Prestet grew up poor. As a teenager, he worked as a servant of the Oratory of Jesus in Paris. He was promoted to secretary for Nicolas Malebranche, who taught him mathematics.
Under the guidance of Malebranche, Prestet began work in 1670 on the textbook Elémens des Mathématiques.[4] Unusually for the time, the textbook focused exclusively on algebra but did not cover geometry at all.[5] Prestet believed that algebra was the most fundamental field of mathematics, and geometry merely applied algebra.[6]: 461 Gert Schubring writes that "[t]he self-confidence of Prestet in claiming superiority for the 'moderns' over the 'ancients' … proved to be a bold and modernizing approach, disseminating Cartesian conceptions and preparing the way for rationalism in France."[6]: 137
The book contained a proof of Descartes' rule of signs that Prestet later acknowledged to be incomplete.[7] It also included a generalization of Euclid's lemma to non-prime divisors.[8]
Elémens was published in 1675 by the Oratorian order for use in the curriculum of the many Oratorian colleges. Starting in the early 17th century, the order had founded colleges in smaller cities and towns to challenge the influence of the Jesuits. Elémens was one of several textbooks published around that time by notable Oratorian mathematics instructors including Bernard Lamy.[6]: 137 Abraham de Moivre used Elémens in an abortive early attempt to teach himself mathematics.[9]
With the publication of Elémens, Prestet's reputation as a mathematics instructor grew. He was appointed the mathematical chair at the University of Angers in 1681. A revised and expanded edition, titled Nouveaux Elémens des mathématiques, was published in 1689.[10] This edition included some early work on the fundamental theorem of arithmetic.[1]
References
^ abGoldstein, Catherine (1992). "On a Seventeenth Century Version of the "Fundamental Theorem of Arithmetic"". Historia Mathematica. 19 (2): 177–187. doi:10.1016/0315-0860(92)90075-m.
^
Schneider, Ivo (2005). "Jakob Bernoulli, Ars Conjectandi (1713)". In Grattan-Guinness, I. (ed.). Landmark Writings in Mathematics 1640–1940. Elsevier. p. 96. ISBN0-444-50871-6.
^Knobloch, Eberhard. "Renaissance Combinatorics". In Wilson, Robin; Watkins, John J. (eds.). Combinatorics: Ancient & Modern. Oxford. p. 141.
^Asselah, Katia (2005). Arithmétique et algèbre dans la deuxième moitié du XVIIe siècle français : les Elemens et Nouveaux éléments des mathématiques de Jean Prestet. University Paris VII (Ph D thesis).
^
Schrubring, Gert (2005). Conflicts Between Generalization, Rigor, and Intuition. Springer. p. 52. ISBN0-387-22836-5.
^
Cajori, Florian (1910), A History of the Arithmetical Methods of Approximation to the Roots of Numerical Equations of One Unknown Quantity, Colorado Springs, Colorado: Colorado College, p. 186
^Euclid. Les Éléments, traduction, commentaires et notes (in French). Vol. 2. Translated by Bernard Vitrac. pp. 338–339.
Robinet, André (1960). "Jean Prestet ou la bonne foi cartésienne (1648–1691)". Revue d'histoire des sciences et de leurs applications (in French). 13 (2): 95–104. doi:10.3406/rhs.1960.3805.
