Alexander Grothendieck Heng Li Alexander Grothendieck's life Alexander Grothendieck was a German born French mathematician. Grothendieck was born on March 28, 1928 in Berlin. His parents were Johanna Grothendieck and Alexander Schapiro. When he was five years old, Hitler became the Chancellor of the German Reich, and called to boycott all Jewish businesses, and ordered civil servants who were not of the Aryan race to retire. Grothendieck's father was a Russian Jew and at that time, he used the name Tanaroff to hide his Jewish Identity. Even with a Russian name it is still too dangerous for Jewish people to stay in Berlin. In May 1933, his father, Alexander Schapiro, left to Paris because the rise of Nazism. In December of the same year, his mother left Grothendieck with a foster family Heydorns in Hamburg, and joined Schapiro in Paris. While Alexander Grothendieck was with his foster family, Grothendieck's parents went to Spain and partici- pated in the Spanish Civil War. After the Spanish Civil War, Johanna(Hanka) Grothendieck and Alexander Schapiro returned to France. In Hamburg, Alexander Grothendieck attended to elementary schools and stud- ied at the Gymnasium (a secondary school). The Heydorns family are a part of the resistance against Hitler; they consider that it was too dangerous for young Grothendieck to stay in Germany, so in 1939 the Heydorns sent him to France to join his parents. However, because of the outbreak of World War II all German in France were required by law to be sent to special internment camps. Grothendieck and his parents were arrested and sent to the camp, but fortunately young Alexander Grothendieck was allowed to continue his education at a village school that was a few miles away from the camp. After the Nazis invaded France, Grothendieck and his parents were sent to different camps. Grothendieck's father was sent to Camp du Vernet. Luckily, Grothendieck was allowed to stay with his mother in Camp de Rieucros, a camp for women. However, while Alexander Grothendieck was in the Rieucros internment camp, somehow, he managed to attend to the College Cevenol, which continued his education. Within a few months after Germany invaded France, France was then completely taken over by Nazi Germany. Unfortunately, in 1942 his father was captured and sent to the Auschwitz concentration camp by Vichy France and was murdered by Nazis in the summer of the same year. After World War II, Grothendieck moved to Montpellier. Grothendieck received some scholarships. With these scholarships, he went to the University of Montpellier to study mathematics. After he graduated from the University of Montpellier, he went to Paris and attended many top mathematicians' lectures and seminars. At that time, he was more interested in topological vector spaces than Algebraic Geometry. After he got this bachelor's degree in the University of Montpellier, he was advised by Elie Cartan, a famous French mathematician, to finish his doctorate degree at the University of Nancy. During that time, he wrote his dissertation on functional analysis. After he finished his doctorate degree at University of Nancy, he join a mathematicians' collective called Nicolas Bourbaki. In the mid 1950s, he went to the University of Sao Paulo and the University of Kansas. While he was at the University of Kansas, he published his Tohoku paper, which has revolutionized the subject of homological algebra. In 1959, Grothendieck joined the Institut des Hautes Etudes (IHES), which was where he found his interest in algebraic topology and algebraic geometry. In the IHES, his contribution to the algebraic topology and algebraic geometry have revolutionized the field. During the time at IHES, he has published "The Elements de geometrie algebrique" and "Fondements de la Geometrie Algebrique," which are his most important publi- cations. Also, in IHES his seminar about Algebraic Geometry was also published as a book by the institution, which also has a huge influence on Algebraic Geometry. The time when Alexander Grothendieck was in IHES, which was also called his golden age. Alexander Grothendieck in 1966 when he won the Fields Medal In 1966, Grothendieck won the world's highest honor in mathematics: the Fields Medal for his work done in on Weil conjecture, Zariski topology, and the idea of the K-theory has completely revolutionized the field of algebraic geometry and homological algebra . The ceremony was held in Moscow that year, but Grothendieck refused to attend to the ceremony as a protest because of the Soviet's aggressive military activities in Europe. Started in 1960s, Grothendieck started to participate in many anti-war movements. He did not only protest the Soviet Union, but he was also involved in many political activities against NATO. In November 1967, he went to Northern Vietnam in the middle of the Vietnam War to protest. Alexander Grothendieck is giving homology lecture in Vietnam After he came back from Vietnam, he gave several lectures and speeches about his trip to Vietnam and the destruction that he had seen. However, his efforts made only his advisor, Laurent Schwartz, start to care about the Vietnam War. Other than Schwartz, Grothendieck was not able to convince other people to be as involved in the war. In 1970, Grothendieck was participating in a violent protest and got arrested because he hit two police officers. 2 That same year after he was arrested, Grothendieck discovered that the IHES was partially funded by the military of France. He left the IHES because he failed to change the fact that IHES was getting funds from the military department. After this, he announced that he would not work on mathematics any further. He became a professor in the institutions, but he started to not to give lecture on math. Instead, he talked about the social and peace related topics. When many universities invited him to give a lecture about mathematics, he will not go unless they agree that he can give a lecture about his political philosophies first. Later, he participated in a political movement, and was put on trial. As a result, he was sentenced for 6 months to prison, and had to pay a heavy fine. Luckily the six months in prison penalty was suspended, however, he still has to pay the heavy fine. Alexander Grothendieck in 1988 In 1988, Grothendieck was awarded with the Crafoord prize due to his achievement on the Weil's conjecture. However, he declined the prize and wrote an open letter to the media. In the letter, he questioned the ethic of science community, and criticized scientists and mathematicians who only focus on their research and ignoring the fact that their funds are from the military. Within the letter, he also apologized to the Royal Swedish Academy of Sciences for rejecting the prize. In the same year, he retired and totally isolated himself from the mathematical community. During the 80s, he also started to have interest in religions. First, he was very interested in Buddhism. However, that did not last very long because in the 80s he started to look into Christianity. At the same time, he start to have some psychological issues. For a period of time, he identified himself as a Catholic nun and stated that he lived on the Eucharist alone for thirty years. Other than this, he had many other religious hallucinations. In the summer of 1991, Grothendieck left his home without telling anyone. Ever since 1991, there were very few people who knew where he was, not even his family. He was trying to erase all of his files, records, and publications. He also tried to avoid any types of human contact. Until 2000, two young mathematicians found him in a small town when he was buying supplies. In the year 2005, another mathematician tried to find Grothendieck but failed. During the time when he was disappeared from public site, he wrote a huge amount of papers about philosophy, meditation, and the existence of evils. In the 2000s, he wrote hundreds of pages about the "mutants." According to his writings, these mutants are a group of individuals who represented the best in the human race. 3 A very rare photo of Alexander Grothendieck in 2013. Alexander Grothendieck passed away on November 13, 2014 at the age of 86. Until his death, Alexander Grothendieck remained stateless and did not have a French citizenship. Even though, he was a French math- ematician. Throughout his life, he traveled with a UN passport, not with a French passport because he had never applied for a French citizenship. Alexander Grothendieck's mathematical works Perhaps the most important work that Alexander Grothendieck did is The Elements de geometrie algebrique or the Elements of Algebraic Geometry in English, also known as EGA. Grothendieck introduced the theory of schemes in the EGA. The theory of schemes is Grothendieck's first huge significant mathematical work. In simplest terms, he proposed attaching to any commutative ring a geometric object, called the Spectrum of the ring or an affine scheme, and patching or gluing together these objects to form the scheme. The ring is to be thought of as the set of functions on its affine scheme. One of the purposes of scheme was to develop the formalism that's needed for solving much deeper algebraic geometry problems. Once it was introduced, the theory has completely changed the field of Algebraic Geometry, because it became the universal framework or the language of Algebraic Geometry. Later on, the theory of scheme led to the proof of Fermat's Last Theorem. Alexander Grothendieck worked with Jean Dieudonne together on the EGA. However, only a small part of the book was actually published.