In the year 2000, the Clay Mathematics Institute offered a prize of $1,000,000 for a proof for any one of the following 7 open (ie. unsolved) problems:
1.
P versus NP problem – A major unsolved problem in computer science
essentially asking whether if a solution to a problem can be verified in
polynomial time, can the problem itself be solved in polynomial time i.e. does
P=NP?
2.
Hodge conjecture – A major unsolved problem in algebraic geometry on the subject of the algebraic
topology of non singular complex solutions to polynomials.
3.
Poincaré conjecture (solved) – Solved by Grigori Perelman using the
principles of Ricci Flow, the problem was on the subject of the topological
characterization of spheres.
4. Riemann
hypothesis – A major unsolved problem on the subject of the distribution of the zeros
of the Riemann Zeta Function.
5.
Yang–Mills existence and mass gap – A major unsolved problem in quantum field theory
underlying the Standard Model in physics. It asks for a proof of the existence
of a non trivial Yang-Mills.
6.
Navier–Stokes existence and smoothness – A major unsolved problem in engineering and
theoretical physics on the subject of the proof of the Navier-Stokes equations
which are one of the pillars of fluid dynamics.
7.
Birch and Swinnerton-Dyer conjecture – A major unsolved problem in number theory on the
subject of the elliptic curves over given number fields.
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