A Quote by William Thurston
Experience has shown repeatedly that a mathematical theory with a rich internal structure generally turns out to have significant implications for the understanding of the real world, often in ways no one could have envisioned before the theory was developed.
Quote Topics
Quote Author
Related Quotes
The most important single thing about string theory is that it's a highly mathematical theory, and the mathematics holds together in a very tight and consistent way. It contains in its basic structure both quantum mechanics and the theory of gravity. That's big news.
Einstein's theory of General Relativity has a mathematical structure very similar to Yang-Mills theory.
(Game theory is) essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in mathematical terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not.
We shall see that the mathematical treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.
Well, gauge theory is very fundamental to our understanding of physical forces these days. But they are also dependent on a mathematical idea, which has been around for longer than gauge theory has.
An old French mathematician said: "A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." This clearness and ease of comprehension, here insisted on for a mathematical theory, I should still more demand for a mathematical problem if it is to be perfect; for what is clear and easily comprehended attracts, the complicated repels us.
Experience arises together with theoretical assumptions not before them, and an experience without theory is just as incomprehensible as is (allegedly) a theory without experience.
It presents a really compelling case against the whole theory of anthropogenic global warming. From my point of view, it is a theory that has completely corrupted public policy making in most of the developed world. It confronts all the dubious claims that the warmists have put out there.
A theory is only as good as its assumptions. If the premises are false, the theory has no real scientific value. The only scientific criterion for judging the validity of a scientific theory is a confrontation with the data of experience.
When we meet a fact which contradicts a prevailing theory, we must accept the fact and abandon the theory, even when the theory is supported by great names and generally accepted.
Even for practical purposes theory generally turns out the most important thing in the end.
And, partly, I had found that theory-structure was a superpower in helping one get what one wanted. As I had early discovered in school wherein I had excelled without labor, guided by theory, while many others, without mastery of theory failed despite monstrous effort. Better theory I thought had always worked for me and, if now available could make me acquire capital and independence faster and better assist everything I loved.
If you're a physicist, for heaven's sake, and here is the experiment, and you have a theory, and the theory doesn't agree with the experiment, then you have to cut out the theory. You were wrong with the theory.
Psychology should be the chief basic science upon which the practices of education depend. It should have supplied education with the information it needs concerning the processes of understanding, learning, and thinking, among other things. One of the difficulties has been that such theory as has been developed has been based primarily upon studies of behavior of rats and pigeons. As someone has said, some of the theory thus developed has been an insult even to the rat.
Many theories of the ancient world seem terribly childish today, a hodge-podge of fables and false comparisons.But our theories will seem childish five-hundred years from now.Every theory is based on some analogy, and sooner or later the theory fails because the analogy turns out to be false. A theory in its day helps to solve the problems of the day.
The sole argument generally given to justify this picture of the world is that perturbative string theories have a massless spin two mode and thus could provide an explanation of gravity, if one ever managed to find an underlying theory for which perturbative string theory is the perturbative expansion.
Related Authors
Ada Lovelace Quotes
English
Mathematician
Alfred North Whitehead Quotes
English
Mathematician
Benoit Mandelbrot Quotes
French
Mathematician
Carl Friedrich Gauss Quotes
German
Mathematician
Charles Babbage Quotes
English
Mathematician
David Hilbert Quotes
German
Mathematician
G. H. Hardy Quotes
British
Mathematician
George Polya Quotes
Hungarian
Mathematician
Hannah Fry Quotes
English
Mathematician
Henri Poincare Quotes
French
Mathematician
Isaac Barrow Quotes
English
Mathematician
Isaac Newton Quotes
English
Mathematician
Norbert Wiener Quotes
American
Mathematician
Pythagoras Quotes
Greek
Mathematician
Rene Descartes Quotes
French
Mathematician
Seymour Papert Quotes
American
Mathematician