A black and white photo of Alexander Grothendieck wearing a hooded cloak and dark glasses, and with a long grey beard Alexander Grothendieck in 2013. Photograph: © Peter Badge/Typos1 in cooperation with the HLFF. All rights reserved 2024 This article is more than 1 month old ‘He was in mystic delirium’: was this hermit mathematician a forgotten genius whose ideas could transform AI – or a lonely madman? This article is more than 1 month old In isolation, Alexander Grothendieck seemed to have lost touch with reality, but some say his metaphysical theories could contain wonders By Phil Hoad Sat 31 Aug 2024 12.00 CEST Share 277 One day in September 2014, in a hamlet in the French Pyrenean foothills, Jean-Claude, a landscape gardener in his late 50s, was surprised to see his neighbour at the gate. He hadn’t spoken to the 86-year-old in nearly 15 years after a dispute over a climbing rose that Jean-Claude had wanted to prune. The old man lived in total seclusion, tending to his garden in the djellaba he always wore, writing by night, heeding no one. Now, the long-bearded seeker looked troubled. “Would you do me a favour?” he asked Jean-Claude. “If I can.” “Could you buy me a revolver?” Jean-Claude refused. Then, after watching the hermit – who was deaf and nearly blind – totter erratically about his garden, he telephoned the man’s children. Even they hadn’t spoken to their father in close to 25 years. When they arrived in the village of Lasserre, the recluse repeated his request for a revolver, so he could shoot himself. There was barely room to move in his dilapidated house. The corridors were lined with shelves heaving with flasks of mouldering liquids. Overgrown plants spilled out of pots everywhere. Thousands of pages of arcane scrawling were lined up in canvas boxes in his library. But his infirmity had put paid to his studies, and he no longer saw any purpose in life. On 13 November, he died exhausted and alone in hospital in the neighbouring town of St-Lizier. The hermit’s name was Alexander Grothendieck. Born in 1928, he arrived in France from Germany as a refugee in 1939, and went on to revolutionise postwar mathematics as Einstein had physics a generation earlier. Moving beyond distinct disciplines such as geometry, algebra and topology, he worked in pursuit of a deeper, universal language to unify them all. At the heart of his work was a new conception of space, liberating it from the Euclidean tyranny of fixed points and bringing it into the 20th-century universe of relativity and probability. The flood of concepts and tools he introduced in the 1950s and 60s awed his peers. A black and white image of a bald man standing by a blackboard in front of a class of students View image in fullscreen Alexander Grothendieck teaching at the elite Institut des Hautes Études Scientifiques in the 1960s. Photograph: IHES Then, in 1970, in what he later called his “great turning point”, Grothendieck quit. Resigning from France’s elite Institut des Hautes Études Scientifiques (IHES) – in protest at funding it received from the ministry of defence – put an end to his high-level mathematics career. He occupied a few minor teaching posts until 1991, when he left his home underneath Provence’s Mont Ventoux and disappeared. No one – friends, family, colleagues, the intimates who knew him as “Shurik” (his childhood nickname, the Russian diminutive for Alexander) – knew where he was. Grothendieck’s capacity for abstract thought is legendary: he rarely made use of specific equations to grasp at mathematical truths, instead intuiting the broader conceptual structure around them to make them surrender their solutions all at once. He compared the two approaches to using a hammer to crack a walnut, versus soaking it patiently in water until it opens naturally. “He was above all a thinker and a writer, who decided to apply his genius mostly to mathematics,” says Olivia Caramello, a 39-year-old Italian mathematician who is the leading proponent of his work today. “His approach to mathematics was that of a philosopher, in the sense that the way in which one would prove results was more important to him than the results themselves.” In Lasserre, he lived in near-complete solitude, with no television, radio, phone or internet. A handful of acolytes trekked up to the village once his whereabouts filtered out; he politely refused to receive most of them. When he did exchange words, he sometimes mentioned his true friends: the plants. Wood, he believed, was conscious. He told Michel Camilleri, a local bookbinder who helped compile his writings, that his kitchen table “knows more about you, your past, your present and your future than you will ever know”. But the