"Discussion imported from philosophy forum"
I think first we need to define genius. I’ll posit the following: invention based on deep or thorough understanding.
Assuming this suffices, mental illness and genius I would not say relates in one way in all cases. I’ll posit two, of what I suspect are many possibilities.
First, someone who is mentally ill but has acquired thorough understanding of a subject may develop a different perspective which may not suffer from prejudices, that happen to be wrong, in the orthodox population, allowing for quick invention.
Second, those that have strove for the deepest understanding they can attain as well as striving to be creative and invent, may develop mental illness. Just like athletes who push themselves to the limit are prone to physical injury, people who push themselves to the limit of knowledge, analysis, and creativity are prone to mental injury.
I think these are the two most common connections between genius and mental illness. Though there are famous examples of the first case, I think the second case is far more common still. The former case I think can only be understood on a case by case basis, as no two mental conditions are really the same (unlike perhaps the comforting over simplistic assumption of society). In the latter case the mental illness is not required for genius but simply the result of over taxation of the mind, or a setup of paralysing conclusions (nihilism for instance).
In terms of paralysing conclusions I think the most common are a bout of some sort of nihilism, and a resulting giving up further thought, research, creativity etc. which I think results in a sort of atrophied of the mind. A athlete that simply stops exercising, or significantly reduces physical effort for a period of time, can suffer various conditions, whereas someone that is already tranquil is in no danger of these specific dangers (though perhaps other long term ones).
There is of course more classical pitfalls such as obsession, arrogance to the point of delusion, losing social skills (sometimes due to obsession, but also ostracisation may occur for holding different ideas or even for reasons that may not have anything to do with mental ability—coincidence may be the only explanation sometimes), and certainly the list goes on.
Or simply, like the athlete, trying to function at over capacity is unstable.
However, true super geniuses, like Leonardo de Vinci, seemed to be smart enough to avoid all these pitfalls and neutralize any pre-existing inefficient tendency.
However, this is just my take on the situation. I think the whole way society thinks about psychology is a sham. I think most people who find themselves in mental difficulty arrive there from genuine doubt of their own life, assumptions about it, the world and the universe, and then prefer to conclude that there misgivings are some sort of disease that can be fixed. They want to go back to simpler times. Not only does this certainly not solve whatever questions about existence and their place in it they may have, but generally doesn’t work and they "solve" the problem with other problems (like addiction to prescription medication), or don’t solve the problem, which is not that they cannot, or aren’t, continuing life as usual but that this life as usual is filled with contradictions that they have become aware of. Many escape into, and join those that never leave, double think.
But again, that’s just my take on the situation. My approach is to try to figure out what is actually true, and what I should actually do abut it. Actually doing it I leave as a matter of will.
If there was some theory that resolved all battles of wills, then one would have to will oneself to subject oneself to the theory. And indeed, then will oneself to understand where and how to subject oneself to the theory, and then will oneself to understand that, and that ad infinitum. Far simpler to assume there is no such magical will-nullifying-theory and that you either do what you conclude is reasonable through mustering what little strength you have, or you don’t because of capitulation to weakness. This latter principle holds no matter what condition, physical or mental, you may find yourself in.