The virtue of difficulty

Why is maths so difficult to understand? I often wondered this as I was trying to understand various mathematical problems. There was almost an innate sense that all things should be easily solvable. It is of course my naivety which makes me think this but it reveals an interesting truth. That a problem is useful only if it is difficult. It's an obvious concept, there is no great conundrum of how to walk (for typical humans). We just do it. However, Fermat's last theorem is a problem which a large number of people and hours of time was spent on. Again an obvious concept, but I did notice an interesting conclusion.

We tend to think about certain problems and how to solve them. For example when you use your phone, you often notice hundreds of problems with the hardware and the software. "Oh if only I could solve these problems, then this would be a perfect phone." But that isn't true, as when one problem is solved, we continue to seek problems until we hit upon a hard thing again, even if it is near useless. Just think about the number of hard problems that have been solved already. Thinking up a computer for solving vastly complex calculations, life saving drugs etc. There is a practically infinite number of problems that can be invented. I may be abusing language but what I mean is: with x number of atoms, there are more problems (even useless ones) that can be invented than solved by that collection of atoms. After all, just think about badly posed, silly questions. This might be at first distressing as if we will never quite work it all out. However, I think it is somewhat refreshing: just keep plodding along and enjoy solving the mass of puzzles. With that in mind, I accept there are lots of hard problems still to go and continue spout useless shit on here instead.


PS(As in, an interesting idea that I didn't manage to shoehorn into the main text): We tend to think of Utopia as the place where all the problems are solved. On second thought however It sounds dull and boring, quite the opposite to heaven. Naturally of course then this is no longer Utopia, it would be (for humans) the optimal amount of challenge and risk/reward.

PPS(As in clarification): When I say hard task, this can include easy tasks which require some complexity to discover. For example, simple group theory is very easy but to discover and understand its significance is considerably more difficult.