Posted by Myrtle on 18:03 Jan 11
In Reply to: Mathy People: Good history of math book? (m) posted by SPH
The Greeks had two different words for math. One was for calculational math, that was what you needed to be a shopkeeper, the other was math theory, a la Plato's Theatetus, Euclid, et al. The Romans didn't give a flip about theory and just did what it took to get the bridges built and there is a wonderful quote by Cicero about this...can't find the quote.
The ancient way of teaching math, for the educated ancients, involved a philosophical approach and justification. We certainly have strived to teach math this way and even have found an old out of print high school algebra book that teaches logic and then applies it proofs in algebra as it develops algebra axiomatically. (Think two column proofs in algebra)
What did folks do without "zero" as a placeholder, a number system with place value, etc? Well, engineering suffered. It's amazing that those pirate ships of the 1600 and 1700 hundreds, and even into the 1800s were built by rules of thumb and intution on the part of innumerate and illiterate shipbuilders!
More on fractions in the Middle Ages: http://liberabaci.blogspot.com/