Mathematics has some of the best aspects of both a science and an art.
Like a science, we observe interesting phenomena, do experiments (with mathematical objects, rather than physical objects), and make conjectures. But unlike science, we aren't satisfied until we have proven these conjectures hold for all cases; we're not happy with simply a good chance that something is true.
As with an art, we look for beauty and elegance in our mathematical theories, our theorems, our structures, and our proofs. In some cases, such as geometry, we can see that beauty with our eyes; in other cases, it's the mind's eye that sees the beauty.
There is no major that gives you more flexibility in what you can do after you graduate than mathematics. Employers are looking for people who can think logically and solve problems, and a bachelor's degree in mathematics prepares you to do this. Mathematics majors can (and many do) go on to medical or law school (or graduate school in mathematics), work in the business and financial sector, work in the government, and do many other things.