**Georges Humbert** never knew his parents since he was orphaned when he was very young. He was brought up by his grandparents in Franche-Comté where his grandfather was an industrialist. His grandparents sent Georges to the Oratorian College of Juilly to become a boarder there. He studied classics at the College, then he went on to study at the Collège Stanislas in Paris. He graduated from this college in 1877 and, was placed first for entry to the École Normale Supérieur and seventh for entry to the École Polytechnique in that year. He chose the École Polytechnique and after graduating in second place he studied engineering at the École des Mines.

After graduating he spent a few years as a mining engineer. His first position in this capacity took him to Vesoul, but after that he moved to Paris where, in addition to his work as a mining engineer, he was soon employed as a teacher at the École Polytechnique and at the École des Mines.

Humbert obtained a doctorate in mathematics in 1885 for his thesis *Sur les courbes de genre un.* He wrote the important work *Application de la théorie des fonctions fuchsiennes à l'étude des courbes algébraiques* which was published in the following year. His work was officially recognised when he was awarded the Poncelet Prize from the Académie des Sciences in Paris in 1891 and the prize from the French Mathematical Society in 1893.

Humbert married Marie Jagerschmidt in 1890 and in the following year his son Pierre was born. Pierre Humbert grew up to be a mathematician and has a biography in this archive. Georges Humbert's delight at the birth of his son was short-lived, however, for his wife died in 1892. Humbert married again in 1900 and with his second wife Suzanne Lambert-Caillemar had two further children.

In 1893 he was elected to the role of president of the French Mathematical Society and, two years later, he was appointed professor of analysis at the École Polytechnique. On the death of Hermite in 1901, Humbert was elected to fill his place in the Académie des Sciences. In fact this was highly appropriate for he continued Hermite's work in number theory and, what is more, did so in a very effective manner producing important contributions. He became Jordan's assistant at the Collège de France in 1904 succeeding to Jordan's chair in 1912.

His doctorate extended Clebsch's work on curves. He then studied Abel's work which he developed and put into a geometric setting. It was as a direct consequence of his work on using abelian functions in geometry which won for him the 1892 Académie des Sciences prize for work on Kummer surfaces. As Costabel writes in [1]:-

He thus enriched analysis and gave the complete solution of the two great questions of the transformation of hyperelliptic functions and of their complex multiplication.

He also, as we noted above, extended work of Hermite considering applications to number theory throughout his life.

Georges Humbert would be better known today if the area of mathematics in which he worked had remained in favour. Since it has now become merely something of an historical curiosity rather than mainstream mathematics, his contribution is less well known. It does, however, indicate the quality of his mathematics that, despite this, his name and results are known today. To some extent this is a consequence of the fact that although he worked in a specialised area he had a remarkably broad knowledge of mathematics and his results form links between areas.

Humbert was a highly respected man who [1]:-

... was remarkably gifted not only in mathematics but also in clarity of expression and intellectual cultivation. He exerted a great influence and was able, by his discretion and objectivity, to assure respect for his religious convictions during a period of some hostility towards religion in French scientific circles.

**Article by:** *J J O'Connor* and *E F Robertson*

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