[lordnacho]

The thing with programming and abstract stuff is it's very hard to know what makes the problem much harder. And you definitely won't have intuition for it if you haven't programmed.

For instance, it's easy to prove that there's an infinite number of prime numbers. There's no biggest prime, because if there were (hand-wave proof coming) you could multiple them all together, add one, and have another prime number. Easy right?

Now tell me if there's also an infinite number of twin primes, ie pairs of prime numbers separated by two.

Here's a good xkcd: http://xkcd.com/1425/