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Could a single individual have the abilities of Gauss in mathematics, play soccer like Messi, write like Dostoyevsky, play chess like Carlsen, have ideas in physics comparable to those of Einstein, have the talent of Mozart in music, and so on for every area?

Since this have never happened, maybe there are limitations to how talented a person can be, or time limitations for a single individual to develop all of them. What does neuroscience have to say about it?

Note: I got this question from Sigma Society (in Portuguese). I've found nothing more about it, maybe because it's too speculative.

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I'm inclined to see it as more a matter of statistics. Since you're asking a question of rank, the possibility depends on the population. For an extreme example, if you were the last man on earth, you'd be your own super polymath by default! Given a population of $N>7\rm B$, competition is of course much fiercer. Since the chance of being #1 in any skill is infinitesimal to begin with, the chance of being #1 in multiple skills is several times more infinitesimal. Granted, these are not independent probabilities; there is evidence of a general factor of intelligence.

Nonetheless, math, soccer, creative writing, chess, physics, and music all involve somewhat different kinds of intelligence; quantitative, kinesthetic, verbal, strategic, spatial, and musical intelligences may all be partially independent. Furthermore, none of these are purely intuitive for anyone. Culture-dependent conventions influence each to at least limited extents. Therefore experience comes into play, and some amount of practice may be necessary to express ability in any of these domains. The more separate domains a person of any innate ability attempts to master through practice is the thinner the person's time for each will be spread, which further reduces one's competitiveness versus specialists.

In issues of rank, sometimes very small practical differences separate the performances of competitors; you need only watch a few minutes of the Olympics to see this principle demonstrated. You may also disagree with scoring systems in the Olympics if you watch a little longer. This indicates another problem with high-level competition: ability measurement becomes less reliable at extremes. See a related question: How can psychometry measure the very high IQ's in adults? Taking this into account, we now face the dual challenge of first producing an incredibly improbable individual with maximally extraordinary abilities, then having identified this individual (itself not a trivial task), performing accurate assessments demonstrating her/his superiority over all others. Again, from a statistical standpoint, odds aren't good.

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Thanks for this very objective and balanced answer! Unless humans undergo some change, the odds really aren't good, and if we were to make the comparison with every genius in history, then the chance would be even more incredibly small that maybe this issue will always be hypothetical (unfortunately!). –  João Rimu Mar 27 '14 at 9:14
Yeah, I'm afraid so...but I don't think it's a bad thing. Time is short for any individual, so all else being equal, I'd rather see talents remain divvied up so that several individuals with their own separate talents can better express each by devoting their time to using them to the fullest. Put all those talents into one individual, and some are bound to go to waste, it seems to me. Then again, IMHO, transcendental genius emerges from the convergence of disparate bodies of knowledge...so maybe this super polymath would do some truly, uniquely incredible things that would waste nothing! –  Nick Stauner Mar 27 '14 at 9:19
I agree with this answer. With each additional measured trait, the probability of them simultaneously being in the 90th+ percentile for a single person approaches 0. So possible? Sure. Probable? Not very. –  Keegan Keplinger Mar 30 '14 at 16:12

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