Why our brain can't fool itself to constantly produce dopamine? There are experiments [1] showing that our brain tries to maximize amount of dopamine. At the same time it is the brain who controls the dopamine level, because the reward system is located in the brain and if we'll stimulate specific brain areas, our body will produce dopamine.

My question is: why can't our brain learn to constantly stimulate this "reward system" area? Why it learns such complex things like doing math, playing chess, helping other people, etc., which in the far end increase dopamine level (by feeling "evrika" moment, winning a competition, seeing other people grateful) when it can just fool its reward system and manually send electrical signals into it? It is a much more easier and    lucrative task.

P.S. I am not a biologist at all and will be very thankful if you formulate your answers easier than wikipedia articles which are a big struggle for me to comprehend.

P.P.S. I'd like to conduct some research in machine learning (neural networks, to be precise) and was thinking about how our brain prevents such devastating overfitting because underlying concepts can be very useful.

[1] Wikipedia page on the 'Reward system', History
Short answer
Continuous activation of the reward system leads to habituation and hence a downregulation of the pleasure feelings. Further, a continuous euphoric state is a potentially harmful state, as behaviors essential to life are undermined. 

Background
I'm having some difficulty what you mean with a brain fooling itself. A brain cannot fool itself. More importantly for the question, however, is that in case of the reward system it definitely doesn't want to 'fool itself'. Below I outline why from two different angles.

The evolutionairy perspective
In its very essence, the reward system is one of the most ancient parts of the brain and the use of dopamine neurons to mediate reward-driven behavior is also seen in worms and flies, which evolved around 1 billion years ago (Mount Sinai Medical School). Indeed, it's evolutionary role is to stimulate behaviors essential to the survival of an individual such as eating, but it is also essential for the survival of the continuity of an entire species by stimulating the drive for sexual reproduction (Melis &amp; Argiolas, 1995). Reward should follow beneficial behaviors - continuous activation wouldn't aid anything other than a continuous euphoric state. An individual being euphoric wouldn't survive long as it wouldn't pursue anything any longer. That would quickly lead to a discontinuation of that trait as the individual would not be fit to reproduce (Darwin's survival of the fittest). 

The physiological perspective
Continuous activation of the dopamine pathways quickly results in habituation (increasing resistance to the drug's effects) and, in the case of illicit drugs, to dependence (craving/compulsory drug seeking), together referred to as addiction (compulsive drug use despite harmful consequences). The downregulation of the receptors for dopamine (mainly D2) is a physiological reason reward sensations should be transient and uncommon, otherwise the reward system is being tuned down.  

Reference
- Melis &amp; Argiolas, Neurosci Biobehav Rev (1995); 19(1): 19-38