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:

    The message you give your children when you discipline with love is “I care too much about you to let you misbehave. I care enough about you that I’m willing to spend time and effort to help you learn what is appropriate.” All children need the security and stability of food, shelter, love, and protection, but unless they also receive effective and appropriate discipline, they won’t feel secure.
    Stephanie Marston (20th century)

    Pain itself can be pleasurable accidentally in so far as it is accompanied by wonder, as in stage-plays; or in so far as it recalls a beloved object to one’s memory, and makes one feel one’s love for the thing, whose absence gives us pain. Consequently, since love is pleasant, both pain and whatever else results from love, in so far as they remind us of our love, are pleasant.
    Thomas Aquinas (c. 1225–1274)

    Take away from the courts, if it could be taken away, the power to issue injunctions in labor disputes, and it would create a privileged class among the laborers and save the lawless among their number from a most needful remedy available to all men for the protection of their business interests against unlawful invasion.... The secondary boycott is an instrument of tyranny, and ought not to be made legitimate.
    William Howard Taft (1857–1930)

    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)