Chapter 2 - A Historical Orientation
China's math was not extensive or influential.
Egyptian priests may have known that the 365-day Egyptian calendar was short a quarter of a day and kept it a secret.
Egyptians and Babylonians did only basic math. What about the pyramids? "A cabinet-maker need not be a mathemetician."
Greeks created new branches of culture: "philosophy, pure science, applied science, political thought and institutions, history writing, almost all literary forms except fictional prose". Their biggest contribution was the elevation of reason. Math only advanced after applying reason.
Romans were practical and didn't spend time on theory (math vs science, philosophers vs engineers).
Arabs contributed little. They incorporated Hindu Indian concepts, which they developed from contact with Greece.
Turks captured Eastern Roman Empire, causing Greek scholars to flee with manuscripts to Europe.
Gauss invented non-Euclidean geometry, with different axioms. Later supported by general relativity. "With the truth of mathematics undermined, realms of philosophy, science, and even some religious beliefs went up in smoke." One step away from a "Carl Gauss DESTROYS Priest" YouTube video. I'm skeptical and wish Kline provided examples.
"Although most Greeks did believe that mathematics existed independently of human beings as the planets and mountains seem to, and that all human beings do is discover more and more of the structure, the prevalent belief today is that mathematics is entirely a human product." Believing math exists independently from humans has been called the "romance of mathematics". The problem to be solved by those who reject it: the "unreasonable effectiveness of mathematics". We have developed math that has led to physics theories that were later verified by observation. If math is just a human tool, how can it predict physics that we have not observed?