"Pythagoras... assumed as first principles the numbers and symmetries existing among them, which he calls harmonies, a…"

"If the early Greeks were cognizant of Babylonian algebra, they made no attempt to develop or even to use it, and ther…"

"With the intrusion of irrational numbers to disrupt the integral harmonies of the Pythagorean cosmos, a controversy t…"

"By the ancients [Greeks], arithmetic was studied through geometry. If a number was regarded as simple, it was a line.…"

"For measurements of time he collected and weighed water flowing from a container at a constant rate of about three fl…"

"A critical step was made sometime before the ninth century AD, when a new partial script was invented, one that could…"

"The arithmetization of mathematics... which began with Weierstrass... had for its object the separation of purely mat…"

"In speaking of arithmetic (algebra, analysis) as a part of logic I mean to imply that I consider the number concept e…"

"In Greek theoretical mathematics (as distinguished from practical or commercial arithmetic) a fraction that we would …"

"Ten is the nature of number. All Greeks and all barbarians alike count up to ten, and having reached ten revert again…"