Alexander Grothendieck

“Discovery is the privilege of the child: the child who has no fear of being once again wrong, of looking like an idiot, of not being serious, of not doing things like everyone else.”

Born: 28th March 1928 in Berlin, Prussia

Died: 13th November 2014 in Saint-Lizier, France

Nationality: French

Previous Occupation: Research Professor

Academic Interests: Algebraic Geometry, Commutative Algebra, Homological Algebra, Sheaf Theory and Category Theory

Childhood and Education

Alexander’s story began somewhat unusually, born to a Russian Jew and a married German woman during an affair. Tad controversial! His mother, Hanka, was married to and shared a daughter with a Mr Raddatz whilst his father, an anarchist and ex revolutionary soldier, had escaped prison and a death sentence and run away from his marriage and son. And the Father of the Year Award goes to… Yeah. Interesting duo, huh? The two met on a trip to Berlin during which Alexander was conceived. Since technically the pair were committing adultery, Alexander’s birth was recorded under the surname Raddatz after his mother’s husband. ‘Course it was – tut tut!

This is the part where it gets a little more serious, thanks to World War II *sigh*. After his mother’s divorce, Alexander lived with both his parents and his half-sister in Berlin where they ran a family photographic studio. They lived here together until, under Hitler’s reign, it became too dangerous and Alexander’s father fled to Paris, joined six months later by Hanka after she found a foster family for her son and admitted her daughter into an institution. Later, the pair moved to Spain to support the Republicans during the Civil War before returning to France.

Becoming increasingly dangerous in Berlin, Alexander’s foster family sent him to join his parents in France where he was later sent with his mother to an internment camp. Whilst here, Alexander continued attending the local village school and received private tutoring. In 1942, they were moved to a different concentration camp during which time, sadly, Alexander’s father was handed over to the Nazis and taken to Auschwitz where he died. Miraculously, Alexander managed to attend the Collège Cévenol in Le Chambon-sur-Lignon and achieved his baccalauréat in 1945. Talk about overcoming obstacles!

Alexander received a scholarship to study Mathematics at the University of Montpellier. Whilst studying for his undergraduate, he found he was dissatisfied with the lack of mathematical definitions, particularly around volumes and became determined to find the answers himself. A lot of ambition for a young man! Care to share some? With no guidance or support, Alexander rediscovered a general version of the Lebesgue integral. Smart guy, ey? I can just about do what I’m asked for on my course, never mind discovering some new, ingenious idea! After graduating, he spent a year in Paris at École Normale Supérieure under the advice of his previous lecturers and attended Cartan’s seminar on algebraic topology and sheaf theory.

In 1949, he moved with his mother (who later died from tuberculosis contracted in the concentration camps) and attended the University of Nancy to work on his areas of interest; topological vector spaces and functional analysis. Here, he had a son with their landlady! During his PhD studies, Alexander developed new techniques to solve problems in discovering a general theory of duality for locally convex spaces. He began further research into functional analysis on which he presented his doctoral thesis before claiming he was no longer interested in topological vector spaces. Least he wasn’t shy in admitting! I think I’d lose interest after sacrificing so much time and effort to one topic too! Consequently, he completed his second thesis on sheaf theory which sparked his initial interest on the main focus for his career; algebraic geometry.

Career

Alexander’s interests developed and after several years, shared between research at the University of São Paulo and the University of Kansas, his focus was on topology and geometry. In 1956, he attended the Centre National de la Recherche Scientifique who had been supporting him in his work since 1950 and became one of the Bourbaki group of mathematicians. Oooh – sounds very fancy!

In 1959, Alexander became a research professor at Institut des Hautes Études Scientifiques (IHÉS) where he stayed until 1970 and accomplished some of his best work. He led the launch of a new school of Mathematics and made the institute a world centre of algebraic geometry with his exceptional advances in number theory, topology and complex analysis. The development of his theories enabled mathematicians to solve conjectures in number theory and provide a proof of the Riemann-Roch theorem as well an algebraic definition of the fundamental group of a curve. Well. Seems like he did an alright job then?

The Fields Medal was awarded to Alexander in 1966 for his profound influence on the fundamentals of algebraic topology and homological algebra. This was displayed through his introducing of Grothendieck groups and rings and publishing of the well-known “Tohoko paper” defining sheaf cohomology using abelian categories. Alexander refused to attend the awards presentation in Moscow as a political protest and arranged for the award to be received on his behalf. Fair.

Intriguingly, Alexander resigned from his position at the IHES due to a dispute over military funding. Wondering what happened there? Well, once he discovered the institute were funded by the military, he along with his fellow professors asked the director to terminate this source of funding to which he agreed, however later retreated. Alexander was the only professor to resign as a result of this dispute. Go Alex! Following this, he decided to take himself away from the mathematical community and focus his efforts on politics instead, particularly for the movement against nuclear proliferation.

Alexander spent several years in the early 1970s as a visiting professor before taking a position as professor at the University of Montpellier in 1973. He remained in this position for eleven years before spending four years directing research at the Centre National de la Recherche Scientifique and finally retiring in 1988 aged sixty. The same year, he declined the Crafoord Prize. – Wait. Sorry, what? He declined it? Okay…

Following his retirement, Alexander focused on writing more mathematical, biological and philosophical publications. In 1991, he suddenly moved to the Pyrenees where he refused any contact with humans and civilisation and lived in isolation until his death in 2014. That’s so sad!! In the later years of his life, he is believed to have been very spiritual. He fasted to the point of starving himself and eventually showed signs of psychosis believing there was a second voice inside him telling him to spread the message of a ‘new age’. Spooky!

Awards and Achievements

  • Speaker at International Congress, 1958
  • Field Medal Winner, 1966
  • Crafoord Prize, 1988 (declined)

Trivia

  • Alexander was also known as Schurik and Alexandre Ruddatz
  • For most of his life he was a ‘stateless’ person since records of his nationality wre destroyed after the fall of Germany and he never applied for French citizenship after the war
  • He was father to five children; one with an old landlady of his, three with his wife and one with an ex housemate

Publications

Grothendieck, Alexander. Sur quelques points d’algèbre homologique, I. Tohoku Math. J. (2) 9 (1957), no. 2, 119–221.doi:10.2748/tmj/1178244839. https://projecteuclid.org/euclid.tmj/1178244839.

For a more extensive list see http://www.grothendieckcircle.org/.

References

  1. http://www-history.mcs.st-andrews.ac.uk/Biographies/Grothendieck.html
  2. https://en.wikipedia.org/wiki/Alexander_Grothendieck
  3. https://www.quora.com/Why-is-Alexander-Grothendieck-revered-by-mathematicians
  4. https://www.thefamouspeople.com/profiles/alexander-grothendieck-466.php
  5. http://www.grothendieckcircle.org/
  6. http://www.famous-mathematicians.com/alexander-grothendieck/