Do very intelligent people suffer from a mental illnes more often than less intelligent people? Is there really a fine line between genius and insanity?

In a word; yes. Anything above the baseline is an anomaly, and what it gives with one hand it takes with the other.

Just look at any historical figure that is regarded as a genius, do a little digging and you'll see that most (if not all) are a little fucked up into the bargain.

Trouble is historical genii are easy to find. What's more difficult is finding renowned idiots to compare them with

I think the only reason that is because if someone mentally ill or not does not stand out from the crowd then they arent going to get noticed.
(well okay I've stated the obvious and prolly havent even answered your question).
I would say though that the majority of 'geniuses' (is that correct?) are not/did not suffer with mental illness but perhaps had very strong off-beat personalities, else they wouldnt have done what they did, would they? They'd be shrinking violets who didnt have the balls to give some whacky idea alot of attention, and get the attention themselves into the bargain.
The less intelligent mentally ill dont have the wherewithall to do that and end up in the corner in some care home mostly I expect.
Look at Steven Wiltshire for instance, no one would have known he was a brilliant artist if no one had bothered to give the poor 'simple' kid some crayons.
Someone else had a 'simple' 3 years old who just happened to be in the right place at the right time and suddenly played mozart or summat on a piano. No one would have known she was a musical genius is she had never had access to a piano - and she was already in a kindergarten for 'low intelligence children'.
And I've waffled.

The trouble you've got there is that there's a very fine line between genuine idiocy and flawed genius. There are plenty of cranks littering the history books. The trouble is its all too subjective.

Look at flat-earthers and the like. Theres definite method applied to their madness, and enough zeal to suggest there's something going on upstairs, but they're still fucking looneytunes. Though to a believer they're the shit.

I think this is going roughly where I expected. It's true that some geniuses end up a bit nutty eg Isaac Newton - revolutionised maths and physics then went on to sing the praises of alchemy. However I suspect that as RG said, the lower profile 'nutters' just end up hidden away, thus biasing the common persception of the spread of such people.

The paranoid schizophrenic often believes that they are the 'normal' ones, but the 'wrong' people have built the world (and made the rules). In other words they are just as sure that the majority of people in so called 'normal society' are the crazy ones.

Genius and madness? I love the film A Beautiful Mind as it portrays this whole idea so perfectly, and as a Nobel prize winner mathematician I found it gave a more positive view of how someone with a long term mental illness can still find a way to share and contribute something of value to the society they have difficulty in being part of.

I have to say, that I also think it's the 'creativity' that holds key to this debate.

When I was at art college, I was fascinated that so many students were having psychiatric treatment but I wonder whether there have been any major studies about mental illness and their representation in the different professions or outstanding skills in a particular area.
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