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)
“Life and language are alike sacred. Homicide and verbicide—that is, violent treatment of a word with fatal results to its legitimate meaning, which is its life—are alike forbidden.”
—Oliver Wendell Holmes, Sr. (1809–1894)
“Computers are good at swift, accurate computation and at storing great masses of information. The brain, on the other hand, is not as efficient a number cruncher and its memory is often highly fallible; a basic inexactness is built into its design. The brain’s strong point is its flexibility. It is unsurpassed at making shrewd guesses and at grasping the total meaning of information presented to it.”
—Jeremy Campbell (b. 1931)
“A theory if you hold it hard enough
And long enough gets rated as a creed....”
—Robert Frost (1874–1963)