Theorem Quotes
The usefulness of observation and measurement in testing economic theories arises because the theorems of economics are supposed to relate to the actual world... Any economic theorem rigorously deduced from given postulates may be regarded as a hypothesis about the actual world which xperience may show to be false.
Richard Stone
Professor Eddington has recently remarked that 'The law that entropy always increases - the second law of thermodynamics - holds, I think, the supreme position among the laws of nature'. It is not a little instructive that so similar a law [the fundamental theorem of natural selection] should hold the supreme position among the biological sciences.
Ronald Fisher
There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.
George Pólya
A human being without the proper empathy or feeling is the same as an android built so as to lack it, either by design or mistake. We mean, basically, someone who does not care about the fate which his fellow living creatures fall victim to; he stands detached, a spectator, acting out by his indifference John Donne's theorem that "No man is an island," but giving that theorem a twist: that which is a mental and a moral island is not a man.
Philip K. Dick
Why can stars do better than the big bang? ...During the big bang, there were only a few minutes when nuclei could form. Very rare processes, or slow ones, played little role. A case in point is the key process from which the sun derives its energy. In this reaction, two protons collide to produce a deuterium nucleus, a neutrino, and a positron. ...This reaction belongs to the family of weak interactions. ...It remains... a remarkable-and for humanity, remarkably fortunate-circumstance that the central reaction that drives the sun is so rare. It is only this extraordinary rarity that allows the average proton in the sun to last so long, billions of years, even though it is colliding with other protons millions of times a second. ...an entertaining example of Treiman's theorem.
Frank Wilczek
Sam Treiman... has quoted something he called Treiman's theorem... Impossible things usually don't happen. ...With the discovery of radioactivity... it suddenly became apparent that the "impossible" was happening all the time. Uranium, thorium, radium... fit all the requirements of chemical elements. They could not be broken down by any of the standard methods... But occasionally... atoms of these elements spontaneously changed into other kinds of atoms. ...So what is left of the doctrine of the elements? Is alchemy reinstated? Not at all. The point is that the doctrine fails only under rare or special conditions. ...We can isolate the conditions in which they do, and retain a more restricted but still useful concept of the "impossible."
Frank Wilczek
Life is not merely persistent, as Jock puts it; life is explosive. The basic theorem of population mathematics to which there has never been found an exception is that population increases always, not merely up to the extent of the food supply, but beyond it, to the minimum diet that will sustain life-the ragged edge of starvation.
Robert A. Heinlein
