The Mathematician who was a Mass Murderer.

Andre Bloch 

‘In the North Eastern corner of France lies Besancon. It is near the border with Switzerland and was an important centre for watch making: the industry was wiped out in a matter of years by competition from Japan. Be that as it may, it is also the birthplace of one of the most brilliant mathematicians of the early twentieth century, who was also a multiple murderer and a madman.

Andre Bloch (not to be confused by the composer with the same name) was one of the three sons of a Alsatian Jewish watchmaker, one of the many who made Besancon a major center of the watch trade. He was born on the 20^th November 1893 and his younger brother Georges was born less than a year later. Both the brothers were in the same class at the Lycee (secondary school) in Besancon. Both the brothers had considerable mathematical talents and their mathematics teacher Professor Carrus, who taught them for two years ( 1908-9) thought that they should compete to enter the Ecole Polytechnique for higher studies. In the following year their new teacher, Georges Valiron had this to say: “The following year, October 1910, I had both Bloch brothers in my class. André had already displayed his interest in the abstract properties to which he would later make such significant contributions. But he spoke rarely and didn't bother to prepare for the examinations. Georges was more lively and perhaps as good a mathematician as his brother. Georges was at the head of the class and clearly the best on the written examinations. André was last in my class of eleven students. André was lucky and got Ernest Vessiot to give him the oral exam [for entry into the École Polytechnique]. Vessiot recognized Andre's aptitude and gave him a19 out of 20 on the oral.”

Both of them did one year of military training before being  admitted to the Ecole Polytechnique in October 1913 André ranked 151st, Georges ranked 229th in the list of students entering that year.  Unfortunately after just one year their studies were interrupted as the First World War broke out. Both the brothers joined the Army.  André served as second-lieutenant in the artillery and was attached to the headquarters of General Noël Édouard, the commander of the Second French Army at the heights of Grand Couronné near Nancy. There was heavy fighting in this sector and André Bloch was part of the French forces here for several months before, during a heavy German bombardment, he fell from the top of an observation post. His injuries were severe and he was hospitalised a number of times but never regained his health sufficiently to return to his unit.

A similar fate awaited his brother who had a head wound and lost the sight in one of his eyes; he was invalidated out of the Army and returned to his studies in the Ecole Polytechnique in October 1917. On the fateful day of November 17, 1917,  Andre Bloch was visiting with his aunt and uncle at their family home in Paris,  he attacked Georges, his  aunt, and uncle at a family meal. After knifing all three of them to death, he then ran shouting into the street where he was arrested without offering any resistance.  As the country was at war and the case involved two army officers, the incident was hushed up.  Andre was quietly committed to the Charenton lunatic asylum at the outskirts of Paris for the duration of his life.

It was not clear what caused his murderous attack, but in later years he apparently justified his actions by claiming that he was carrying out his eugenic duty by eliminating his family as there was a family history of mental illness.

Ironically it was at the asylum that his talents as a mathematician came to the fore. He began working on various mathematical problems and came up with some stunning results which he often shared with the great mathematicians of his day. Jaques Hadamard was one the leading academic mathematicians of that time in France. He was also the editor of a mathematical journal. One day he received an unsolicited mathematical proof from a then unknown mathematician. This was Andre Bloch. Hadamard was very taken by the elegance of the proof which related to a branch of geometry involving paratactic circles, “systems of two circles with orthogonal planes with the intersection being the common diameter of the two circles and cut according to a harmonic division.” (No, I have no idea what this means) .  Bloch apparently showed that parataxy remained invariant under inversion and any inversion with respect to a point situated on one of them transforms them into a circle.

Whatever that may be, the mathematician in Hadamard was intrigued and he wrote to Andre inviting him for dinner. Bloch wrote back saying that he would be unable to come, but asked Hadamard to visit him instead. It was only then that Hadamard realized that the address 57, Grnad Rue, Saint –Maurice was the address of the Charenton lunatic asylum. It is recorded that the visit went ahead and the two mathematicians talked at length about their favourite subject.

He was entirely self-taught, all his mathematical knowledge gleaned from mathematics books and journals. Henri Baruk, who was a psychiatrist with an international reputation working at the hospital described André Bloch's typical day.  “Every day for forty years this man sat at a table in a little corridor leading to the room he occupied, never budging from his position, except to take his meals, until evening. He passed his time algebraic or mathematical signs on bits of paper, or else plunged into reading and annotating books on mathematics whose intellectual level was that of the great specialists in the field. ... At six-thirty he would close his notebooks and books, dine, then immediately return to his room, fall on his bed and sleep through until the next morning. While other patients constantly requested that they be given their freedom, he was perfectly happy to study his equations and keep his correspondence up to date.”

Bloch communicated with many other mathematicians. They included George Polya, Georges Valiron, Charles Emile Picard, and Paul Montel.  He always gave the street address of his aylum without mentioning that it was one, but in later years most of his correspondents were aware of his identity. He however had the odd habit of dating all his letters April 1 no matter when they were written.

 Along with four papers on holomorphic and meromorphic functions (which have since become standard), Andre Bloch wrote papers on function theory, number theory, geometry, and algebraic equations among other topics.  He was also keenly interested in the elections at the Academie des Sciences (the leading scientific academic body in France ) and expressed the  hope that he would eventually be allowed to present his work in person at the College de France and the University of Strassbourg.  Bloch allowed however that "in all probability, that will not be for quite a while".    Even during the Nazi occupation, Bloch continued to publish but was careful to write under assumed names to avoid calling attention to his Jewish origins . He called himself Rene Binaud in one paper published in 1941 and Marcel Segond in two others published in 1941-42.

Andre Bloch was a model inmate and lived his life in monastic fashion with little interaction with the other inmates or staff.  He did all his work at a small table installed for him at the end of a corridor and even avoided going out onto the hospital grounds stating that "Mathematics is enough for me".  According to family members, Andre Bloch's main enjoyment came from his mathematics work and long games of chess with staff or inmates.

His surviving brother Henry who had been living in Mexico came to visit him when he was in Paris . Andre was extremely cold to him and showed no signs of affection or welcome. It was on the following day that he detailed the motive for his actions to his psychiatrist Henri Baruk saying that “It's a matter of mathematical logic. There were mentally ill people in my family, on the maternal side, to be exact. The destruction of the whole branch had to follow as a matter of course. I started my job at the time of the famous meal, but never got a chance to finish it.” Perhaps Henri was lucky to have escaped unscathed!

Bloch is today best known for "Bloch's theorem". As a mathematician puts it: ”An extremely pretty result in complex function theory concerns Bloch's theorem, a universal covering property for any non-constant analytic function. Although there is a simple classification of Riemann surfaces (hyperbolic, elliptic, parabolic), any specific Riemann surface can be a nasty, brutish, intricate object. Bloch's theorem provides a touch of beauty, a surprising quantitative invariance to the class of normalized hyperbolic Riemann surfaces.

Bloch's theorem, which appears in his 1925 paper, Les théorèmes de M Valiron sur les fonctions entières et la théorie de l'uniformisation , was (as the title of the paper suggests) inspired by a result by Georges Valiron. Related to Bloch's theorem is Bloch's constant B.

Towards the end of his life he with Gustave Guillaumin published  Sur le volume des polyèdres non euclidiens  (1947), Sur les fonctions bornée à zéros multiples, les fonctions à valeurs ramifiées, et les couples de fonctions soumise à certaines conditions  (1948) and the 141-page book, written with Gustave Guillaumin, La Géométrie intégrale du contour gauche  (1949).  According to one source,the Académie des Sciences awarded him the Becquerel Prize just before his death .

Bloch developed leukemia and was admitted to the Sain-Anne Hospital for an operation on 21 August and he died there on October 11, 1948 , about  a month before his 56^th birthday.