Subject: Re: [HM] Hudde
From: Paul Vitanyi (Paul.Vitanyi@cwi.nl)
Date: Tue Mar 28 2000 - 07:45:29 EST
> http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Hudde.html
>
> we read:
>
> <quote>
> Hudde worked on maxima and minima and the theory of equations. Hudde
> gave an ingenious method to find multiple roots of an equation which
> is essentially the modern method of finding the highest common factor
> of a polynomial and its derivative.
> </quote>
>
> Antreas
This does Hudde little justice. One of the very few mathematicians who
were also prominent in government (others being Johan de Witt and Isaac
Newton (after a fashion) and more recently Paul Painleve (French Prime
Minister in the early 1900's), he is often credited as a father of
Actuarial Mathematics (insurance mathematics) together with Johan de Witt
(then Governor of the Dutch Republic). This was related to the new
mercantile enterprizes of the new Dutch Republic which required
cooperations between merchants and insurance of their common enterprizes.
This also spawned the first stock exchange in Amsterdam (1602?):
Johann van Waveren Hudde
Born: 23 April 1628 in Amsterdam, Netherlands
Died: 15 April 1704 in Amsterdam, Netherlands
Johann Hudde attended the University of Leiden to study law. However he
was introduced to mathematics at Leiden by his teacher van Schooten. From
1654 until 1663 he worked on mathematics as part of van Schooten geometry
research group at Leiden. From 1663 he worked in various roles for the
Amsterdam City Council. He served for 30 years as burgomaster of Amsterdam
being first appointed in 1672.
All of Hudde's mathematics was done before he began to work for the city
council in 1663. Van Schooten edited and published a second two-volume
translation of Descartes's La Ge/ome/trie (1659-1661) which contained
appendices by de Witt, Hudde and van Heuraet.
Hudde worked on maxima and minima and the theory of equations. Hudde gave
an ingenious method to find multiple roots of an equation which is
essentially the modern method of finding the highest common factor of a
polynomial and its derivative.
He was the first to treat the coefficients in algebra without considering
whether they were positive or negative in De reductione aequationum. In
1656 he gave the power series expansion of ln(1+x). The following year he
directed the flooding of parts of Holland to block the advance of the
French army.
Hudde also worked on optics, producing microscopes and constructing
telescope lenses.
Hudde corresponded with Huygens on problems of canal maintenance,
probability and life expectancy. Leibniz studied Hudde's manuscripts and
reported finding many excellent results. The manuscripts must have had an
important influence on Leibniz's introduction of the calculus.
Descartes produced an important method of determining normals in La
Ge/ome/trie in 1637 based on double intersection. De Beaune extended his
methods and applied it to tangents where double intersection translates
into double roots. Hudde discovered a simpler method, known as Hudde's
Rule, which basically involves the derivative. Descartes' method and
Hudde's Rule were important in influencing Newton.
John Hudde (1633-1704) was first to allow a letter to represent a positive
or negative number, in 1657 in De reductione aequationum, published at
the end of the first volume of F. Van Schooten's second Latin edition
of Ren/e Descartes' G/eom/etrie (Cajori vol. 2, page 5).
This archive was generated by hypermail 2b28 : Tue Mar 28 2000 - 10:31:13 EST