Mathematician with Harsh Early Life
If a child who survived a war living in a refugee camp, can become a world-famous mathematician, surely you can, too!
FAMILY BACKGROUND
As a child living in Europe during World War 2, AG was separated from his parents while confined to living in a primitive camp to escape from evil people (Nazi’s) who would have killed him and all others hiding in the camp, solely because of their nationality or religion.
EARLY CHILDHOOD THOUGHTS OF AN ADULT CAREER
Sadly, AG’s early years were focused on survival till the next day, without realistic thoughts of living in peace as an adult. The five thousand ‘undesirables’ (mostly children) were served food, which was mostly boiled chestnuts, three times a day. Mushrooms or chicken was added if available. Sometimes the children were sent deep into the woods to hide for a few days.
To distract himself from the harsh realities of his daily life as a child whose parents’ whereabouts were unknown, AG spoke exclusively in rhymes, which he loved and believed that their sonic connections pointed to a mystery beyond words. Fortunately, he abandoned rhyming as he grew older.
While living in the internment camp, AG was tutored in mathematics by another prisoner, a girl. AG was only 12 when he was taught the definition of a circle: all the points that are equidistant from a given point. That definition impressed him with its “simplicity and clarity” he wrote years later. The property of perfect rotundity had until then appeared to him to be “mysterious beyond words.”
After the war, AG was reunited with his mother and attend public schools. Apparently, an independent thinker during his high school years, AG long remembered a teacher who unfairly gave him a bad grade for a math proof that AG performed in his own way, ignoring the textbook. He also recalled that his textbooks lacked ‘serious’ definitions of length, area and volume.
As an older teenager, AG worked in vineyards to support himself and his sister, who was weak from tuberculosis, which she had contracted in the refugee camp.
UNIVERSITY EDUCATION
The university in France, where AG was able to enroll, was not an important center of mathematics so AG independently pursued research on ideas having to do with measures, a field that less gifted students might dismiss as obvious, but AG ended up rediscovering a celebrated problem, Lebesque’s theorem and from that moment forward, AG thought of himself as a mathematician.
HAVING CHOSEN A CAREER PATH, HE WANTED TO LEARN MORE BUT STILL THINK INDEPENDENTLY
Following his university years, AG sought to learn from the most important French mathematicians of the time. AG eventually became a revered mathematician. His work involved finding the right vantage point – from there, solutions to problems would follow easily. He rewrote definitions, even of things as basic as a point; his reframings uncovered connections between seemingly unrelated realms of math. He spoke of his mathematical work as the building of houses, contrasting it with that of mathematicians who make improvements on an inherited house or construct only a piece of furniture.
Later in his career, AG was involved with some American universities through being asked to lecture students and developing professional relationships with American mathematics professors. One of AG’s projects involved leadership of a group to develop proofs of a math problem for which others had only developed a ‘conjecture.’ The project consisted of looking at algebraic geometry from a new point of view. AG saw a way to prove the conjectures, using what are now called ‘schemes, sheaves (a mathematical bundling system) and motives.’
AG spoke of problem-solving as akin to opening a hard nut. You could open it with sharp tools and a hammer, but that was not his way. He said that it was better to put he nut in liquid, to let it soak, even to walk away from it, until eventually it opened. He also spoke of ‘the rising sea’ method of problem solving: imagine a rocky and difficult shore, which you must somehow get your boat across. There may be a variety of ingenious engineering feats that can respond to this challenge. But another solution is to wait for the sea to rise, providing a smooth surface to cross effortlessly. Another mathematician said of AG’s work on schemes: “Once you set it up this way, it doesn’t read like a style or trend. It feels inevitable, like: This is what it is.”
(Editor’s note – This story is based upon an article published in the May 16, 2022, edition of The New Yorker Magazine, pages 28-33, which deal with the fascinating and mysterious life of Alexander Grothendieck, who “revolutionized mathematics and then he disappeared.” The article explains many math concepts improved by AG, including details which are unnecessary for this introductory summary of how one person overcame a harsh, early life, to successfully pursue a career field, which he improved through applying his independent, critical thinking to challenge conventional math wisdom, despite some initial, professional opposition.
If you are interested in pursuing a career as a mathematician, you should search for more information regarding Mr. Grothendieck, hopefully including the aforementioned magazine article.)
