Effective Results In Number Theory
For historical reasons and in order to have application to the solution of Diophantine equations, results in number theory have been scrutinised more than in other branches of mathematics to see if their content is effectively computable. Where it is asserted that some list of integers is finite, the question is whether in principle the list could be printed out after a machine computation.
Read more about Effective Results In Number Theory: Littlewood's Result, The 'Siegel Period', Later Work, Theoretical Issues
Famous quotes containing the words effective, results, number and/or theory:
“Social questions are too sectional, too topical, too temporal to move a man to the mighty effort which is needed to produce great poetry. Prison reform may nerve Charles Reade to produce an effective and businesslike prose melodrama; but it could never produce Hamlet, Faust, or Peer Gynt.”
—George Bernard Shaw (1856–1950)
“I have no doubt that it was a principle they fought for, as much as our ancestors, and not to avoid a three-penny tax on their tea; and the results of this battle will be as important and memorable to those whom it concerns as those of the battle of Bunker Hill, at least.”
—Henry David Thoreau (1817–1862)
“To finish the moment, to find the journey’s end in every step of the road, to live the greatest number of good hours, is wisdom. It is not the part of men, but of fanatics, or of mathematicians, if you will, to say, that, the shortness of life considered, it is not worth caring whether for so short a duration we were sprawling in want, or sitting high. Since our office is with moments, let us husband them.”
—Ralph Waldo Emerson (1803–1882)
“Psychotherapy—The theory that the patient will probably get well anyway, and is certainly a damned ijjit.”
—H.L. (Henry Lewis)