Automation of Higher Algebra
(Research project, not presently formalised. Description to come later.)
Computer algebra is a topic with a complicated state of maturity. On one hand, it has for several decades been well established; several major commercial and some free Computer Algebra Systems (CASes) are extant, and computer algebra is even available as a service on the web. On the other hand, the kind of algebra these systems do is generally quite elementary; even if they may succeed at tasks that are more difficult and much larger than those that a freshman student faces, they do typically not rise to any higher level of mathematics than what a student encounters in the first couple of university courses. This, unfortunately, is quite insufficient for the needs of Higher Algebra; the researcher who seeks to use traditional CASes at the frontiers of science may have to spend as much time keeping them from doing incorrect simplifications as is spent getting the work done!
The idea for the Automation of Higher Algebra project is instead to do mathematics with a computer in the way that modern algebra suggests it should be done -- not as one big game of symbolic manipulation, but through the stepwise construction of increasingly complex objects.