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The Amazing, Incredible Life of the
Mathematician, Alexander Grothendieck

Alexander Grothendieck was a mathematician who was active in mathematics from about 1950 to 1968. He revolutionized one particular field of mathematics, algebraic geometry, and was awarded the prestigious Fields Medal for his work. Some consider him to be amongst the top, say twenty, mathematicians of all time. The French thought so highly of him that they created a special institution just for him, the Institut des Hautes Études Scientifiques (IHES), the Institute of Advanced Scientific Studies. It was located just outside of Paris and in time became the place to go for students of extraordinary mathematical talent. In the IHES Grothendieck blossomed into a world leader in mathematics.

In about 1968 Grothendieck became involved in the antiwar movement, specifically the movement in France against the war in Vietnam. Moreover Grothendieck was anti-military. In 1970 he participated in a violent demonstration and was arrested for hitting two policemen. He was released but he then discovered that some of the funding for his IHES came from the budget of the French Ministry of Defense. Grothendieck was so incensed about this funding that he left the IHES and ultimately he left mathematics as well.

He did not formally leave mathematics but in effect he did. He secured other academic appointments but instead of lecturing on mathematics as he was supposed to and as his students expected he gave polemics about war, politics and the military. Those appointments were not renewed. He agreed to attend conferences concerning mathematics but instead of delivering a paper on mathematics he went into a diatribe about war and politics. His former admirers became annoyed and irritated. Grothendieck then began to destroy his manuscripts on mathematics.

His academic career effectively ended in 1973 and he retreated to the Pyrenees. He maintained a house in a small town there but was often gone into the mountains. In 1977 he participated in a political incident and was put on trial. He was sentenced to six months imprisonment and had to pay a heavy fine. The prison sentence was suspended.

He was given one more academic appointment, at the University of Montpellier where he had received his bachelor's degree in mathematics. Formally he was on the faculty but he hardly lectured and then not on mathematics. In 1991 he burned thousands of pages of his manuscripts in mathematics. He went to live in the mountains and only maintained a post office box as a link with the outside world. In 1993 even that link disappeared. Around the year 2000 two young French mathematicians found him at a small town where Grothendieck came to buy supplies. He talked with them. Others who have communicated with him say he is obsessed with the Devil whom he sees as being behind the turmoil of the world. Grothendieck wrote a document of a hundred pages in which he describes a small group of individuals whom he calls mutants who represent the best in the human race. In 2005 another mathematician tried to locate Grothendieck and was unsuccessful.

Grothendieck's Parents

Alexander Grothendieck's father was Alexander Shapiro, a man of Jewish descent who grew up the part of the Russian Empire known as the Pale of Settlement, the region where Russia, the Ukraine and Belarus come together. This was only the only area of the Empire where Jews were allowed to settle. At 16 years of age Alexander Shapiro participated in the abortive revolution of 1905 and was sent to prison in Siberia. After twelve years he was released in 1917, just in time to participate in the revolutions against the Czarist government. He became the leader of the Social Revolutionary Party of the Left. Shapiro opposed Lenin and the Bolshevik Party of Lenin took its revenge upon its opponents, even and especially among the Left. Alexander Shapiro then left Russia to join the revolution in Hungary. From there he went to join revolutionary uprisings in Berlin and Munich. He then returned to the former Russian Empire, to the Ukraine where he joined Nestor Makhno's anarcho-communist guerilla force which was fighting both the Czarist and the Bolshevik forces. The Russian police captured him and sentenced him to death. Before his execution he escaped but in the course of his escape he suffered an injury that resulted in the loss of an arm. Soon after his escape, with help of a woman named Lia, he fled to Poland. From Poland the couple traveled through Germany and Belgium and settled in Paris. After two years Alexander Shapiro left Lia and journeyed to Germany. In Germany he made contact with the local anarchists and met Hanka Grothendieck.

Hanka Grothendieck was from Hamburg. She had married a journalist named Raddatz and was herself a journalist writing about the sex trade (prostitution) in Germany. Her husband was also an anarchist and continually traveling. During one of these separations she and Alexander Shapiro began living together.

On March 28th of 1928 Hanka gave birth to Alexander who ultimately was given her maiden name of Grothendieck. When Alexander was five years old Adolph Hitler came to power in Germany and Alexander Shapiro decided that he, as a foreign Jewish anarchist, better leave Germany. He went back to Paris where he tried to survive as a street photographer. This was a difficult profession for a man with only one arm but he survived, just barely. Soon Hanka decided to join Shapiro in Paris. She left her son Alexander in the care of a Lutheran pastor.

In Paris in 1936 Hanka and Shapiro decided to go to Spain to fight against Francisco Franco's rebellion against the radical Republican government. After Franco's victory Shapiro escaped Spain and returned to Paris but Hanka Grothendieck temporarily had to live in the city of Nîmes before joining Shapiro in Paris.

In 1939 the Lutheran pastor who was taking care of the couple's son, Alexander, decided that he could no longer do so. He sent the eleven year old Alexander alone by train to Paris to his parents. The French authorities viewed revolutionary anarchists like Alexander Shapiro and Hanka Grothendieck as threats to French security and the family was soon arrested. Alexander Shapiro was sent to a camp in France and later transferred to Auschwitz where he died in 1942. Hanka and her son Alexander were imprisoned in various camps and during this time she contracted tuberculosis. Shortly after the end of the war Hanka Grothendieck died.

Alexander Grothendieck's Career as a Mathematician

Somehow during his life in those camps Alexander Grothendieck taught himself mathematics. He, in fact, developed on his own what is known in mathematics as measure theory. After the war Alexander at age 18 or so was able to attend a university and began acquiring formal training in mathematics at the University of Montpellier in southern France. He soon caught and surpassed his contemporaries, even surpassing his instructors. After graduating from Montpellier in 1948 he went to Paris where he met some the greatest mathematicians of the time. He entered the doctoral program in mathematics at the University of Nancy. He completed his doctorate in 1955.

After graduation he went to Paris and some of the top mathematicians became aware of his brilliance. He temporarily joined a mathematicians' collective known as Nicolas Bourbaki but he functioned best where he could be the acknowledged leader.

It was then that the French government created the Institut des Hautes Études Scientifiques (IHES), the Institute of Advance Scientific Studies. It was located just outside of Paris and became known as Grothendieck's School. In time it became the place to go for students of extraordinary mathematical talent. At the IHES in the late 1950's and 1960's Grothendieck blossomed into a world leader in mathematics. In 1966 Alexander Grothendieck was awarded the International Medal for Outstanding Discoveries in Mathematics, popularly known as the Fields Medal. It goes only to mathematicians under the age of forty. It is awarded every four years and in 1966 it was awarded to Michael Atiyah, Paul Joseph Cohen, Stephen Smale as well as Alexander Grothendieck. The award took place in Moscow that year and Alexander Grothendieck declined to attend the ceremonies because of Soviet military activities which had occurred in Eastern Europe. Stephen Smale did attend and created some embarrassment for the Soviet authorities by his political statements there.

Alexander Grothendieck's Life After Mathematics

Alexander Grothendieck was a stateless person and traveled throughout his life on a UN passport. He never applied for French citizenship. He was honored as a French mathematician and the French treated him with dignity and respect. As mentioned previously, about 1968 he became enraged at finding that the IHES was funded in part by grants from the French Ministry of Defense. He was caught up in the ant-Vietnam War movement in particular and an anti-military movement in general. He left the IHES in 1970 after he could not convince the administration to reject any further grants from the Ministry of Defense and effectively he left mathematics. He announced that he would do no more mathematics. He was given other academic appointments. One was to the most prestigious research institution, the Collége de France, but he did not or could not bring himself to lecture on mathematics. Instead he talked about social issues such as war and the environment. His academic appointment at the Collége de France was not renewed in 1973 and he left to live in the Pyrenees. He took an appointment at the University of Montpellier but lectured not on mathematics but on the political and social issues that concerned him at the time. In 1977 he was arrested and tried for participation in some political incent and was given a fine and six month sentence of incarceration. The prison sentence was suspended but not the fine. He burned his manuscripts and asked that all of his writings be within drawn from circulation.

In 1979 he disappeared into the Pyrenees with only a post office box as a link to the world. In 1993 he discontinued his post office box. As mentioned before around the year 2000 two young French mathematicians found him at a small town where he came to buy supplies. He talked with them. Others who have communicated with him say he is obsessed with the Devil whom he sees as being behind the turmoil of the world. Grothendieck wrote a document of a hundred pages during this time in which he describes a small group of individuals whom he calls mutants who represent the best in the human race. In 2005 another mathematician tried to locate Grothendieck and was unsuccessful. His was a meteoric career, shiny brightly for a brief time and then also like a meteor extinguished somewhere in the wilderness.

Source:
Amir D. Aczel, A Strange Wilderness: The Lives of the Great Mathematicians, Sterling Publishing Co,, New York, 2011.


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