I've liked math all my life, but it was mainly the puzzle aspect I liked. It is fun trying to figure out math problems. As I went on to study math in college and statistics in graduate school, I came to realize that abstraction is really the most important concept that math teaches. It is the ability to take a problem and separate the essential features from the local details. Open source research .
Mathematical research is essentially open source.
In mathematics, the proof of the pudding is in the proof, so you have to publish it. Anyone can use your theorems and lemmas, and even proofs, if they give proper attribution. Third Voice . Jeremy Bowers discusses uTOK and Third Voice . My guess is that uTOK is on slightly firmer legal grounds.