Schapiro and his partner, the German writer Johanna Grothendieck, left the five-year-old Grothendieck in foster care in Hamburg when they fled Nazi Germany in 1933 to fight for the socialist cause in Europe. He was reunited with his mother in 1939, and lived the remainder of the war in a French internment camp or in hiding. But his Jewish father, interned separately, was sent to Auschwitz and murdered on arrival in 1942. It was this legacy of abandonment, poverty and violence that drove the mathematician and finally overwhelmed him, Matthieu suggests: “Artists and geniuses are making up for flaws and traumas. The wound that made Shurik a genius caught up with him at the end of his life.” Matthieu leads me into the huge, broken-down barn behind the house. Heaped on the bare-earth floor is a mound of glass flasks encased in wicker baskets: inside them are what remains of the mathematician’s plant infusions, requiring hundreds of litres of alcohol. Far removed from conventional mathematics, Grothendieck’s final studies were fixated on the problem of why evil exists in the world. His last recorded writing was a notebook logging the names of the deportees in his father’s convoy in August 1942. Matthieu believes his father’s plant distillations were linked with this attempt to explain the workings of evil: a form of alchemy through which he was attempting to isolate different species’ properties of resilience to adversity and aggression. “It’s hard to understand,” says Matthieu. “All I know is that they weren’t for drinking.” A dark image of an old barn with many whicker covered class bottles piled up View image in fullscreen Some of Grothendieck’s plant infusions. Photograph: Ulrich Lebeuf/MYOP/The Guardian Later, Matthieu agrees to let me look at his father’s Lasserre writings – a cache of esoterica scanned on to hard disk by his daughter. At the start of 2023, the family were still negotiating their entry into the French national library; the writings have now been accepted and at some point will be publicly available for research. Serious scholarship is needed to decide their worth on mathematical, philosophical and literary levels. I’m definitely not qualified on the first count. I open a first page at random. The writing is spidery; there are occasional multicoloured topological diagrams, namechecks of past thinkers, often physicists – Maxwell, Planck, Einstein – and recurrent references to Satan and “this cursed world”. His children are struggling to fathom this prodigious output, too. “It’s mystic but also down to earth. He talks about life with a form of moralism. It’s completely out of fashion,” says Matthieu. “But in my opinion there are pearls in there. He was the king of formulating things.” After a couple of hours’ reading, head spinning, I feel the abyss staring into me. So imagine what it was like for Grothendieck. According to Matthieu, a friend once asked his father what his greatest desire was. The mathematician replied: “That this infernal circle of thought finally ceases.” The colossal folds of Mont Ventoux’s southern flank are mottled with April cloud shadow as cyclists skirt the mountain. In the Vaucluse département of Provence, this is the terrain where Alexander Grothendieck took his first steps into mysticism. Now, another of his sons, Alexandre, lives in the area. I wander up a bumpy track to see the 62-year-old ambling out of oak woods, smiling, to meet me. Wearing a moth-eaten jumper, dark slacks and slippers, Alexandre is slighter than his brother, with wind-chafed cheeks. He leads me into the giant hangar where he lives. It is piled with amps and instruments; at the back is a workshop where he makes kalimbas, a kind of African thumb piano. In 1980, his father moved a few kilometres to the west, to a house outside the village of Mormoiron. In the subsequent years, Grothendieck’s thoughts turned inwards towards bewildering spiritual vistas. “Even with all his wisdom and the depth of his insight, there was always a sense of excessiveness about my father,” says Alexandre. “He always had to put himself in danger. He searched for it.” Grothendieck had abandoned the commune he had been part of since 1973 in a village north of Montpellier, where he still taught at the university. From 1970 onwards, he had been one of France’s first radical ecologists and became increasingly preoccupied with meditation. In 1979, he spent a year dwelling intensely on his parents’ letters, a reflection that stripped away any lingering romanticism about them. “The myth of their great love fell flat for Shurik – it was a pure illusion,” says Johanna Grothendieck, who bears her grandmother’s name. “And he was able to decrypt all the traumatic elements of his childhood. He realised he had been quite simply abandoned by his own mother.” A creased, black and white portrait of a boy with curly hair and wearing a cord jacket View image in fullscreen Alexander Grothendieck as a child … Photograph: Shutterstock