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:
“As in political revolutions, so in paradigm choicethere is no standard higher than the assent of the relevant community. To discover how scientific revolutions are effected, we shall therefore have to examine not only the impact of nature and of logic, but also the techniques of persuasive argumentation effective within the quite special groups that constitute the community of scientists.”
—Thomas S. Kuhn (b. 1922)
“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 ones memory, and makes one feel ones 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. 12251274)
“Among a hundred windows shining
dully in the vast side
of greater-than-palace number such-and-such
one burns
these several years, each night
as if the room within were aflame.”
—Denise Levertov (b. 1923)
“No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
—Anna Quindlen (20th century)