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:
“The only effective way to help well-intentioned, intelligent persons to do the best they can in raising children is to encourage and guide them always to do their own thinking in their attempts at understanding and dealing with child-rearing situations and problems, and not to rely blindly on the opinions of others.”
—Bruno Bettelheim (20th century)
“Intellectual despair results in neither weakness nor dreams, but in violence.... It is only a matter of knowing how to give vent to one’s rage; whether one only wants to wander like madmen around prisons, or whether one wants to overturn them.”
—Georges Bataille (1897–1962)
“The growing good of the world is partly dependent on unhistoric acts; and that things are not so ill with you and me as they might have been, is half owing to the number who lived faithfully a hidden life, and rest in unvisited tombs.”
—George Eliot [Mary Ann (or Marian)
“It makes no sense to say what the objects of a theory are,
beyond saying how to interpret or reinterpret that theory in another.”
—Willard Van Orman Quine (b. 1908)