[alphydan]

I think you're right that there was always notation. But perhaps he is referring to the birth of algebraic notation (the manipulation of symbols to represent unknown quantities).

Although the roots of Algebra start in the middle east around the VIIIth century, the current notation doesn't really develop until the XIIIth or XIVth [0]

[0] http://cerebro.xu.edu/math/math147/02f/algebra/algebra.html

[jordigh]

I don't know, I think that dismissing Diophantus or the Greeks as not being modern enough is a bit strange. After all, we still use the exact algorithm as Euclid for finding gcds. We simply don't state it in geometric terms like he did.

I suppose if by modern mathematics one means algebra, then it's fair to place it somewhere in the 12th century.