Alexander Grothendieck, childhood and adolescence.

Tell me in detail about Alexander Grothendieck's childhood and adolescence and include details about his parents and siblings.

Alexander Grothendieck, one of the most influential mathematicians of the 20th century, had a tumultuous and unconventional childhood shaped by political upheaval, exile, and personal tragedy. His early life provides context for the unique intellectual path he later took.

Early Life and Family Background

Alexander Grothendieck was born on March 28, 1928, in Berlin, Germany, to politically radical parents who lived in exile for much of their lives.

Parents

Father: Alexander "Sascha" Shapiro (Shapiro is sometimes spelled Schapiro)

Born in 1889 in Russia, Sascha was a committed anarchist and revolutionary.
He participated in the Russian Revolution of 1905, for which he was arrested and eventually fled Russia.
After escaping to Western Europe, he continued his anarchist activities, living in various countries under assumed names. His work and beliefs made him an itinerant political exile, constantly on the move, which strongly influenced the family's unstable life.
Sascha eventually settled in Germany, where he met Alexander's mother, Hanka.

Mother: Johanna "Hanka" Grothendieck

Born in 1900 in Hamburg, Germany, Hanka was the daughter of a bourgeois family, but she rejected her middle-class upbringing.
Like Sascha, she was a staunch leftist, actively participating in anti-fascist and anarchist circles.
Hanka was a writer and journalist, known for her defiant and radical ideas. She wrote under pseudonyms, and some of her work reflected the couple’s radical political views.
Both of Alexander’s parents were staunch opponents of fascism, and when Hitler came to power in Germany in 1933, they fled the country, leaving Alexander in the care of a foster family.

Grothendieck’s Childhood

When Alexander was five years old, in 1933, his parents fled Nazi Germany to avoid persecution. They initially settled in France, leaving Alexander behind in Hamburg, where he was placed with foster parents for several years.
By 1939, as the threat of war loomed, Alexander rejoined his parents in France. However, when World War II began, his father, Sascha, was arrested as a “undesirable foreigner” and interned in various camps, including the infamous Le Vernet camp in southern France. Hanka and Alexander were also interned for a time, in a camp called Rieucros, though Hanka was released before the war ended.
Tragically, in 1942, Sascha was deported to the Auschwitz concentration camp, where he was killed. This marked a profound turning point in Alexander’s life, as he lost his father during the Holocaust.

Adolescence in Wartime France

After his father's death, Grothendieck and his mother lived in extreme poverty. The war years were filled with hardship, displacement, and hunger. They were effectively stateless, as Grothendieck had no official nationality at this time.
Despite the chaos, Alexander attended school sporadically. In the early 1940s, he found refuge in a Protestant school for displaced children in the town of Le Chambon-sur-Lignon, a community known for its resistance to the Nazis and protection of Jewish refugees.
There, Grothendieck began to show an aptitude for mathematics. However, due to his erratic schooling, he had large gaps in his formal education, and much of his early learning was self-directed. He nurtured his mathematical talent in isolation, relying on his sharp intellect and deep curiosity.

Post-War Years and the Beginning of an Intellectual Journey

After the war, Grothendieck was able to attend the University of Montpellier starting in 1945, where he initially studied mathematics. However, he quickly realized that the level of teaching there was elementary, and he sought out more challenging material.
By 1948, Grothendieck moved to Paris to immerse himself in the center of mathematical research. His mother accompanied him, and despite their strained financial situation, Alexander began to make a name for himself in the academic world.
During this period, Hanka’s health began to deteriorate, and she suffered from mental health issues. Grothendieck cared for her for much of his early adulthood, a responsibility that further isolated him.

Family and Siblings

Grothendieck grew up as an only child in a deeply unconventional family. While he had no biological siblings, the instability of his family life and the political commitment of his parents led him to have a wide and varied network of comrades and friends in anarchist and anti-fascist circles.

Hanka and Sascha’s intense political beliefs and constant exiles meant that Grothendieck never experienced a traditional family environment. His mother remained a major influence on his life, but it was the intellectual freedom and intensity of thought in his childhood that contributed to Grothendieck’s later radical ideas about mathematics, philosophy, and even society.

Impact of Childhood on His Work

Grothendieck’s early life, marked by displacement, loss, and a lack of formal education, contributed to his remarkable independence of thought. He developed a unique mathematical vision, often working in isolation, fueled by his ability to think abstractly and beyond traditional boundaries. His childhood, devoid of the stability most children experience, shaped his approach to mathematics, which was similarly radical and revolutionary.

His rejection of conventional paths in life mirrored his rejection of established approaches in mathematics, allowing him to produce groundbreaking work in algebraic geometry, topology, and category theory.

Did he write journals or notes during his childhood?

There is no record of Alexander Grothendieck writing detailed journals or notes during his childhood and adolescence, at least not in the formal sense that became characteristic of his later life. His early years were marked by upheaval, displacement, and survival, so it’s unlikely that he had the stability or resources to keep regular journals during that time.

However, later in life, Grothendieck became known for his extensive and reflective writing, both in mathematics and about his personal and philosophical views. These writings often touched on his childhood experiences and the deep influence they had on his worldview.

Later Writings: "Récoltes et Semailles"

One of Grothendieck's most famous written works, "Récoltes et Semailles" (Reapings and Sowings), written in the 1980s, is part memoir, part philosophical reflection, and part critique of the mathematical community. In this sprawling document, he reflects on his childhood, his relationship with his parents, and the psychological and emotional struggles he faced as a result of his early life experiences. He delves into how the loss of his father and the harsh conditions of his upbringing shaped his intellectual and emotional development. This work offers insights into how Grothendieck viewed his childhood retrospectively, especially in relation to his later mathematical and spiritual journey.

While "Récoltes et Semailles" wasn't written during his childhood, it gives a deep insight into how Grothendieck processed those early experiences in adulthood. His later writings are filled with personal reflections, demonstrating a kind of self-analysis that may have grown from years of quiet introspection, even if it wasn’t formally recorded during his youth.

Mathematical Notes from Early Adulthood

In terms of mathematics, once Grothendieck reached adolescence and early adulthood, he was known to fill notebooks with extensive, detailed notes. Much of this started in his university years when he began working intensely on mathematics, often exploring problems in isolation. This habit of writing became a major part of his mathematical practice, and he would later become famous for his massive troves of unpublished notes, letters, and manuscripts, many of which have only recently been discovered or digitized.

In summary, while Grothendieck didn’t keep journals or notes during his childhood in the way he did later in life, his later writings, particularly "Récoltes et Semailles," provide profound insight into how his early years influenced his thought process. His reflective nature later manifested in his monumental written works, both in mathematics and philosophy.

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