Response from Daniel J. Velleman on November 9, 2005

Math has many applications. To take one of your examples, a physicist might use a linear equation to describe the position of an object moving at a constant velocity. Some areas of mathematics have applications to other areas of mathematics (which may then have applications outside of mathematics). Polynomials may be a good example of this. Polynomials are sometimes used to approximate other, more complicated functions, and such approximations may be useful for solving a variety of mathematical problems (which may then have applications outside of mathematics).

But you also ask why math was created. Often when mathematicians create mathematics, they are not thinking about applications, they are just trying to solve a problem because they find it intriguing. You might say that in many cases mathematicians solve mathematical problems for the same reason that mountain climbers climb mountains: because they are there. The applications often come later.

A good example of this might be prime numbers. Euclid proved that there are infintely many prime numbers, and I suspect that he didn't have applications in mind when he did it. But today, prime numbers are very important for the security of electronic communications--an application that Euclid surely had no idea about!