When I disagree with a friend, I will try to convince him. If I am wrong,
I will learn; if I am right, he will -- in any case we both search the
truth.
In my opinion, your "when" seems first to beg the question of "what is".
I have been digesting mathematics (and its history) all my life and am
still puzzled by the _naive_ questions "what's maths, really? ... Could
it have flowered quite differently? ..."
Courant & Robbins [1941], however, seemed to be fairly happy with their
well-known "characterization":
"Mathematics as an expression of the human mind reflects
the active will, the contemplative reason, and the desire
for aesthetic perfection. Its basic elements are logic
and intuition, analysis and construction, generality and
individuality. Though different traditions may emphasize
different aspects, it is only the interplay of these
antithetic forces and the struggle for their synthesis
that constitute the life, usefulness, and supreme value
of mathematical science."
Kind regards,
Julio GC
For scholars and laymen alike it is not
philosophy but _active play_ in chess
itself that alone can answer the basic
question: What is Chess? -- JGC