“**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! 🙂

Dave.

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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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