The French mathematician Charles-Julien Brianchon was born in Sèvres, France on December 19, 1783. He died in Versailles, France on April 29, 1864.

Little is known of Brianchon's early life, except that he entered the École Polytechnique in 1804, where he studied under the geometer Gaspard Monge and read Carnot's work. As a student, he published his first paper in 1806, which contained a theorem that now bears his name. This theorem was an extension of a long-forgotten theorem that Pascal had proved in 1639, namely that if a hexagon is inscribed in a conic section, then the three points of intersection of the opposite sides always lie in a straight line. Brianchon's theorem stated that in any hexagon circumscribed about a conic section, the three diagonals cross each other at a single point. The theorems of Pascal and Brianchon later proved fundamental to the study of conics, and in special cases, to the study of pentagons, quadrilaterals, and triangles.

After graduating at the top of his class in 1808, Brianchon joined Napoleon's army as a lieutenant in the artillery. Serving in Spain and Portugal, he is said to have distinguished himself there. Military life took its toll on Brianchon's health, however, and after the end of the Napoleonic Wars in 1813, he applied for a teaching position. In 1818, he received an appointment as professor to the Artillery School of the Royal Guard.

Between 1816 and 1818, Brianchon published several works in geometry. In 1820, he co-authored an article with another graduate of the École Polytechnique, Jean-Victor Poncelet (1788-1867), that gave the first complete proof of the nine-point circle theorem, and made the first use of that term. By 1822, the focus of Brianchon's research had changed to include chemistry. Later, he ceased writing all together, and devoted his time entirely to teaching.

The theorems of Brianchon and Pascal formed the first clear instance of a pair of theorems that remain valid in plane geometry if the words point and line are interchanged. This notion was later exploited more fully by Poncelet.