What is the solution to David Hilbert’s Sixteenth Problem?

Hilbert’s 16th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, as part of his list of 23 problems in mathematics.[1]

The original problem was posed as the Problem of the topology of algebraic curves and surfaces (Problem der Topologie algebraischer Kurven und Flächen).

Actually the problem consists of two similar problems in different branches of mathematics:

The first problem is yet unsolved for n = 8. Therefore, this problem is what usually is meant when talking about Hilbert’s sixteenth problem in real algebraic geometry. The second problem also remains unsolved: no upper bound for the number of limit cycles is known for any n > 1, and this is what usually is meant by Hilbert’s sixteenth problem in the field of dynamical systems…”

Source Link: https://en.wikipedia-on-ipfs.org/wiki/Hilbert’s_sixteenth_problem.html.

Good Luck! 🙂


Published by Dave

I am currently a science researcher at researchgate.net (https://www.researchgate.net/profile/David_Cole29). My interests include number theory, mathematical analysis, and energy theory (physics)... And we (Cole, Montgomery, Lagarias, Odlyzko, Hardy, Riemann, Gauss, and other mathematicians) proved the Riemann Hypothesis! 🙂

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