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.
They didn't rejected it for computational reason. They rejected it because it didn't fit in their framework of how number works.
That's the whole point of the evolution of math that culminated into the subject of real analysis.
If that wasn't the point of why you brought the greek up then it doesn't make sense why you bought it up other than the main topic of the Chinese, computation, etc...
This isn't just the chinese. The ancient greeks rejected ( or ignored ) irrational numbers too. Also, western math was just as computationally driven. Pretty much all math everywhere developed for practical purposes ( ie to divide land, more accurate calendar, etc ).
> There is a profound difference in philosophy, as evidenced by the title of this entire thread: the Chinese were "solving" 14th degree polynomials
No there isn't. The ancient greeks also "solved" equations, such as for volume of geometrical objects, by approximation. That's why they didn't invent calculus ( though sometimes math historians try to twist the definition and meaning and understanding of calculus to claim ancient greeks did ).
The fundamental difference is that ancient greeks developed explicit axiomatic mathematics while the chinese didn't. But practical computational mathematics is the foundation of all mathematics.