There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include:
The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named seven "Millennium Prize Problems," selected by focusing on important classic questions in mathematics that have resisted solution over the years. A $7 million prize fund has been established for the solution to these problems, with $1 million allocated to each. The problems consist of the Riemann hypothesis, Poincaré conjecture (solved!), Hodge conjecture, Swinnerton-Dyer Conjecture, solution of the Navier-Stokes equations, formulation of Yang-Mills theory, and determination of whether NP-problems are actually P-problems.
In 1900, David Hilbert proposed a list of 23 outstanding problems in mathematics (Hilbert's problems), a number of which have now been solved, but some of which remain open. In 1912, Landau proposed four simply stated problems, now known as Landau's problems, which continue to defy attack even today. One hundred years after Hilbert, Smale (2000) proposed a list of 18 outstanding problems.
Weisstein, Eric W. "Unsolved Problems." From MathWorld: A Wolfram Web Resource. https://mathworld.wolfram.com/UnsolvedProblems.html
How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of reality?
—Albert Einstein
Tyson, P. (2011, November 10). Describing nature with math. NOVA. https://www.pbs.org/wgbh/nova/article/describing-nature-math/