Jan Hudde’s Second Letter: On Maxima and Minima - Historical Setting: Life and Letters

Daniel J. Curtin (Northern Kentucky University)


The title page of van Schooten's 1659 second edition of Descartes' Geometria is shown above. (Source: Convergence's "Mathematical Treasures")

Jan Hudde (1628–1704) was born in Amsterdam and lived there his whole life, except for a year or two studying law in Leiden as a young man around 1648. There he also learned mathematics from Frans van Schooten, who emphasized the work of René Descartes. They continued to correspond on mathematical matters for another twenty years.

Hudde produced several mathematical works between 1654 and 1663, but largely abandoned the subject once he embarked on a career of political service in Amsterdam. He served several terms as one of the four Burgomasters who ran the city and held a number of other offices. We know that he used his mathematical abilities while in office, reducing Danish shipping charges by showing errors in their calculation, and championing Jan de Witt's new approach to life annuities, which employed careful mathematical analyses.

The Letters

Hudde wrote two intriguing letters to van Schooten (the second is translated here), both of which van Schooten included in the second edition of his Latin translation of Descartes’ Géometrie in 1659. Van Schooten had seen the need for a translation from Descartes’ French into the standard language of scholars, producing his first Latin translation in 1649. In fact, van Schooten related in his preface to his 1659 edition that in order to include Hudde’s two letters, which were written in Dutch (Belgicè), he translated them into Latin as well [Descartes] (see Note 1).

Perhaps more importantly, van Schooten also recognized that a commentary expanding Descartes’ often cryptic explanations was desirable. Florimond de Beaune contributed to van Schooten’s commentary, which included several works extending ideas found in the Géometrie. Among these were Hudde’s two letters.

Frans van Schooten inscribed the copy shown above of his Exercitationes mathematicae libri quinque (Five Books of Mathematical Exercises, 1657) to his student, Jan (or Johann) Hudde. This copy resides in the Columbia University Library; this image is part of Convergence's collection of "Mathematical Treasures." You may use the image in your classroom; for all other purposes, please seek permission from the Columbia University Library.

Note 1. I thank a referee for spotting this. See the third page of van Schooten’s Praefatio in [Descartes]. This is Screen 11 in the referenced 1695 photocopy, and image 15 in the referenced 1683 photo-image.