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Jules Antoine Richard

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12 Aug 1862

Blet, Cher, France

14 Oct 1956

Châteauroux, Indre, France

Jules Richard taught at Lycées in Tours, Dijon and Châteauroux. He obtained a doctorate on Fresnel waves from Paris in 1901.

Jules Richard wrote on the philosophy of mathematics in 1903 and 1908 wrote Sur la nature des axiomes de la géométrie in which he looked critically at four different approaches to geometry:

i) Geometry is founded on arbitrarily chosen axioms - there are infinitely many equally true geometries.

ii) Experience provides the axioms of geometry, the basis is experimental, the development deductive.

iii) The axioms of geometry are definitions.

iv) Axioms are neither experimental nor arbitrary, they force themselves on us.

Jules Richard is remembered 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.

Source:School of Mathematics and Statistics University of St Andrews, Scotland