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.