In 2000, the Clay Mathematics Institute announced the Millennium Prize problems. These were a collection of seven of the most important math 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 math problems so important that solving any one of them is worth $1 million.
P vs NP
Some problems are easy, and some problems are hard.
In the world of math and computer science, there are a lot of problems that we know how to program a computer to solve "quickly" — basic arithmetic, sorting a list, searching through a data table. These problems can be solved in "polynomial time," abbreviated as "P." It means the number of steps it takes to add two numbers, or to sort a list, grows manageably with the size of the numbers or the length of the list.
But there’s another group of problems for which it’s easy to check whether or not a possible solution to the problem is correct, but we don’t know how to efficiently find a solution. Finding the prime factors of a large number is such a problem — if I have a list of possible factors, I can multiply them together and see if I get back my original number. But there is no known way to quickly find the factors of an arbitrary large number. Indeed, the security of the Internet relies on this fact.
For historical and technical reasons, problems where we can quickly check a possible solution are said to be solvable in “nondeterministic polynomial time,” or “NP.”