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Ferdinand François Désiré Budan de Boislaurent (September 28, 1761 – October 6, 1840) was a French mathematician, best known for a theorem of 1807 that provides an upper bound on the number of the real roots a polynomial has inside an open interval. The statement of Budan's theorem had been forgotten for about 150 years and had been replaced by the statement of an equivalent theorem by Fourier.

François Budan was born in Limonade, Cap-Francis, Saint-Domingue (now Haiti) on 28 September 1761.

Budan was educated in Juilly, France, before studying medicine in Paris where he received his doctorate degree for his thesis entitled "Essai sur cette question d'économie médicale : Convient-il qu'un malade soit instruit de sa situation?"

In 1803, Budan made his greatest mathematical discovery, with a rule which explains how a polynomial equation may have n real roots between two given numbers. The rule was published in 1807, and his proof was prepared in 1811 and published in 1822.

Budan died in Paris on 6 October 1840.
Published works

Nouvelle méthode pour la résolution des équations numériques d'un degré quelconque, Dondey-Dupré, Paris, 1822

Sources

Bio at School of Mathematics and Statistics, University of St Andrews, Scotland
Ferdinand François Désiré Budan de Boislaurent bio at gap-system.org
Livres Numérisés Mathématiques, Université Joseph Fourier
The MathNet, Korea

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