**Pierre Fatou** was a French mathematician and astronomer who worked in several branches of analysis.

- Ernest Fatou began his navy career in 1847 and became a Lieutenant in 1861.
- Fatou studied at the lycée in Lorient.
- Leaving Lorient in 1894, Fatou went to Paris where he studied elementary mathematics and special mathematics at the Collège Stanislas for three years.
- Fatou spent the year 1897-98 at the lycée Saint-Louis in Paris preparing for the entrance examinations to the École Normale Supérieure and the École Polytechnique.
- Fatou entered the École Normale Supérieure in Paris in 1898 to study mathematics having been ranked first in the entrance examination.
- Fatou was just such a graduate and having a position in the Paris Observatory would benefit both the Observatory and allow him to work on his thesis in Paris without having teaching commitments.
- Having been appointed to the astronomy post at the Paris Observatory in November 1901, Fatou worked under Maurice Loewy (1833-1907) who had been made director of the Observatory in 1896 and had done much in reorganising it.
- Fatou made a promising start to his career at the Observatory and was rapidly promoted but by 1906 his colleagues were feeling that his heart wasn't in his work.
- One should treat this with a little caution since Fatou's health was poor and he applied for sick leave from the Observatory from 1 May 1906 to 31 August 1906.
- However it was mathematics rather than astronomy that was Fatou's passion.
- Fatou proved that if a function is Lebesgue integrable, then radial limits for the corresponding Poisson integral exist almost everywhere.
- Although not giving a complete solution, Fatou's work also made a major contribution to finding a solution to the related question of whether a conformal mapping of Jordan regions onto the open disc can be extended continuously to the boundary.
- Fatou seems also to quite readily suppose that everybody knows or sees the same thing as he does and gives rather few explanations.
- This report is quite in keeping with the modesty we know that Fatou displayed.
- After considering Lebesgue's suggestions, he resubmitted the thesis and, on 14 February 1907, Fatou received his doctorate for this important work.
- Fatou enters this history in a rather complicated way and the book does an excellent job in explaining an interesting episode in the history of mathematics.
- Fatou wrote a long memoir which did indeed use Montel's idea of normal families to develop the fundamental theory of iteration in 1917.
- Given that the topic had been proposed for the prize, it is not surprising that another mathematician would also work on the topic, and indeed Gaston Julia also produced a long memoir developing the theory in a similar way to Fatou.
- Fatou, on the other hand, published an announcement of his results in the note Sur les substitutions rationnelles Ⓣ(On rational substitutions) in the December 1917 part of Comptes Rendus.
- Almost certainly as a result of these letters Fatou did not enter for the Grand Prix and it was awarded to Julia.
- Fatou did not lose out completely, however, and even though he had not entered for the prize, the Académie des Sciences gave him an award for his outstanding 280-page paper on the topic, Sur les équations fonctionnelles Ⓣ(On functional equations) published in 1920.
- Whether Julia or Fatou deserves the credit of having priority matters little since their work was certainly totally independent.
- Among the candidates were Fatou and Lebesgue.
- It was decided that the Academy of Sciences would be asked to recommend which candidate should be appointed and the Academy cast 35 votes for Lebesgue and 29 for Fatou.
- Using existence theorems for the solutions to differential equations, Fatou was able to prove rigorously certain results on planetary orbits which Gauss had suggested but only verified with an intuitive argument.
- The position of "astronomer" at the Observatory became open in 1927 and Pierre Salet (1875-1936), Armand Lambert (1880-1944) and Fatou competed for the position.
- Salet was appointed in 1927 but the position of "astronomer" again became vacant in 1928 and Armand Lambert and Fatou competed again.
- The Observatory voted to appoint Lambert but the final decision was made by the Academy of Sciences which reversed the decision, voting in favour of Fatou on 25 June 1928.
- From the time that Fatou joined the French Mathematical Society in 1904 he took a major role in its operations.
- Perhaps Fatou's most famous result is that a harmonic function u>0u > 0u>0 in a ball has a non-tangential limit almost everywhere on the boundary.
- Edouard Goursat invited Fatou to prepare a revised second edition of Appell and Goursat's Théorie des Fonctions Algébrique Ⓣ(Algebraic complex analysis) (1895) and add material on automorphic functions.
- Fatou wrote such a major exposition of the subject that it was decided to publish Fatou's material on automorphic functions as a separate volume, becoming Volume 2 of the new edition of Théorie des Fonctions Algébrique Ⓣ(Algebraic complex analysis) which was published in 1930, the year after Fatou's death, as a three author work.
- In the summer of 1929 Fatou went on holiday to Pornichet, a seaside town to the west of Nantes.
- Fatou's funeral was held on 14 August in the church of Saint-Louis, and he was buried in the Carnel Cemetery in Lorient.
- We have already quoted from Fatou's nephew Robert Fatou saying a little of Fatou's character.
- One passion in Fatou's life, other than mathematics, was music.

Born 28 February 1878, Lorient, France. Died 9 August 1929, Pornichet, France.

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Analysis, Astronomy, Geometry

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