**Louis Antoine** was a French mathematician famous for his invention of *Antoine's necklace*.

- Louis was a successful pupil at school, excelling in mathematics and science.
- In Paris, Antoine was awarded a baccalaureate in Latin and Sciences in 1905 and, in the following year, a baccalaureate in mathematics.
- Gaston Julia, who was four years younger than Antoine, entered the École Normale Supérieure in 1911 and, despite the fact that they did not overlap at the École for very long, Antoine and Julia became firm friends.
- Following his graduation, Antoine became a mathematics teacher at the Lycée de Dijon in Saint-Cyr.
- Events had been moving quickly and Antoine, who was a reserve lieutenant in the 72nd Infantry Regiment of Amiens, was mobilised on 2 August as France geared up for war.
- Antoine and his section were sent to Belgium to meet the German advance.
- In a trench near Ramscapell, Antoine was wounded by shrapnel on 25 August but was able to continue fighting.
- On 16 April 1917, Antoine led his men to attack Fort Brimont on the banks of the river Miette.
- Antoine is observing the German trenches through binoculars when a bullet removes both his eyes.
- Julia and Antoine met frequently in the Val-de-Grâce hospital, even sharing a room for a while.
- As Antoine slowly recovered he began to worry about his future.
- As this was a new area, there were few papers in that area so Antoine's inability to read would be a smaller disadvantage.
- Now there was no way that Antoine could have studied mathematics on his own but he had the help of a number of good friends: Henri Lebesgue, Marcel Brillouin and Gaston Julia made Braille copies of the leading mathematical treatises of the day so that Antoine could bring his mathematical knowledge up to the level needed for research.
- However, there was no standard Braille representation of mathematical symbols so Antoine, assisted by Bourguignon who was a student at the École Normale Supérieure of Saint-Cloud, invented Braille versions of mathematical symbols.
- From 1919, Antoine had a position at the University of Strasbourg while he worked on his thesis.
- Antoine was trying to prove a three-dimensional analogue of the Jordan-Schönflies theorem, which says that, given a simple closed curve in the plane, there exists a homeomorphism of the plane that takes the curve into the standard circle.
- What Antoine tried to prove is that, given an embedding of the two-sphere into three-space, there is a homeomorphism of three-space that takes the embedded sphere into the standard sphere.
- Antoine eventually realized that this theorem is false.
- He came up with the first "wild embedding" of a set in three-space, now known as Antoine's necklace, which is a Cantor set whose complement is not simply connected.
- Using Antoine's ideas, J W Alexander came up with his famous horned sphere, which is a wild embedding of the two-sphere in three-space.
- Ibisch explains how J W Alexander realised that Antoine's "remarkable point set" could be easily modified to obtain a counterexample to the Schönflies conjecture which he published in 1924.
- Despite his brilliant qualities, without the war, M Antoine would perhaps never have undertaken his own research.
- Antoine was not particularly happy in Strasbourg.
- He went on to become Antoine's assistant and much later became Dean of Science at Rennes.
- After the interrogation ended, there was no anxious waiting, for Antoine immediately gave the result to the applicant.
- Antoine published a textbook based on courses he had taught on the differential and integral calculus; the 234 page volume Calcul différentiel et calcul intégral: Calcul intégral Ⓣ(Differential and integral calculus: Integral calculus) (1948) and the 194 page volume Calcul différentiel et calcul intégral: Calcul différentiel Ⓣ(Differential and integral calculus: Differential calculus) (1949).
- The proceedings of the meeting was published as Journée Louis Antoine (1988).

Born 23 November 1888, Mirecourt, Vosges, France. Died 8 February 1971, Rennes, Bretagne, France.

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