Except that the Chinese did not reject irrational numbers, but simply did not find the distinction to be important enough to explore. They had a notion of numb

Except that the Chinese did not reject irrational numbers, but simply did not find the distinction to be important enough to explore. They had a notion of numbers that could not be computed exactly (i.e. they could only get a sequence of better approximations) but they were satisfied as long as an algorithm existed (I imagine they might have rejected the concept of non-computable numbers, had such a concept existed at the time). There was a time when the Greeks firmly believed that all numbers are rational and explicitly rejected (not simply ignored) irrational numbers, and later they had a strong interest in the separation between rationals and irrationals. The difference between the Chinese and the Greeks was not just explicitly stating axioms (Chinese math was also a system built from basic principles, they just did not organize things as neatly as the Greeks), but their view of what computation is. The Greeks tried to map all computation onto Euclidean geometry, whereas the Chinese generally viewed computation as symbolic manipulation and tried to map all math (including geometry) into computation problems. I see that as a very big difference that had a big impact on how the two traditions developed.