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.
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