Person: Richard (2), Jules
Jules Richard worked on Geometry but is best known for Richard's paradox involving the set of real numbers which can be defined in a finite number of words.
Mathematical Profile (Excerpt):
 Jules Richard wrote on the philosophy of mathematics in 1903 publishing Sur une manière d'exposer la géométrie projective Ⓣ(On a way to describe projective geometry) in that year.
 Having given these four separate approaches, Richard then proceeds to point out unacceptable aspects of each of the four.
 Richard was thinking about geometry at a time when the noneuclidean geometries had been discovered.
 Jules Richard is remembered mainly, however, for Richard's paradox involving the set of real numbers which can be defined in a finite number of words.
 The paradox first appeared in a letter from Richard to Louis Olivier, the director of Revue générale des sciences pures et appliquées Ⓣ(General review of pure and applied sciences).
 (Actually, of course, Richard used French but since we are writing this biography in English, we will have to explain the paradox in English.) Examples of English descriptions or real numbers are "one third", "the base of natural logs", and "the ratio of the circumference of a circle to its diameter", etc.
 Richard then created a list of all real numbers which could be described in English.
 If Richard's paradox tells us anything then perhaps it is a warning not to use English (or any other language for that matter) when we are doing mathematics.
Born 12 August 1862, Blet, Cher, France. Died 14 October 1956, Châteauroux, Indre, France.
View full biography at MacTutor
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References
Adapted from other CC BYSA 4.0 Sources:
 O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive