Why are challenges fun?

Satisfaction for completing a challenge.

I don't think everyone enjoy random challenges.
It also depends what the reward is among other things.

If all i wanted is a challenge then I would be studying comlicated math on the einstein level until i get some sort of epiphany or maybe I'd even enjoy learning programming.
I don't enjoy programming even though it's challenging, I only like the reward of making something you're interested in with programming... as in a cool game, not just any game.

If you mean something like a mission within a larger game that I have to attempt a few times before I beat it, I like that for a few reasons. One it actually gets be to do some creative strategizing - a lot of games don't elicit that from me at all because they are too easy or too repetitive, and that's the kind of game I find myself wishing were more challenging.

On the other hand I don't like games where the "challenge" comes from random bad luck or a constant shortage of some resource.

When you pay close attention to a series of actions/events and learn/master a new skill in the process, your hypothalamus releases dopamine, which causes feelings of enjoyment in order to reinforce repetition of the activity to help consolidate the newly generated neural networks.

Your brain is wired to reinforce the creation/strengthening of useful structures within itself.

It's not challenge itself that is rewarding to a player, but learning and then (hopefully) mastering new skill sets and overcoming obstacles.

Check out these Lost Garden articles on "what activities can be turned into games" and "the chemistry of game design".

Challenge and enjoyment are also highly goal-oriented. For example, in a RPG, some players derive satisfiction from designing the most powerful character they can. This is a sort of strategic challenge, and the satisfaction is highly dependent on their perception of how successful their build is. Their goal is to design the most successful character possible within the game, considering the game from the perspective of combat.

Conversely, other players, playing the same game, confronted with the same choices and employing the same mechanics, derive satisfaction from the quality of their role-playing and don't care about how optimal their build is. They have a different goal: to be immersed and stay in character. If an action satisfies these requirements (is it believable? would my character behave this way?) they will take a penalty or adopt a handicap, actually making their character less successful in the game, but the build will be more satisfying to them because it better achieves their goal.

In other words, players may have two different strategies for enjoying the same set of mechanics and derive two different types of challenge and satisfaction from using them. When talking about why we enjoy a challenge, it isn't enough to talk about learning, you have to include goals, or, as glhf said, what the player enjoys, the reward that they're after. If the player's goal doesn't align with the challenge, then they're not going to enjoy it. It will seem more like doing math exercises (if you don't like math). That's why games have to be built with specific demographics in mind and have to be very careful about broadening their appeal to other demographics.

If all i wanted is a challenge then I would be studying comlicated math on the einstein level until i get some sort of epiphany or maybe I'd even enjoy learning programming.
I don't enjoy programming even though it's challenging, I only like the reward of making something you're interested in with programming... as in a cool game, not just any game.

In every single way the game is the challenge and the reward is the ending. Whatever happens in between, like getting a new weapon for completing a level is obsolete after you are done with the game. Off course the game needs to be fun to engage in the challenge but that was not the question since for some people racing games are fun, for others online FPS and there are even people that are finding fun at studying math up to the einstein level.

In my opinion it is related to skill and competition with your peers. Ie, your self esteem/confidence is slightly raised when you overcome a challenge. We're also hardwired to be competitive as it is an advantageous trait from the perspective of evolution, so perhaps at a subconscious level we're considering the fact that we've moved ahead of our peers?

The key element is that the player must realise there is a challenge to be overcome. If they blindly blunder through a puzzle and happen upon the correct solution by accident, there's very little feeling of achievement.

Ideally each challenge a player faces is *just* beyond their reach, requiring them to raise the bar each time, to receive an incrementally better reward. Managing this difficulty curve is one of the biggest challenges in game design.