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 know no method to secure the repeal of bad or obnoxious laws so effective as their stringent execution.”
—Ulysses S. Grant (1822–1885)
“In the works of man, everything is as poor as its author; vision is confined, means are limited, scope is restricted, movements are labored, and results are humdrum.”
—Joseph De Maistre (1753–1821)
“To finish the moment, to find the journey’s end in every step of the road, to live the greatest number of good hours, is wisdom. It is not the part of men, but of fanatics, or of mathematicians, if you will, to say, that, the shortness of life considered, it is not worth caring whether for so short a duration we were sprawling in want, or sitting high. Since our office is with moments, let us husband them.”
—Ralph Waldo Emerson (1803–1882)
“Thus the theory of description matters most.
It is the theory of the word for those
For whom the word is the making of the world,
The buzzing world and lisping firmament.”
—Wallace Stevens (1879–1955)