For what reason are all men [driven] insane who according to philosophy or politics or literature or the arts appear to be geniuses [of great genius]. Compare a similar quote by Aristotle, cited here: http://www.translatum.gr/forum/index.php?topic=9564.0
"Driven insane" seems to capture the verbal aspect of the perfect γεγόνασιν, if I am reading it correctly.

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Note added at 19 mins (2010-03-12 00:09:25 GMT)
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Oops. Obviously, this sentence is a question. I failed to punctuate with a question mark. Please amend.

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Note added at 13 hrs (2010-03-12 13:33:30 GMT)
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Note the further discussion on the thread I provided: At long last, harrisimo02, thanks to the kindness of an old friend (Prof. Edwin Floyd at the University of Pittsburg), we're able to give you the text of "Aristotle" that you requested.
Introducing his 30th "problem," the author raises the question, Διὰ τί πάντες ὅσοι περιττοὶ γεγόνασιν ἄνδρες ἢ κατὰ φιλοσοφίαν ἢ πολιτικὴν ἢ ποίησιν ἢ τέχνας φαίνονται μελαγχολικοὶ ὄντες …"Why it is that all who have turned out to be outstanding men of science or politics or literature or the arts are apparently of melancholic temperament."
[In those days, "melancholic" (literally, "black-biled") meant pretty much what we mean by "depressive" or "manic-depressive" today.]
Boiling the sentence down to its core, we have the statement that Seneca focused on, and that you wanted to discover: All who have turned out to be outstanding men are apparently of melancholic temperament. "Apparently" here seems synonymous with "manifest."
I originally posted this at 01:00 GMT, not sure why it is not listed here.

For what reason do all who have become eminent through science or politics or literature or the arts manifest depression [melancholy]?
See my previous discussion. This is my amended answer. Notice that γεγόνασιν is translated as a perfect, which I respectfully believe is a better option than Mr. Tucker recommends.

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Note added at 16 hrs (2010-03-12 16:15:47 GMT)
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Note also that my reply takes a different approach than Dylan's to how to translate μελαγχολικοὶ ὄντες. As I have noted in the reference provided, Seneca cites it as dementia, while in a contemporary setting we would translate it as "depression." If this citation were to be used in a work on psychology, I think this information would support the claim that Aristotle gave criteria to diagnose a primitive manifestation of depressive disorders.

Or 'of an impulsive disposition', somewhat less likely 'of a cranky disposition'. πάντες ὅσοι implies 'all men whosoever, as many men who have...' and τέχνας includes both what we would call '(fine) arts' (e.g., sculpture) and 'crafts' (e.g., pottery). ὄντες is here a circumstantial participle, equivilent to an infinitive.


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Note added at 16 hrs (2010-03-12 16:22:57 GMT)
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The complete rendering is:

Why do all men who have become outstanding either in philosophy or politics or poetry or arts seem to be of a melancholic disposition?