What are some of the most intriguing mathematical problems known?

2023 Jan 13
  1. The Riemann Hypothesis, a conjecture about the distribution of prime numbers that has stumped mathematicians for over a century.
  2. The Poincaré Conjecture, a problem in topology that was solved in 2002 by Grigori Perelman, who was later awarded the Fields Medal for his work.
  3. The Collatz Conjecture, a simple problem about a sequence of numbers that remains unsolved despite much effort.
  4. The Birch and Swinnerton-Dyer Conjecture, a problem in number theory that relates the behavior of elliptic curves to the distribution of prime numbers.
  5. The P vs NP problem, which asks whether every problem whose solution can be verified quickly by a computer can also be solved quickly by a computer.
  6. The Hodge Conjecture, a problem in algebraic geometry that remains unsolved despite much progress in the field.
  7. The Goldbach Conjecture, a problem in number theory, which states that every even number greater than 2 can be written as the sum of two prime numbers.
  8. The Navier–Stokes existence and smoothness problem, a problem in mathematical physics that asks whether a solution exists for the Navier–Stokes equations, which describe the motion of fluids.