Descartes: A Biography

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 Descartes: A Biography

Cartesian mathematics, were doing their best to discredit it. Given their

limited ability, their objections did not make him work hard. However,

they did enough to distract him ‘in the same way that two or three flies,

flying around the face of a man who tries to relax by lying in the shade of

awood, are often able to prevent him from doing so’ (ii.).

In retrospect, the row between Fermat and Descartes was sustained by

misunderstandings on both sides, by the extreme sensitivity of Descartes

to any criticism of hisGeometry, and by a difference in temperament

that made it difficult for either of them to sympathize with the other.

Fermatwas primarily a mathematician rather than a physicist, and his

initial reaction to Descartes’Dioptricsshows that he suspected its author of

constructing an a priori proof of the sine law of refraction. He was unaware

of the background principles on which Descartes based his work, because

they were available only in the unpublishedWorld, and his own natural

tendency was toward an empiricist approach to optics.Since Fermat was

unwilling to have his mathematical results published, he is probably best

understood as a relatively innocent and reluctant critic of an extremely

defensive opponent who thought of his reputation as depending on the

originality of the analytic methods that he had independently developed

in theGeometry.

The lack of resolution in the dispute with the French mathemati-

cians contrasts with the pragmatism and diplomacy involved in resolving

another mathematical row between supporters and critics of Descartes in

the United Provinces. Johan Stampioen (the younger) was highly respected

as a mathematician by his contemporaries. He taught mathematics at a

‘higher school’ in Rotterdam, and he issued a number of public chal-

lenges, on placards, into Dutch engineers to calculate the most

effective angles for shooting canon shells at a fortress wall. He then pub-

lished a book, dedicated to Prince Frederik Hendrik, in which he claimed

to provide the only solution to such problems.

These claims were challenged by Jacob van Waessenaer, who not only

offered an alternative solution for extracting cube roots, using Descartes’

mathematics, but also claimed that there were ‘gross errors’ in Stampioen’s

book. In defence of his honour and reputation, Stampioen challenged his

critic to support his claims by a wager. This challenge was accepted, and

both disputants lodged six hundred guilders with an impartial referee

and agreed on a three-person jury of mathematical experts to decide the

question.Stampioen argued in favour of a one-person jury, claiming that