Greek Mathematical Thought and the Origin of Algebra

Description

Jeff Kalb cites this in his Music and Measurement: An the Eidetic Principles of Harmony and Motion (St. Cecilia's Feast Day, 2016).

Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13 th–16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

Historians of science have usually assumed that the mathematicians of the Renaissance took up where prior mathematicians had left off. This important work argues that during the sixteenth century a crucial change in the concept of number took place which distinguishes ancient and modern mathematics once and for all. The author regards Francois Vieta as "the true founder of modern mathematics" and demonstrates that to this development of symbolic algebra corresponds a fundamental change in the concept of the number. "...it is to be hoped that someone before long will make searching a study of Arabic algoristic impulsion toward modern algebra as Klein has made of Greek philosophical stimuli. Historians...will be grateful... for the very welcome inclusion of a long-desired English translation of Vieta's Introduction to the Analytical Art." --Science "Historians of ideas will be reminded of numerous struggles in other fields paralleling these attempts to overcome or accommodate vestiges of the traditional but no longer useful concept of the number. The thoroughness of this work will ensure that it will remain a standard reference for a long time to come." --British Journal for the Philosophy of Science

Jacob Klein (1899-1978) came to St. John's College, Annapolis, in 1938, and remained a Tutor there until his death. From 1949 to 1958 he was Dean. In addition to the lectures and essays collected here, he was author of three books: Greek Mathematical Thought and the Origin of Algebra, A Commentary on Plato's Meno , and Plato's Trilogy: Theaetetus, the Sophist, and the Statesman.