François Budan de Boislaurent

Who was François Budan de Boislaurent?

Ferdinand François Désiré Budan de Boislaurent was a French amateur mathematician, best known for a tract, Nouvelle méthode pour la résolution des équations numériques, first published in Paris in 1807, but based on work from 1803.

Budan was born in Limonade, Cap-Francis, Saint-Domingue on 28 September 1761. His early education was at Juilly, France. He then proceeded to Paris where he studied medicine, receiving a doctorate for a thesis entitled Essai sur cette question d'économie médicale : Convient-il qu'un malade soit instruit de sa situation? Budan died in Paris on 6 October 1840

Budan explains in his book how, given a monic polynomial p(x), the coefficients of p can be obtained by developing a Pascal-like triangle with first row the coefficients of p(x), rather than by expanding successive powers of x+1, as in Pascal's triangle proper, and then summing; thus, the method has the flavour of lattice path combinatorics. Taken together with Descartes' Rule of Signs, this leads to an upper bound on the number of the real roots a polynomial has inside an open interval.