Person: Hudde, Johann van Waveren
Johann Hudde was a Dutch mathematician who worked on maxima and minima and the theory of equations. He gave an ingenious method to find multiple roots of an equation.
Mathematical Profile (Excerpt):
- From around 1648 Johann attended the University of Leiden where he studied law.
- Van Schooten had established a vigorous research school in Leiden which included Hudde, and this school was one of the main reasons for the rapid development of Cartesian geometry in the mid 17th century.
- Sluze, Huygens, van Schooten, Hudde and van Heuraet corresponded regarding the properties of curves, in particular Hudde was interested in techniques for determining tangents and finding maxima and minima.
- From 1654 until 1663 Hudde worked on mathematics as part of van Schooten geometry research group at Leiden.
- This meant that Hudde was reappointed twenty-one times from his first appointment until his death.
- All of Hudde's mathematics was done before he began to work for the city council in 1663.
- A second two-volume translation of the same work (1659-1661) contained appendices by de Witt, Hudde and van Heuraet.
- Hudde worked on maxima and minima and the theory of equations.
- An example of Hudde's rule appeared first in van Schooten's Exercitatione mathematicae Ⓣ(Mathematical practice) in 1657.
- Hudde had no notion of the derivative, but his approach to finding maxima of algebraic expressions is procedurally similar to ours - and yet curiously different ...
- A fuller account of Hudde's rule was given in a letter he wrote dated 21 November 1659 which was not published at the time but, was published during the Newton-Leibniz controversy on who deserved priority for discovering the calculus, Hudde's letter was published as part of the evidence.
- This was entirely appropriate since Newton refers to Hudde's rule many times.
- Leibniz also studied Hudde's manuscripts and reported finding many excellent results.
- But Hudde made many more outstanding contributions.
- Hudde proposed a "mechanical" solution, which was not mathematically exact.
- In 1671 the city of Amsterdam was preparing to raise funds through the sale of a life annuity, and Johannes Hudde, a mathematician and city magistrate, investigated the appropriate price to set for the annuities.
- Using the theories of probability and demography being developed by his contemporaries Huygens and Graunt, Hudde gathered data from the records of a previous annuity issued in Amsterdam during the years 1586-90.
- Hudde's recommendations were used to establish the form of a life annuity issued by the city in 1672 and 1674.
- Hudde arranged the data that he had collected into a table headed by the age of the nominee at the time of purchase.
- We still have Hudde's table, for he included it in a letter he sent to Huygens on 18 August 1671.
- Hudde also corresponded with de Witt concerning annuities with letters between September 1670 and October 1671.
- In this correspondence he framed the law of mortality which today is attributed to De Moivre but properly should be attributed to Hudde.
- Although, on Hudde's recommendations, Amsterdam sold annuities at age dependent prices in 1672, there was no rapid move for others to adopt the practice.
- Hudde also corresponded with Huygens on problems of canal maintenance and together they undertook a review of the lower Rhine and IJssel rivers so that they could produce a strategy to prevent the rivers from silting up.
- Greatly respected and a man of great influence, many dedicated their works to Hudde.
Born 23 April 1628, Amsterdam, Netherlands. Died 15 April 1704, Amsterdam, Netherlands.
View full biography at MacTutor
Tags relevant for this person:
Analysis, Origin Netherlands
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive