Gradient conjecture

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In mathematics, the gradient conjecture, due to René Thom (1989), was proved in 2000 by three Polish mathematicians, Krzysztof Kurdyka (University of Savoie, France), Tadeusz Mostowski (Warsaw University, Poland) and Adam Parusiński (University of Angers, France). It states that given a real-valued analytic function f defined on Rn and a trajectory x(t) of the gradient vector field of f having a limit point x0 ∈ Rn, where f has an isolated critical point at x0, there exists a limit (in the projective space PRn-1) for the secant lines from x(t) to x0, as t tends to zero.

Mathematics Field of study concerning quantity, patterns and change

Mathematics includes the study of such topics as quantity, structure, space, and change.

René Thom mathematician

René Frédéric Thom was a French mathematician. He made his reputation as a topologist, moving on to aspects of what would be called singularity theory; he became world-famous among the wider academic community and the educated general public for one aspect of this latter interest, his work as founder of catastrophe theory. He received the Fields Medal in 1958.

University of Angers university located in Angers, France

The University of Angers is an institution of higher education in the town of Angers in western France.

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Pierre Deligne mathematician

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Dennis Sullivan mathematician

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