"The Greek search for essences had led the Pythagoreans to picture the universe as a multitude of mathematical points completely subject to the laws of number—a sort of arithmetic geometry... The rival Eleatic philosophy of Parmenides upheld the essential "oneness" of the universe and the impossibility of analyzing it in terms of the "many." Zeno of Elea sought dialectically to defend his master's doctrine by demolishing the Pythagorean association of multiplicity with number and magnitude. ...The paradoxes, as one sees now, involve such notions as infinite sequence, limit, and continuity, concepts for which Zeno nor any of the ancients gave precise definition. ...their influence was profound. The Greeks banned from their mathematics any thought of an arithmetic continuum or of an algebraic variable, ideas which might have led to analytic geometry; and they refused to place any confidence in infinite processes, the methods which would have led to calculus. Whereas the Pythagoreans had envisioned a union of arithmetic and geometry, Greek mathematicians after Zeno saw only the mutual incompatibility of the two fields."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Carl B. Boyer, History of Analytic Geometry (1956)
https://en.wikiquote.org/wiki/Ancient_Greek_mathematics
Revision History
No revisions have been submitted for this quote.
Categories
Ancient Greek mathematics
Ancient was developed from the 7th century BC to the 4th century AD by Greek speaking peoples along the shores of the Eastern Mediterranean. The period following Alexander the Great is sometimes referred to as Hellenistic mathematics. The word "mathematics" itself derives from the ancient Greek μάθημα (mathema), meaning "subject of instruction". The use of generalized mathematical theories and proofs is the key difference between Greek mathematics and those of preceding civilizations.
57 quotes on TrueQuotesView all quotes by Ancient Greek mathematics →
Related Quotes
"Had the early Greek mind been sympathetic to the algebra and arithmetic of the Babylonians, it would have found plent…"
"The Greeks ordinarily are regarded as the founders of mathematics in the strict sense... for they emphasized the valu…"
"That the discovery of incommensurability of lines made a strong impression on Greek thought is indicated by the story…"
"In mathematics... the Greek attitude differed sharply from that of the earlier potamic cultures. The contrast was cle…"
"In the Greek world mathematics was more closely related to philosophy than to practical affairs, and this kinship has…"
"These three problems—the , the duplication of the cube, and the trisection of the angle—have since been known as the …"
"Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the pro…"
"Euclid, Archimedes, and Apollonius brought geometry to as high a state of perfection as it perhaps could be brought w…"
"Thus, it is again a conclusion to be assumed in advance, only waiting for a confirmation, that Greek mathematics had …"
"If the early Greeks were cognizant of Babylonian algebra, they made no attempt to develop or even to use it, and ther…"