It sounds like you're thinking of (or working towards) Peano Arithmetic¹, which (to oversimplify) basically starts with "0", "1", "=" and "+", and works from th

It sounds like you're thinking of (or working towards) Peano Arithmetic¹, which (to oversimplify) basically starts with "0", "1", "=" and "+", and works from there. Whether that's "enough" rather depends on what you're trying to achieve, though. There's subgenres of mathematics that don't necessarily involve numbers at all, like geometry and topology. It would be difficult to reduce them to addition. ¹: http://en.wikipedia.org/wiki/Peano_axioms http://en.wikipedia.org/wiki/Peano_axioms