Michio Kaku, the co-founder of Field String Theory explains why the universe has 11 dimensions rather than any other number.
String Theory explains why the universe has 11 dimensions rather than any other number. Also called F-Theory, "F" for father, the father of strings. It's not known whether F-Theory will survive or not; however, M-Theory in 11 dimension is the mother of all strings. And that theory works perfectly fine. In case you are wondering, what about other dimensions beyond 11? We have problems with stability, these theories are unstable, they decay back down to 11 dimensions, they have what are called anomalies, singularities, which kill an ordinary theory. So the mathematics itself forces you to 11 dimensions.
Also because this is a Theory of Everything, there's more room in higher dimensions to put all the forces together. When you put gravity, electromagnetism and the nuclear force together, four dimensions is not big enough to accommodate all these forces. When you expand to 11 dimensions, bingo, everything forms perfectly well.