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Abstract
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The aim of this lecture is to explain how the Jacobian Conjecture is an eloquent illustration of “simplicity as source of complexity” in mathematical research, and how the “connectivity” of the Jacobian Conjecture with all main streams of mathematics, thanks to its surprising equivalent formulations and heuristic generalizations, is an illustration of a “significiant idea in mathematics” according to G. H. Hardy who wrote : “a mathematical idea is significant if it can be connected, in a natural and illuminating way, with a larg complex of other mathematical ideas”. For these reasons, the Jacobian Conjecture, stated by O. Keller in 1949, is incontestably one of “the greatest mathematical challenges on the thresold of the third millennium”, in which could be interested researchers in almost all branches of mathematics.
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