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:
“[Madness] is the jail we could all end up in. And we know it. And watch our step. For a lifetime. We behave. A fantastic and entire system of social control, by the threat of example as effective over the general population as detention centers in dictatorships, the image of the madhouse floats through every mind for the course of its lifetime.”
—Kate Millett (b. 1934)
“The chief benefit, which results from philosophy, arises in an indirect manner, and proceeds more from its secret, insensible influence, than from its immediate application.”
—David Hume (1711–1776)
“Of all reformers Mr. Sentiment is the most powerful. It is incredible the number of evil practices he has put down: it is to be feared he will soon lack subjects, and that when he has made the working classes comfortable, and got bitter beer into proper-sized pint bottles, there will be nothing left for him to do.”
—Anthony Trollope (1815–1882)
“Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.”
—Martin H. Fischer (1879–1962)