Apr 02, 2013— read in full
The Millennium Prize Problems
The Millennium Prizes were set up in 2000 to reward anyone who could solve one of seven unsolved problems in mathematics. So far, only one has been solved - although the mathematician who solved it turned down the prize.
Perhaps the best-known is the P versus NP problem, which is all about solving other problems. P and NP are names for two groups of problems. Put simply, P problems are ones that a computer can work out an answer to quickly. For an NP problem, a computer can check if an answer is correct quickly.
The question is whether these groups are actually the same. This would mean that if an answer to a problem can be checked quickly, there is also a way to work out the answer from scratch quickly.
Most mathematicians believe that the groups are different - so there are some problems you can check quickly but not solve quickly - but it has never been proved. It's an important question for areas like cryptography, which rely on certain problems being hard to solve. If someone proved that the two groups were the same, it would have huge consequences for mathematics, computing and science.
You can find out more about the other problems on the Clay Mathematics Institute website.