Vibrating strings in 10 dimensions is just a weird fact... An explanation of that weird fact would tell you why there are 10 dimensions in the first … - Edward Witten

I think one has to regard it as a long term process. One has to remember that String theory, if you choose to date it from the Veneziano model, is already eighteen years old... that quantum electrodynamic theory towards which Planck was heading [in 1900], took fifty years to emerge.

It's been said that string theory is part of the physics of the twenty-first century that fell by chance into the twentieth century. That's a remark that was made by a leading physicist about fifteen years ago. ...String theory was invented essentially by accident in a long series of events, starting with the Veneziano model... No one invented it on purpose, it was invented in a lucky accident. ...By rights, string theory shouldn't have been invented until our knowledge of some of the areas that are prerequisite... had developed to the point that it was possible for us to have the right concept of what it is all about.

Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle.