Descartes: A Biography

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Retreat and Defence (–) 

Etienne Pascal, while Descartes sent the manuscript of the ́ Essaysto

Mersenne.

Before the unlikely coincidence of two mathematicians independently

developing analytical methods inspired by Viete, Descartes had already`

criticized both Beaugrand and Roberval. When Beaugrand claimed that

Descartes had plagiarized some of his results from Viete, the author of the`

G ́eometriecommented very negatively on Beaugrand’sGeostatics.Gilles

Personne de Roberval (–) was an outstanding mathematician,

six years younger than Descartes, who had been appointed to the Ramus

Chair of Mathematics at the Coll`ege Royal in. The chair was filled

byopen competition, and the successful appointee had to re-enter the

competition every three years in order to maintain his post. Roberval

managed to do this for thirty-four years, until he died in;however,

he could maintain his advantage over the other competitors only by not

publishing his results and reserving them for the triennial competition.

During the first competition for appointment in, when candidates

were set various questions to resolve, Descartes commented acidly that

he should have been asked ‘a more difficult question, to see if he could

resolve it – such as, for example, the Pappus problem that I was given three

years ago by Mr. Golius’ (i.). It is obvious that Descartes thought of

Roberval as an inferior mathematician, and he seems to have been jealous

of the high respect in which their common correspondent, Mersenne, held

him.

The first contact between Descartes and Fermat occurred when Beau-

grand received the text of Descartes’Essaysin his capacity as secretary to

the French chancellor. He passed on a copy of theDioptricsto his friend

Fermat,and invited him to comment. Fermat penned his comments in

April or May.It is clear from the style of this first letter to Descartes

that Fermat did not know the author of theDioptrics, that he was unaware

of earlier animosities between Descartes and Roberval or Beaugrand, and

that he was stumbling into a potentially explosive situation based on a

very brief perusal of a book that was destined to become famous.The

initial correspondence between the two mathematicians was also compro-

mised because theDioptricshad been released without authorization by

Beaugrand, before its official publication, and because Fermat implied

that Descartes was ‘groping about...in the shadows’ in search of the

truth, a procedure that he had explicitly disavowed in the unpublished

Rules.