Theoretical Issues
The difficulties here were met by radically different proof techniques, taking much more care about proofs by contradiction. The logic involved is closer to proof theory than to that of computability theory and computable functions. It is rather loosely conjectured that the difficulties may lie in the realm of computational complexity theory. Ineffective results are still being proved in the shape A or B, where we have no way of telling which.
Read more about this topic: Effective Results In Number Theory
Famous quotes containing the words theoretical and/or issues:
“The hypothesis I wish to advance is that ... the language of morality is in ... grave disorder.... What we possess, if this is true, are the fragments of a conceptual scheme, parts of which now lack those contexts from which their significance derived. We possess indeed simulacra of morality, we continue to use many of the key expressions. But we have—very largely if not entirely—lost our comprehension, both theoretical and practical, of morality.”
—Alasdair Chalmers MacIntyre (b. 1929)
“The current flows fast and furious. It issues in a spate of words from the loudspeakers and the politicians. Every day they tell us that we are a free people fighting to defend freedom. That is the current that has whirled the young airman up into the sky and keeps him circulating there among the clouds. Down here, with a roof to cover us and a gasmask handy, it is our business to puncture gasbags and discover the seeds of truth.”
—Virginia Woolf (1882–1941)