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:
“... effective magic is transcendent nature ...”
—George Eliot [Mary Ann (or Marian)
“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 (18171862)
“My idea is that the world outsidethe so-called modern worldcan only pervert and degrade the conceptions of the primitive instinct of art and feeling, and that our only chance is to accept the limited number of survivorsthe one- in-a-thousand of born artists and poetsand to intensify the energy of feeling within that radiant centre.”
—Henry Brooks Adams (18381918)
“The weakness of the man who, when his theory works out into a flagrant contradiction of the facts, concludes So much the worse for the facts: let them be altered, instead of So much the worse for my theory.”
—George Bernard Shaw (18561950)