#### Explore the life and contributions of Gilles Personne de Roberval, a French mathematician known for his work on quadrature, tangents, and his contentious relationship with René Descartes. Learn about his significant works and diverse intellectual pursuits.

**Gilles Personne de Roberval (August 10, 1602 – October 27, 1675),** a French mathematician, was born in Roberval near Beauvais, France on August 10, 1602. Originally named Gilles Personne or Gilles Personier, Roberval’s birthplace gave him his surname.

### Biography

Roberval’s early years intersected with historical events; he, like René Descartes, was present at the siege of La Rochelle in 1627. His intellectual pursuits led him to Paris the same year, and by 1631, he assumed the philosophy chair at Gervais College, Paris. In 1633, he was also appointed to the prestigious chair of mathematics at the Royal College of France. A unique condition of this position was that the holder, in this case Roberval, would propose mathematical questions for solution and resign if anyone solved them better. Despite this provision, Roberval retained the chair until his passing.

Roberval belonged to a group of mathematicians who, just before the advent of the infinitesimal calculus, focused on problems that demanded solutions involving limits or infinitesimals, later addressed by calculus. His work delved into the quadrature of surfaces and the cubature of solids, which he achieved, particularly in simpler cases, through an original method he termed the “Method of Indivisibles.” However, his credit for this discovery was somewhat diminished as he kept his method private, while Bonaventura Cavalieri independently published a similar approach he had devised.

Another significant contribution by Roberval was a broad method for drawing tangents, conceptualizing a curve described by a moving point whose motion is the result of several simpler motions. Additionally, he developed a method to derive one curve from another, a technique used to calculate finite areas equal to the regions between specific curves and their asymptotes. Evangelista Torricelli later dubbed these curves “Robervallian lines,” which were also employed in certain quadratures.

However, a notable aspect of Roberval’s career was his contentious relationship with René Descartes. Roberval harbored ill will towards Descartes due to criticisms of his methods, alongside those of Pierre de Fermat. This animosity led Roberval to critique and oppose the analytical methods Descartes introduced to geometry during this era.

Beyond his contributions to pure mathematics, Roberval also delved into other scientific realms. He authored a work on the system of the universe, where he supported the Copernican heliocentric system and proposed a mutual attraction among all particles of matter. Additionally, he invented a special kind of balance known as the Roberval Balance.

### Works

Roberval’s significant works include:

*Traité de Mécanique des Poids Soutenus par des Puissances sur des Plans Inclinés à l’Horizontale*(1636).*Le Système du Monde d’après Aristarque de Samos*(1644).*Divers Ouvrages de M. de Roberval*(1693).

In these works, he delves into mechanics, the system of the world according to Aristarchus of Samos, and various other topics that showcase the breadth of his intellectual pursuits.