After graduation, Rodrigues became a banker. A close associate of the Comte de Saint-Simon, Rodrigues continued, after Saint-Simon's death in 1825, to champion the older man's socialist ideals, a school of thought that came to be known as Saint-Simonianism. During this period, Rodrigues published writings on politics, social reform, and banking.
In 1840 he published a result on transformation groups, which applied Leonhard Euler's four squares formula, a precursor to the quaternions of William Rowan Hamilton, to the problem of representing rotations in space. 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 noted for the first recorded use of term, avant-garde, in his essay, "L'artiste, le savant et l'industriel" ("The artist, the scientist and the industrialist", 1825). He calls on artists to "serve as [the people's] avant-garde", insisting that "the power of the arts is indeed the most immediate and fastest way" to social, political and economic reform.
He died in Paris in 1851.
- Simon Altmann, "Rotations, Quaternions and Double Groups"(Clarendon Press, Oxford, 1986, ISBN 0-19-855372-2): "The family is often said to have been of Spanish origin, but the spelling of the family name rather suggests Portuguese descent (as indeed asserted by the 'Enciclopedia Universal Illustrada Espasa-Calpe')". For more information on the Rodrigues as Portuguese Jews in Bordeaux see also the Jewish Encyclopedia "?". Jewish Encyclopedia.
- Altmann and Ortiz(2005), p. 12
- Olinde Rodrigues (January 1816). "De l'attraction des sphéroïdes". Correspondence sur l'École Impériale Polytechnique 3 (3): pp. 361–385.
- Olinde Rodrigues (1840) "Des lois géométriques qui régissent les déplacements d'un système solide dans l'espace, et de la variation des coordonnées provenant de ces déplacements considérés indépendamment des causes qui peuvent les produire" (On the geometrical laws that govern the displacements of a solid system in space, and on the change of coordinates resulting from these displacements considered independently of the causes that can produce them), Journal de Mathématiques Pures et Appliquées, vol. 5, pages 380-440.
- John H. Conway, Derek A. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry. AK Peters, 2003, ISBN 1-56881-134-9, p. 9
- Calinescu, Matei (1987). The Five Faces of Modernity: Modernism, Avant-Garde, Decadence, Kitsch, Postmodernism. Duke University Press.
- Simon L. Altmann (1989). "Hamilton, Rodrigues and the quaternion scandal". Mathematics Magazine 62 (5): 291–308. doi:10.2307/2689481. JSTOR 2689481.
- Simon L. Altmann (2005). Rotations, Quaternions and Double Groups. Dover Publications. ISBN 0-486-44518-6.
- Simon L. Altmann; & Eduardo L.Ortiz (eds.) (2005). Mathematics and social utopias in France: Olinde Rodrigues and his times. American Mathematical Society, Providence, RI. ISBN 0-8218-3860-1. Corrects some of the traditional thinking about Rodrigues as a mathematician
- Jeremy J. Gray: Olinde Rodrigues' paper of 1840 on Transformation Groups. In: Archive for History of Exact Sciences. Bd. 21, Nr. 4, 1980, ISSN 0003-9519, S. 375–385, doi:10.1007/BF00595376.