On 20th August 1672 a lynch mob killed Jan de Witt (1625 – 1672) and his brother Cornelis and mutilated their corpses in what was the high point or better said low point in the political power struggle in the United Provinces that followed the invasion of the country by the French at the start of the Franco-Dutch War. Jan de Witt had been Grand Pensionary of the State of Holland for the preceding twenty years and thus effectively the political leader of the county. The mob that murder him and his brother were Orangists, the political supporters of William of Orange who succeeded de Witt as the political leader of the United Provinces and who would become King of England in 1688.
Now regular readers of my scribblings are probably wondering why I have suddenly started to blog about 17th century Dutch politics instead of my usual diet of the history of science. The answer is quite simple Jan de Witt was not only a leading European politician but also a member of a group of prominent Dutch Cartesian mathematicians. I find this fascinating; just imagine a combination of David Cameron and Marcus du Sautoy, the mind boggles!
To explain the origins of this group we need to go back and look at the development of Dutch mathematics in the 17th century. The story of the United Provinces is truly fascination, in the 16th century the area we now know as Holland and Belgium was known as the Spanish Netherlands part of the feudal territories of the Spanish Habsburgs. Although the Habsburgs were also Holy Roman German Emperors their territories in the Low Countries were not part of the German Empire. In 1568 the Netherlands led by William I of Orange (William the Silent) rebelled against their Spanish overlords, the start of a long drawn out war with the original seven Untied Provinces declaring independence in 1581. The war actually dragged on for many more years with, for example, the telescope first seeing the light of day at one of the peace conferences in The Hague in 1608.
The new country began to acquire the trappings of statehood and in 1574, during the war, they established their own university in the city of Leiden. Previously students from the Low Countries had studied in Leuven, which was now in the provinces still controlled by Spain. The good burghers wanted their sons to have the best modern education and established a first class humanist university. However their concept of a good education did not include mathematics so at the beginning there was no chair for the subject. This was at the time not unusual; thanks to Phillip Melanchthon the Lutheran universities had chairs for mathematics whilst Christoph Clavius was still battling to get them established in Catholic universities. In England Oxford would first get its chairs for mathematics in the 1620s whereas Cambridge would have to wait till the 1660s. The students in Leiden had to wait until 1580 before the university appointed Rudolph Snel as its first professor for mathematics; Snel was succeeded by his son Willebrord at his death in 1613.
The university course was very theoretical although Holland had a strong tradition of practical mathematics and one of Snel’s contemporaries was Simon Stevin an engineer, practical mathematician and mathematical physicist on a level with Galileo. This changed in 1598 when the University of Franeker, established in 1585, called Adriaen Adriaenzoon, known as Metius, the son of the engineer Adriaen Anthonisz to their chair of mathematics. Metius, who had studied under Rudolph Snel and also Tycho Brahe in Denmark, lectured on practical mathematics, navigation, cartography, surveying etc. in Dutch and not Latin filling a great need in the young sea going nation. In 1600 Leiden obviously stung into action by the competition established a second lectureship for practical mathematics with lectures in the vernacular, the Duytsche mathematique. The course was designed by Stevin and the first lecturer was Ludolph van Ceulen famous for calculating Pi to 35 decimal places. During his time in Leiden Van Ceulen was also one of Willebrord Snel’s teachers. In 1610 his successor was one of his own students Frans van Schooten senior. Van Schooten’s eldest son was Frans van Schooten junior born in 1615. The younger van Schooten taught by his father became a student in Leiden in 1631. In 1632 he met Descartes for the first time and in 1637, having graduated two years earlier, he was asked by Descartes to help him prepare his La Géométrie for the press. With Descartes help he also took an extended study tour to France where he learnt the newest developments in mathematics. In 1643 he returned to Leiden and became his father’s assistant succeeding him as professor two years later.
Now established in Leiden van Schooten junior set up a Cartesian research group including four of his private pupils, Jan de Witt, Johann Hudde, Hendrick van Heuraet and Christiaan Huygens. These four were all the sons of rich politically influential burghers with a genuine interest for higher mathematics. The first three would all write important works on the analytical geometry of Descartes, which van Schooten published in his extended Latin translation of Descartes seminal work. This is not the place to go into Huygens’ spectacular career but with time he would rise to the position of Europe’s leading mathematical scholar before being deposed in his old age by Newton. Van Heuraet seemed content to enjoy the life of a rich heir with the fortune inherited from his father and plays not further part in our story.
Hudde and de Witt both studied law and went into politics. Jan de Witt, as we have already seen rose to become the most powerful politician in Holland whereas his friend Hudde became Mayor of Amsterdam and Governor of the Dutch East India Company. Interestingly both of them combined their interest in mathematics and politics and made fundamental contributions to the then emerging discipline of social statistics.
Van Schooten’s small Cartesian research group does not have a very high profile in the history of science but his Latin edition of The Geometry containing their combined efforts became the standard textbook for analytical geometry throughout Europe, its most famous reader being Isaac Newton who taught himself the new analytical mathematics using his copy.