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)

    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 said truth is that it is the greatest happiness of the greatest number that is the measure of right and wrong.
    Jeremy Bentham (1748–1832)

    Lucretius
    Sings his great theory of natural origins and of wise conduct; Plato
    smiling carves dreams, bright cells
    Of incorruptible wax to hive the Greek honey.
    Robinson Jeffers (1887–1962)