A Quote by Hendrik Lenstra
Recreational number theory [...] is that part of number theory that is too difficult to study.
Related Quotes
At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate.
Number theorists say that number theory is too complicated, so let's pretend that there is only one prime number, and then let's combine all these results. Surprisingly, sometimes it works.
After preliminary work by a number of other distinguished mathematicians and economists, game theory as a systematic theory started with von Neumann and Morgenstern's book, 'Theory of Games and Economic Behavior,' published in 1944.
As soon as science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the 'truth' of the theory lies.
There's not a single shred of evidence for the multiverse. If, in order to explain this universe, you need a theory that invents an infinite number of parallel universes - that's not a very good theory.
Music is part of Number Theory. Nowadays when a number-theorist applies for a grant, he says that it is good for security, but in those days, way before America, he would say that it's good for music. I will not comment whether we have progressed.
The whole action of the laws tended to increase the number of consumers of food and to diminish the number of producers, was due the invention of the Malthusian theory of population.
Renormalization is just a stop-gap procedure. There must be some fundamental change in our ideas, probably a change just as fundamental as the passage from Bohr's orbit theory to quantum mechanics. When you get a number turning out to be infinite which ought to be finite, you should admit that there is something wrong with your equations, and not hope that you can get a good theory just by doctoring up that number.
In these researches I followed the principles of the experimental method that we have established, i.e., that, in presence of a well-noted, new fact which contradicts a theory, instead of keeping the theory and abandoning the fact, I should keep and study the fact, and I hastened to give up the theory.
The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.
If the theory accurately predicts what they [scientists] see, it confirms that it's a good theory. If they see something that the theory didn't lead them to believe, that's what Thomas Kuhn calls an anomaly. The anomaly requires a revised theory - and you just keep going through the cycle, making a better theory.
the truth and value of a theory does not depend on the number of people who are interested in it - otherwise you might compare the number of people who follow the predictions of astrologers in the daily press with those who attend lectures by Einstein, and conclude that astrology was more valuable and true than physics.
Topology and number theory are my faves.
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.
The standard theory may survive as a part of the ultimate theory, or it may turn out to be fundamentally wrong. In either case, it will have been an important way-station, and the next theory will have to be better.
It is naïve to suppose that the acceptance of evolution theory depends upon the evidence of a number of so-called "proofs"; it depends rather upon the fact that the evolutionary theory permeates and supports every branch of biological science, much as the notion of the roundness of the earth underlies all geodesy and all cosmological theories on which the shape of the earth has a bearing. Thus antievolutionism is of the same stature as flat-earthism.
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