Since this question has been placed under the topic of Literature, the assumption will be made that the topic is not to be treated as a scientific one. Perhaps, then, an introduction to this subject can first present a poem written by Emily Dickinson:
Much Madness is divinest Sense--
To a discerning Eye--
Much Sense--the starkest Madness--
'Tis the Majority
In this , as All, prevail--
Assent--and you are sane--
Demur--you're straightway dangerous
And handled with a Chain--
A topic sentence that could follow this introduction might read: Often there is a thin line between genius and insanity.
The Greek mathematician Pythagoras was obviously a genius, having arrived at his famous theorem. Also, he was the first to declare that natural phenomena can be explicated mathematically, an idea that gave rise to the study of physics. But, he often had some rather bizarre ideas; for one thing, he founded his own religion, which had two basic tenets: souls can be reincarnated and there is an evil in beans. He feared other things such as letting swallows nest under a roof and he thought all wrinkles must be smoothed out of pillows. He had a belief in pacifism, too, but he died in a fight.
There are other famous people who were both geniuses and a bit mad: Michelangelo, Charles Darwin, Lord Byron, and Sylvia Path.
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