the average mathematician. One is tempted to look more closely and perhaps more critically at the foundations of mathematics. Although our present "Cantorian" mathematics is highly successful in its treatment of abstractions, one must not overlook the fact that from the very beginning the use of infinite processes was regarded with suspicion by many people.
Paul CohenRelated topics
appear beginning classical hypothesis known mathematician mathematics now perhaps present problem set state suspicion truth use affairs todayRelated quotes
A second devaluation would be regarded all over the world as an acknowledgement of defeat, a recognition that we were not on a springboard, but a slide. I myself have always deprecated-perhaps rightly, perhaps wrongly-in crisis after crisis, appeals to the Dunkirk spirit as an answer to our problem, because what is required in our economic situation is not a brief period of inspired improvisation, work and sacrifice, such as we had under the leadership of the right hon. Member for Woodford (Sir W. Churchill), but a very long, hard, prolonged period of reorganisation and rededication. It is the long haul, not the inspired spurt, that we need.
Harold Wilson
This difficulty - am I a mathematician because my degree says so? Am I an engineer because I'm interested in things? Am I a social scientist because I don't think there's a difference between the turbulence in stock markets in terms of unpredictability? At IBM I wouldn't have to worry about that. The names of departments were totally strange and totally meaningless, so it looked like a promising situation for a short time. As it turned out I was going to spend thirty-five years and twelve days at IBM, almost from the beginning to the day when IBM decided that successful research was no longer going to be carried on in that division.
Benoît Mandelbrot
It is known that very distant nebulae, probably galactic systems like our own, show remarkably high receding velocities whose magnitude increases with the distance. This curious phenomenon promises to provide some important clues for the future development of our cosmological views. It maybe of advantage, therefore, to point out some of the principal facts which any cosmological theory will have to account for. Then a brief discussion will be given of different theoretical suggestions related to the above effect. Finally, a new effect of masses upon light will be suggested which is a sort of gravitational analogue of the Compton effect.
Fritz Zwicky
There cannot be a greater mistake than that of looking superciliously upon the practical applications of science. The life and soul of science is its practical application; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.
William Thomson
Perhaps the first fire, the first tool, the first wheel, the first carving in a limestone cave, had each possessed a symbolic rather than a practical value, had each been pressed to serve distortion rather than reality. It was a sort of madness that had driven man from his humble sites on the edges of the woods into towns and cities, into arts and wars, into religious crusades, into martyrdom and prostitution, into dyspepsia and fasting, into love and hatred, into this present cul-de-sac; it had all come about in pursuit of symbols. In the beginning was the symbol, and darkness was over the face of the Earth.
Brian Aldiss