I finished a PhD in pure mathematics three years ago and then abandoned academia because it's stale. My degree opens a lot of doors, enables me to attack proble

I finished a PhD in pure mathematics three years ago and then abandoned academia because it's stale. My degree opens a lot of doors, enables me to attack problems that nobody else can fathom, and generally allows me to do whatever the hell I'd like. While completing my degree, I devoted all of my spare time to building real products, coding all night, and learning to sell my ideas. A math degree is a valuable asset if you love to do math. It'll give you the opportunity to solve lots of interesting problems, but only if you also make things that non-mathematical folks can understand. You must learn to communicate your ideas to anyone that will listen. Develop proficiency in some platform, build a product, solve a problem, and learn how to talk about it -- this is all trivially routine, but it goes a long way when it comes to executives, investors, managers, and their ilk. Eventually, you'll reach a point where you'll need to focus exclusively on mathematics... that's fine and everyone will understand. But before then, be sure to do something practical.