**Louis Bachelier** was a French mathematician who is credited with being the first person to model the stochastic process now called Brownian motion.

- The Bachelier Society, named in his honour, is the world-wide financial mathematics society and mathematical finance is now a scientific discipline of its own.
- The probabilist William Feller had originally called it the Bachelier-Wiener Process.
- It appears that Einstein in 1905 was ignorant of the work of Bachelier.
- Louis Bachelier was born in Le Havre in 1870.
- At the age of 22, Bachelier arrived in Paris at the Sorbonne where he followed the lectures of Paul Appell.
- After some 8 years, in 1900, Bachelier defended his thesis Théorie de la Spéculation Ⓣ(Theory of speculation) before these three men, the favourable report being written by no less a figure than Henri Poincaré, one of the most eminent mathematicians in the world at the time.
- Paul Levy thought that Bachelier had made a mistake in his paper by making the tangent of the path (up or down) constant and Bachelier failed to be appointed at Dijon.
- Bachelier was furious and wrote to Levy, who, apparently, was unrepentant over this calumny.
- It seems extraordinary that Levy was, apparently, unfamiliar with Bachelier's work as Bachelier had by this time (1926) published 3 books and some 13 papers on probability and regarded showing how a continuous distribution could be derived from a discrete distribution as his most important achievement.
- Levy once told J L Doob that "reading other writers' mathematics gave him physical pain" (see website below) so perhaps it was the case that Levy had never read Bachelier.
- Borel, however, must have known Bachelier (he had approved the scholarships to Bachelier).
- It should be pointed out that Poincaré, who would not have made this mistake over the interpretation of Bachelier's work, had died some 14 years earlier.
- It seems that Bachelier, was regarded as being of lesser importance in the eyes of the French mathematical élite (Hadamard, Borel, Lebesgue, Lévy, Baire).
- However, Levy, a few years later, was apparently surprised to find Kolmogorov referring to Bachelier's work.
- In 1931, Levy wrote a letter of apology to Bachelier and they were reconciled.
- Bachelier moved back to Besançon (this time as permanent professor) in 1927 and retired aged 67 in 1937.
- Bachelier's treatment and understanding of the theory of Brownian Motion (originally called Brownian Movement) is more elegant and mathematical than in Einstein's 1905 paper.
- The work of Bachelier leads on to the work of Wiener (1923), Kolmogorov (1931), Itô(1950), and Black, Scholes and Merton (1973).
- Bachelier was ahead of his time and his work was not appreciated in his lifetime.
- In the light of the enormous importance of international derivative exchanges (where the pricing is determined by financial mathematics) the remarkable pioneering work of Bachelier can now be appreciated in its proper context and Bachelier can now be given his proper place.

Born 11 March 1870, Le Havre, France. Died 26 April 1946, St-Servan-sur-Mer, France.

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