Analysis of information sources in references of the Wikipedia article "Jacobian conjecture" in English language version.
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The Jacobian Conjecture was first formulated as a question by O. Keller in the case n = 2 for polynomials with integer coefficients ([35], 1939).
For more variables, many people believe it is not even true.
The two-dimensional case has been especially well studied.
There is strong evidence for the two-variable Jacobian Conjecture, but not for the n-variable conjecture.
The Jacobian Conjecture was first formulated as a question by O. Keller in the case n = 2 for polynomials with integer coefficients ([35], 1939).
For n = 2 the conjecture might be true, however ... there is an enormous difference between and !
It shows the conjecture is false for every dimension larger than 2, with the original conjecture in two dimensions remaining open.
The Jacobian Conjecture was first formulated as a question by O. Keller in the case n = 2 for polynomials with integer coefficients ([35], 1939).