Effective Results in Number Theory

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:

    I am sorry to think that you do not get a man’s most effective criticism until you provoke him. Severe truth is expressed with some bitterness.
    Henry David Thoreau (1817–1862)

    Social improvement is attained more readily by a concern with the quality of results than with the purity of motives.
    Eric Hoffer (1902–1983)

    Even in ordinary speech we call a person unreasonable whose outlook is narrow, who is conscious of one thing only at a time, and who is consequently the prey of his own caprice, whilst we describe a person as reasonable whose outlook is comprehensive, who is capable of looking at more than one side of a question and of grasping a number of details as parts of a whole.
    G. Dawes Hicks (1862–1941)

    Osteopath—One who argues that all human ills are caused by the pressure of hard bone upon soft tissue. The proof of his theory is to be found in the heads of those who believe it.
    —H.L. (Henry Lewis)