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:
“Relying on any one disciplinary approachtime-out, negotiation, tough love, the star systemputs the parenting team at risk. Why? Because children adapt to any method very quickly; todays effective technique becomes tomorrows worn dance.”
—Ron Taffel (20th century)
“The ideal reasoner, he remarked, would, when he had once been shown a single fact in all its bearings, deduce from it not only all the chain of events which led up to it but also all the results which would follow from it.”
—Sir Arthur Conan Doyle (18591930)
“Cultivated labor drives out brute labor. An infinite number of shrewd men, in infinite years, have arrived at certain best and shortest ways of doing, and this accumulated skill in arts, cultures, harvestings, curings, manufactures, navigations, exchanges, constitutes the worth of our world to-day.”
—Ralph Waldo Emerson (18031882)
“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 (18871962)