Progress in mathematics comes from research. To contribute something new, you often need a lot of background knowledge and university is the place for this. A

Progress in mathematics comes from research. To contribute something new, you often need a lot of background knowledge and university is the place for this. As with all things, there are exceptions - Ramanujan for example. To be a financially successful programmer, you often just need a few books, courage to step outside your comfort zone, and a good idea. There are lots of examples of this, but for me the embodiment is Ken Williams of Sierra fame who made out pretty well, and I don't recall that he had a degree in CS.