You actually hit the jackpot! The Traveling Salesman Problem is part of a list of special problems known as NP-Complete problems. So, what's so big about them? They are central to one of the most important unsolved problems in both mathematics and computer science, known as P=NP?

P=NP? is a problem that basically asks: are difficult or consuming problems really that hard? When we found something that takes to much time to found out, is it that we looked the wrong way?

Let's give an example. Sudoku: to solve sudoku, you can go ahead and try all possible number combinations, but that will take a lot of time. You can usually solve a 9x9 sudoku easily in other ways. But if you make a bigger sudoku, the usual methods won't do, and the problem will take a lot of time to solve.

So we have 3 different concepts here:

-P: those are a list of all problems that can be solved in a reasonable amount of time by a computer. This is define precisely in a mathematics, but we really don't need to go there.

-NP: These, on the other hand, are problems where you can check if an answer is a correct one in a reasonable amount of time. For example, if they ask you if a sudoku is correct, you can easily scan the boxes to see that everything is correct.

-NP-Complete: This are the hardest problems of NP. Basically, if you were to prove that one of this problems can be solve easily, you'll be able to prove that all NP problems are easy, so NP=P.

What's so big about NP=P? A lot of things. But probably the most important one for everyone has to do with security. Nowadays, all transactions over the net rely on the difficulty of difficult problems. If you were to prove that difficult problems can be solved easily (that is, NP=P), the world won't be able to rely on any reasonable security protocol, so I guess civilization as we know it will collapse.

You can find more of these problems all over the internet, as I told you, these are the big thing. As a matter of fact, if you were able to prove either that NP=P or NP≠P, then you might be able to get $1 million dollars from the Clay Mathematics institute.