All in a day’s work: After you’ve finished responding to these ten most vexing unanswered questions in contemporary physics New York Times, try your hand at these seven major unsolved mathematical posers. The solution to each of the latter is worth $1 million US. Here’s an example:

It is Saturday evening and you arrive at a big party. Feeling shy, you wonder whether you already know anyone in the room.

Your host proposes that you must certainly know Rose, the lady in the corner next to the dessert tray. In a fraction of a

second you are able to cast a glance and verify that your host is correct. However, in the absence of such a suggestion, you are

obliged to make a tour of the whole room, checking out each person one by one, to see if there is anyone you recognize. This is

an example of the general phenomenon that generating a solution to a problem often takes far longer than verifying that a

given solution is correct. Similarly, if someone tells you that the number 13,717,421 can be written as the product of two

smaller numbers, you might not know whether to believe him, but if he tells you that it can be factored as 3607 times 3803

then you can easily check that it is true using a hand calculator. One of the outstanding problems in logic and computer science

is determining whether questions exist whose answer can be quickly checked (for example by computer), but which require a

much longer time to solve from scratch (without knowing the answer). There certainly seem to be many such questions. But so

far no one has proved that any of them really does require a long time to solve; it may be that we simply have not yet

discovered how to solve them quickly. Stephen Cook formulated the P versus NP problem in 1971.