Benjamin Olinde Rodrigues (1795–1851), more commonly known as Olinde Rodrigues, was a French

France

The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 banker, mathematician

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, and social reformer

Reform movement

A reform movement is a kind of social movement that aims to make gradual change, or change in certain aspects of society, rather than rapid or fundamental changes...

.

Rodrigues was born into a well-to-do Sephardi Jewish family in Bordeaux

Bordeaux

Bordeaux is a port city on the Garonne River in the Gironde department in southwestern France.The Bordeaux-Arcachon-Libourne metropolitan area, has a population of 1,010,000 and constitutes the sixth-largest urban area in France. It is the capital of the Aquitaine region, as well as the prefecture...

.

Rodrigues was awarded a doctorate

Doctorate

A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder to teach in a specific field, A doctorate is an academic degree or professional degree that in most countries refers to a class of degrees which qualify the holder...

 in mathematics on 28 June 1815 by the University of Paris

University of Paris

The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...

. His dissertation contains the result now called Rodrigues' formula

Rodrigues' formula

In mathematics, Rodrigues's formula is a formula for Legendre polynomials independently introduced by , and...

.

After graduation, Rodrigues became a banker. A close associate of the Comte de Saint-Simon

Claude Henri de Rouvroy, comte de Saint-Simon

Claude Henri de Rouvroy, comte de Saint-Simon, often referred to as Henri de Saint-Simon was a French early socialist theorist whose thought influenced the foundations of various 19th century philosophies; perhaps most notably Marxism, positivism and the discipline of sociology...

, Rodrigues continued, after Saint-Simon's death in 1825, to champion the older man's socialist

Socialism

Socialism is an economic system characterized by social ownership of the means of production and cooperative management of the economy; or a political philosophy advocating such a system. "Social ownership" may refer to any one of, or a combination of, the following: cooperative enterprises,...

 ideals, a school of thought that came to be known as Saint-Simonianism

Saint-Simonianism

Saint-Simonianism was a French political and social movement of the first half of the 19th century, inspired by the ideas of Claude Henri de Rouvroy, comte de Saint-Simon ....

. During this period, Rodrigues published writings on politics, social reform, and banking.

In 1840 he published a result on transformation groups, which amounted to a discovery of the quaternion

Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...

s, in all but name, three years prior to William Rowan Hamilton

William Rowan Hamilton

Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...

's. However, during his own times, his work on mathematics was largely ignored, and he has only been rediscovered late in the twentieth century.

Rodrigues is remembered for three results: Rodrigues' rotation formula

Rodrigues' rotation formula

In the theory of three-dimensional rotation, Rodrigues' rotation formula is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix from an axis-angle representation...

 for vectors; and the Rodrigues formula about series of orthogonal polynomials

Orthogonal polynomials

In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...

; and the Euler–Rodrigues parameters.

He died in Paris in 1851.