Before we get over ourselves (structuralism in mathematics? game theory? please), I'd point out the simple things:
The deductive method (some Greek did it, most likely not Euclid). The basis of everything;
Logic (from Aristotle onward). The basis of almost everything;
The indo-arabic Decimal (and positional) system, which vastly increased computational capabilities and ways to think about quantities (including logarithms and the concept of order of magnitude);
The method of coordinates, introduced by Descartes and Fermat, which has
changes our idea of geometry,
established a relation between
algebra and geometry, and laid the
bais for the concept of space and
Calculus, by Leibnitz and Newton.
Need I say more?
The concept of probability (Fermat-Pascal), and the connection between probability and measure.