**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.

- 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.

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Analysis, Origin Netherlands

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive