Friday 27 August 2010


Glancing through an old MAA Mathematics Magazine in a list of prominent contributors to the early science of analytic geometry was the name the Dutch politician, Johann Hudde.....

Johann WHO, dude? How do they list a guy with Pascal and Fermat and Descartes and I never heard the name?

It appears that the rise of Leibniz/Newtons calculus based on limits essentially obliterated the record (for most of us) of a brief period when the early calculus flourished with a method that was based on analytic geometry and no Limits...that’s right, calculus without limits.

I searched for Hoode and was hooked when I found a quote that described a comment about him by Leibniz
Leibniz in particular was impressed with Hudde’s work, and when Johann Bernoulli proposed the brachistochrone problem, Leibniz lamented:
If Huygens lived and was healthy, the man would rest, except to solve your problem. Now there is no one to expect a quick solution from, except for the Marquis de l’H╦ćopital, your brother [Jacob Bernoulli], and Newton, and to this list we might add Hudde, the Mayor of Amsterdam, except that some time ago he put aside these pursuits .

When I found the whole article, it turned out to be an interesting historical, mathematical journal entry, "The Lost Calculus (1637-1670), Tangency and Optimization without Limits", by Jeff Suzuki in the MAA Mathematics Magazine, Dec, 2005.

In A History of Mathematics, by Cajori, we find that Hudde was the first to use three variables in analytic geometry.

The article by Suzuki would seem to be a wonderful historical read for calculus teachers who, like me, never heard of Hudde’s rule.

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