<snip> >> (DS): All it would take is to present a problem from >> one of the "numbery" maths (arithmetic, algebra, >> analytical geometry, trigonometry, probability, >> statistics, calculus, for example) that one would not >> naturally solve by a sequence of fundamental additions >> and/or multiplications. > > > > Can anyone come up with a "textbook" problem that > > shoots my assertion down? > Try, for instance, the 'Fundamental Theorem of Calculus': ++++++ Prove that differentiation and integration are essentially inverses of each other.
This is a standard 1st year graduate school exercise in mathematics. ++++++
Or, try the 'Fundamental Theorem of Algebra': ++++++ Prove that every non-constant polynomial in a single variable with complex coefficients has at least one complex root.
This too is a standard 1st year graduate school exercise.
(As I recall, I had quite a difficult time before I had convinced myself that I had understood it properly. I'm not sure I'll be able to do it now). ++++++
I personally believe you may find it not worth the effort to prove these basic theorems assuming only addition and multiplication. (I will NOT be willing to read and verify your proofs. In fact, I would tend to believe that only someone entirely innocent about math would attempt to prove these in this way).