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?