In 2000, the Clay Mathematics Institute announced the Millennium Prize problems. These were a collection of seven of the most important maths problems that remain unsolved.
Reflecting the importance of the problems, the Institute offered a $1 million prize to anyone who could provide a rigorous, peer-reviewed solution to any of the problems.
While one of the problems, the Poincare Conjecture, was famously solved in 2006 (with the mathematician who solved it, Grigori Perelman, equally famously turning down both the million dollar prize and the coveted Fields Medal), the other six problems remain unsolved.
Here are the six maths problems so important that solving any one of them is worth $1 million.
i) P vs NP
ii) The Navier-Stokes equations
iii) Yang-Mills theory and the quantum mass gap
iv) The Riemann Hypothesis
v) The Birch and Swinnerton-Dyer conjecture
vi) The Hodge conjecture
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