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:
“Recent studies that have investigated maternal satisfaction have found this to be a better prediction of mother-child interaction than work status alone. More important for the overall quality of interaction with their children than simply whether the mother works or not, these studies suggest, is how satisfied the mother is with her role as worker or homemaker. Satisfied women are consistently more warm, involved, playful, stimulating and effective with their children than unsatisfied women.”
—Alison Clarke-Stewart (20th century)
“It would be easy ... to regard the whole of world 3 as timeless, as Plato suggested of his world of Forms or Ideas.... I propose a different view—one which, I have found, is surprisingly fruitful. I regard world 3 as being essentially the product of the human mind.... More precisely, I regard the world 3 of problems, theories, and critical arguments as one of the results of the evolution of human language, and as acting back on this evolution.”
—Karl Popper (1902–1994)
“He is the greatest artist who has embodied, in the sum of his works, the greatest number of the greatest ideas.”
—John Ruskin (1819–1900)
“By the “mud-sill” theory it is assumed that labor and education are incompatible; and any practical combination of them impossible. According to that theory, a blind horse upon a tread-mill, is a perfect illustration of what a laborer should be—all the better for being blind, that he could not tread out of place, or kick understandingly.... Free labor insists on universal education.”
—Abraham Lincoln (1809–1865)