I was just wondering if any one has ever tried to make a new fundamental system for solving problems, ranging from Algebra to complex analysis and beyond in a more simplistic and less time consuming way?
maybe I don't understand what you mean but the software Mathematica is a system for operating on equations and solving them. it can simplify equations so it must have a set of rules for doing so.
If you're talking about a new mathematical method for solving problems then no.