**Charles Méray** was a French mathematician who published an early work on the arithmetical theory of irrational numbers.

- After graduating, Méray taught at the Lycée of St Quentin for two years but then left teaching for seven years during which time he lived in a small village near Chalon-sur-Saône.
- Following these seven years when he chose not to work, Méray took up a teaching position again in 1866, this time lecturing at the University of Lyon for a year before being appointed as Professor of Mathematics at the University of Dijon.
- Méray is remembered for having anticipated, clearly and with only minor differences of style, Cantor's theory of irrational numbers, one of the main steps in the arithmetisation of analysis.
- However, as happened many times throughout history, Méray was unlucky for the genius of his work was not recognised at the time.
- Others (we give details below) published the same ideas and it would be their work rather than that of Méray which influenced the direction of mathematics.
- All we can do now is to give Méray the credit he deserves for his remarkable work, even if fate did not allow Méray a role of importance in the development of the subject.
- In 1869 Méray was the first to publish an arithmetical theory of irrational numbers in his paper Remarques sur la nature des quantités définies par la condition de servir de limites à des variables données Ⓣ(Notes on the nature of variables defined by the condition that they serve as limits of given variables).
- Méray's is the earliest coherent and rigorous theory of the irrational numbers to appear in print.
- Méray followed Lagrange's earlier work but gave rigorous proofs of what Lagrange had only conjectured.
- Méray published a second important work in 1872.
- It is another rigorous work and in fact between 1872 and 1894 Méray produced a series of papers which remove geometric considerations from analytic proofs.
- Méray's work consistently follows Lagrange in basing the whole of analysis on the concept of functions written as Taylor series.
- We have noted above that Méray's work had no real influence on the development of mathematics despite being almost exactly the same as the work which would transform the direction of mathematics.
- It was not that Méray's work went unnoticed.
- At that time there was not in France - as there was in Germany - a sufficient appreciation of the kind of problem considered by Méray, and not until much later was it realised that he had produced a theory of a kind that had added lustre to the names of some of the greatest mathematicians of the period.

Born 12 November 1835, Chalon-sur-Saône, France. Died 2 February 1911, Dijon, France.

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Analysis

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive