Results
Wang (1980) proved the Jacobian conjecture for polynomials of degree 2, and Bass, Connell & Wright (1982) showed that the general case follows from the special case where the polynomials are of degree 3. Moh (1983) checked the conjecture for polynomials of degree at most 100 in 2 variables.
The Jacobian conjecture is equivalent to the Dixmier conjecture.
Read more about this topic: Jacobian Conjecture
Famous quotes containing the word results:
“The chief benefit, which results from philosophy, arises in an indirect manner, and proceeds more from its secret, insensible influence, than from its immediate application.”
—David Hume (1711–1776)
“The peace conference must not adjourn without the establishment of some ordered system of international government, backed by power enough to give authority to its decrees. ... Unless a league something like this results at our peace conference, we shall merely drop back into armed hostility and international anarchy. The war will have been fought in vain ...”
—Virginia Crocheron Gildersleeve (1877–1965)
“It amazes me when I hear any person prefer blindness to deafness. Such a person must have a terrible dread of being alone. Blindness makes one totally dependent on others, and deprives us of every satisfaction that results from light.”
—Horace Walpole (1717–1797)