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)
“For every life and every act
Consequence of good and evil can be shown
And as in time results of many deeds are blended
So good and evil in the end become confounded.”
—T.S. (Thomas Stearns)
“Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components.”
—Noam Chomsky (b. 1928)
“There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.”
—Albert Einstein (1879–1955)