Jean Prestet (1648–1690) was a French Oratorian

priest A priest is a religious leader authorized to perform the sacred rituals of a religion, especially as a mediatory agent between humans and one or more deity, deities. They also have the authority or power to administer religious rites; in parti ...

and

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

who contributed to the fields of

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

and

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

. Prestet grew up poor. As a teenager, he worked as a servant of the

Oratory of Jesus The Congregation of the Oratory of Jesus and Mary Immaculate (, ), best known as the French Oratory or Oratory of Jesus, is a society of apostolic life of Catholic priests founded in 1611 in Paris, France, by Pierre de Bérulle (1575–1629), w ...

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

. He was promoted to secretary for

Nicolas Malebranche Nicolas Malebranche ( ; ; 6 August 1638 – 13 October 1715) was a French Oratorian Catholic priest and rationalist philosopher. In his works, he sought to synthesise the thought of St. Augustine and Descartes, in order to demonstrate the ...

, who taught him mathematics. Under the guidance of Malebranche, Prestet began work in 1670 on the textbook ''Elémens des Mathématiques''. Unusually for the time, the textbook focused exclusively on algebra but did not cover geometry at all. Prestet believed that algebra was the most fundamental field of mathematics, and geometry merely applied algebra. Gert Schubring writes that " e 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 philosophy, rationalism is the Epistemology, epistemological view that "regards reason as the chief source and test of knowledge" or "the position that reason has precedence over other ways of acquiring knowledge", often in contrast to ot ...

in France." The book contained a proof of Descartes' rule of signs that Prestet later acknowledged to be incomplete. It also included a generalization of

Euclid's lemma In algebra and number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers: For example, if , , , then , and since this is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well. In ...

to non-prime divisors. ''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 The Society of Jesus (; abbreviation: S.J. or SJ), also known as the Jesuit Order or the Jesuits ( ; ), is a religious order (Catholic), religious order of clerics regular of pontifical right for men in the Catholic Church headquartered in Rom ...

. ''Elémens'' was one of several textbooks published around that time by notable Oratorian mathematics instructors including Bernard Lamy. Abraham de Moivre used ''Elémens'' in an abortive early attempt to teach himself mathematics. 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. This edition included some early work on the

fundamental theorem of arithmetic In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 is prime or can be represented uniquely as a product of prime numbers, ...

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