As one of the leading French mathematicians of his generation and author of two books on elementary geometry, Jacques Hadamard was always fascinated by new mathematical ideas. When he received a mathematical proof in the mail from a previously unknown mathematician named Andre Bloch, Hadamard was mesmerized by its elegance. The proof related to a branch of elementary 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. According to Bloch, parataxy remained invariant under inversion and any inversion with respect to a point situated on one of them transforms them into a circle and it's axis.

Hadamard was so intrigued by Bloch's discovery that he immediately decided to invite him to dinner. Since he had no other way of contacting Bloch, Hadamard wrote to the return address of 57 Grand Rue, Saint- Maurice with the invitation. Bloch wrote back that a visit would be impossible but asked the great mathematician to visit him instead. It was only when Jacques Hadamard finally took him up on his offer that he discovered why Bloch was unable to come to him: 57 Grand Rue, Saint-Maurice was the address of the Charenton lunatic asylum (now the Esquiral hospital) where Andre Bloch was an inmate. He had been involuntarily committed to the hospital following a brutal murder in 1917 and would never be allowed to leave. Although Hadamard was astonished by his discovery, he and Bloch talked at length about mathematics and he learned more about the inmate's story.

Born in 1893 in Besancon, France, Andre Bloch was one of three sons of an Alsatian Jewish watchmaker and his wife. Orphaned at an an early age, Andre and his brother Georges were in the same class despite Georges being younger. While Andre was a poor student at first, he and George entered the Ecole Polytechnique together but only finished their first year when World War One broke out. Both brothers were drafted and Andre served in the artillery as a second lieutenant. Although George and Andre were both wounded in the war (Georges lost an eye while Andre fell from an observation post) only George was discharged and allowed to return to school. Due to linging injuries, Andre was hospitalized several times and eventually placed on indefinite leave.

On November 17, 1917, while Andre Bloch was visiting with his aunt and uncle at their family home in Paris, he attacked his brother, 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 resistance. Given that the country was still at war and the case involved two army officers, there was little publicity involved. Andre was quietly committed to the Charenton asylum for the duration of his life.

His reason for the murders remains unclear although he would later justify his action by telling his doctors that he had been fulfilling his eugenic duty. As he explained it, the laws of eugenics were indisputable and his actions had been clearly necessary given the family history of mental illness. In all other respects, he seemd perfectly sane and he devoted his time to working on various mathematical proofs. This was all the more remarkable considering that he was entirely self-taught. He wrote to various prominent mathematicians on a range of different topics in theoretical and applied mathematical proofs. Everything that he knew about mathematics was learned about through the mathematics books which had been provided to him and the mathematics journals to which he subscribed (including the *Bulletin des Sciences Mathematiques*). Along with Jacques Hadamard, he also maintained regular correspondence with George Polya, Georges Valiron, Charles Emile Picard, and Paul Montel. Although he always gave the Charenton hospital as his return address without revealing his actual circumstances, Bloch's status as an inmate became an open secret. Since many of the letters are still in existence, they represent a fascinating look at Bloch's contributions to the field of mathematics.

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 and expressed 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 (the irony of having to hide from his fellow eugenicists was probably lost on him though). According to available records, 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.

As for the murders that led to his being sent to the asylum, he never showed any real remorse. In his classic book, *Des Hommes Come Nous*, prominent psychiatrist Henri Baruk devoted part of one chapter to the "Mathematician of Charenton" (Bloch wasn't named in the book). Baruk commented on his patient's "rational morbidity" in describing how the murders had been necessary to eliminate that branch of his family that he considered defective. Even late in life, Bloch would argue that his actions had been "a matter of mathematical logic. There had been mental illness in my family. The destruction of the whole of the branch had to follow as a matter of course". When his physician protested, Bloch accused him of "emotional language" and insisted his actions were based on his philosophy of "pragmatism and absolute rationality".

After developing leukemia, Andre Bloch was admitted to Saint-Anne Hospital for an operation and died on October 11, 1948. Shortly before his death, Bloch had been notified that he had been awarded the Becquerel prize by the Academic des Sciences (the prize was given to him posthumously several months after his death). He is still remembered for his numerous contributions to mathematics including Bloch's theorem, Bloch space, and Bloch's constant.

Would his contributions have been more extensive if he hadn't been confined for most of his life? Did his traumatic experiences in the war lead to his explosive violence? These are questions that will likely never be answered. Still, Andre Bloch's case represents a fascinating example of how even institutionalized psychiatric patients can continue having an influence on the world if their determination (or obsession?) is great enough.

There's a quote from GK Chesterton which I'm sure you've heard:

"Imagination does not breed insanity. Exactly what does breed insanity is reason. Poets do not go mad; but chess-players do. Mathematicians go mad, and cashiers; but creative artists very seldom."

Someone else (I forget who) said "Insanity is not unreason. Insanity is reason with nothing else".

After reading about Goedel and now Bloch, I can't help suspecting Chesterton had a point. Highly focused people are often eccentric, but that's not the same thing. What do you think? Is there a significantly above average proportion of mathematicians and hard scientists who (by whatever standard) go 'over the edge'?

Posted by: Kapitano | February 22, 2011 at 03:02 AM

My impression is that madness can strike someone from any walk of life. Scientists and mathematicians can go mad, but so can poets, artists, and writers. Madness is truly democratic.

Posted by: Romeo Vitelli | February 22, 2011 at 07:03 AM

Madness is always an obsession lasting longer than 7 days. We carry our obsessions around with us each day and heaven forbid anyone should enquire deeply into our obsessive thoughts or question our carefully built collection of obsessive acts. Obsessions are created, those created in difficult times of our life are bad, and those created in happier times are good. A good collector of obsessive thoughts know to avoid those created in anger, or when voices were raised in temper. Take away our obsessions and we become bored and irritable.

Posted by: Passerby | January 19, 2015 at 06:49 PM