To make games on your own, it really helps to be a Renaissance Man, a Jack of All Trades.
Big name game studios, of course, have specialists for each aspect, and managers to somehow put them all together (My specialty is actually mathematics, and a former boss of mine said in a speech that managing mathematicians was like herding cats).
But if you are alone or a very small team, it helps to be a programmer, mathematician, musician, artist, algorithm designer, expert in game mechanics, and so on all at the same time.