Person: Van Schooten, Frans
Frans van Schooten was a Dutch mathematician who was one of the main people to promote the spread of Cartesian geometry.
Mathematical Profile (Excerpt):
- Sometimes the Latin version Franciscus van Schooten is used.
- Frans van Schooten Senior studied mathematics under Ludolph van Ceulen at the Engineering School in Leiden.
- However, van Ceulen died in 1610 while van Schooten Senior was still a student.
- In 1612 van Schooten Senior filled the vacant position at the Engineering School, and he was given the title of professor three years later.
- Van Schooten Senior published works such as a treatise on perspective in 1600, Tabulae sinuum tangentium secantium, ad radium 10000000 Ⓣ(Tables of sines, tangents and secants, to a radius of 10000000) in 1627, and a Dutch translation of Euclid's Elements.
- Stevin drew up the mathematical teaching programme for the School and Ludolph van Ceulen and Simon Fransz van Merwen were appointed as the first lecturers in the School.
- He had read Ludolph van Ceulen's Arithmetische en geometrische Fondamenten Ⓣ(Arithmetic and geometric fundamentals), Albert Girard's Invention nouvelle en l'algèbre Ⓣ(A new discovery in algebra), as well as Girard's edition of Stevin's Arithmetique and Bonaventura Cavalieri's work on indivisibles.
- Van Schooten was also familiar with the classical Greek texts having read Frederico Commandino's editions of works by Archimedes, Apollonius and Pappus.
- It was through Gool that van Schooten Junior was first introduced to Descartes in 1632.
- Van Schooten Junior graduated with his Artium Liberalium Magister from the University of Leiden in 1635.
- Two years later when Descartes was visiting Leiden he again met van Schooten Junior.
- At this stage Discours de la méthode Ⓣ(Discourse on method) with its appendix La Géométrie Ⓣ(Geometry) had not been published and Descartes asked van Schooten Junior to assist with making the illustrations.
- Strongly influenced by Descartes, van Schooten Junior wrote Recueil de calcul pour l'intelligence de la Geometrie de Monsr des Cartes Ⓣ(Compendium of calculation for the understanding of the geometry of Descartes), a short work on symbolic algebra, around 1639.
- This contact with Descartes proved important for van Schooten since Descartes provided contacts for van Schooten to become acquainted with Marin Mersenne's circle in Paris on an extended period of travel.
- Around 1641 he set out, travelling first to Paris where he met Mersenne and learnt about the mathematical advances made by Viète and Fermat as well as having the opportunity to further his studies of Descartes' works.
- Fermat's results were contained in treatises that were circulating in manuscript form and van Schooten took the opportunity to make copies of them.
- Continuing his travels, van Schooten left Paris and went to London where he stayed until 1643 discussing mathematics with leading mathematicians there, finally visiting Ireland before returning to Leiden.
- The house was in Herensteeg, a street overlooking the Pieterskerk (St Peter's Church) which contained van Ceulen's grave with a tombstone on which 35 places of π were engraved.
- Van Schooten was one of the main people to promote the spread of Cartesian geometry and this is a more important contribution than the results of his own researches.
- It is claimed that Descartes, who went to Stockholm in 1649, opposed this project by van Schooten.
- Living a retired bachelor's life, he made his ideas known through highly advanced books and correspondence with his peers.
- The triumph of Cartesian ideas in mathematics, the creation of a Cartesian school of thought, both in Holland and to a certain extent also abroad, is in no small degree due to the Leiden professor Frans van Schooten.
- Van Schooten established a vigorous research school in Leiden which included his private pupils Christiaan Huygens, Henrik van Heuraet and Johannes Hudde, and this school was one of the main reasons for the rapid development of Cartesian geometry in the mid 17th century.
- After his students had left Leiden, van Schooten, Huygens, Hudde and van Heuraet corresponded regarding the properties of curves and other topics at the forefront of research at the time.
- Most of the correspondence was directed through van Schooten in the sense that his students would write to him to explain their discoveries and he would inform the others as well as publish certain of their results as appendices to his own publications.
- but on the whole van Schooten confined himself to mathematics proper.
- Van Schooten had several bright private students, Christiaan Huygens, Johannes Hudde, Henrik van Heuraet, Johan Witt and others, constituting an active audience for Cartesian mathematics.
- The structure of the group primarily depended on personal contacts with van Schooten, who guided his chosen students into doing research, and would include their results in his own publications, especially in the 1659-1661 edition of the 'Géométrie'.
- This 1659-1661 edition contained appendices by three of van Schooten disciples, Jan de Witt, Johan Hudde, and Hendrick van Heuraet.
- In this book van Schooten gives a methods to find these numbers which he hoped would lead to the discovery of further pairs of amicable numbers - this however did not happen.
- Typical of van Schooten's publications, Exercitationes mathematicae Ⓣ(Mathematical exercises) also contained an appendix by one of his students.
- It was from Exercitationes mathematicae Ⓣ(Mathematical exercises) by van Schooten that Isaac Newton learnt much of his mathematics while a student at Cambridge.
- Pieter van Schooten continued in this position until his death in 1679.
Born 15 May 1615, Leiden, Netherlands. Died 29 May 1660, Leiden, Netherlands.
View full biography at MacTutor
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Origin Netherlands
Thank you to the contributors under CC BY-SA 4.0! 
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- @J-J-O'Connor
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References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
