In mathematics, the Jacobian conjecture is a celebrated problem on polynomials in several variables. It was first posed in 1939 by Ott-Heinrich Keller. It was later named and widely publicised by Shreeram Abhyankar, as an example of a question in the area of algebraic geometry that requires little beyond a knowledge of calculus to state.
The Jacobian conjecture is notorious for the large number of attempted proofs that turned out to contain subtle errors. As of August 2012, there are no plausible claims to have proved it.
Read more about Jacobian Conjecture: The Jacobian Determinant, Formulation of The Conjecture, Results
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