The root cause for his departure from mathematics was his categorical refusal to let the military-industrial complex invest in his research at Bures-sur-Yvette.
Source: https://www.jp-petit.org/Nouvelles/Grothendieck.htm
- I know the story. He was a man viscerally opposed to militarism. He once said "he'd rather be shot than wear a uniform." One day a letter arrived at IHES in Bures, where the army's scientific services, called DRET at the time (Direction of Research and Technical Studies), now DGA (Delegation for Armament Applications), offered a grant of four thousand francs (650 euros). When he came across this paper, he flushed red, saying "No way we're accepting a penny from these people!" His colleagues tried to change his mind: "Listen, Alexandre, don't be so rigid. It'll pay for photocopies..."
- And then?
- He said, "It's not difficult, we'll put it to a vote. The IHES scientific council will decide whether or not to accept money from the soldiery. But if you accept this grant, I solemnly warn you: you'll have my resignation in your hands within the minute that follows."
- And what happened?
- They didn't take his threat seriously. The vote took place and the four thousand francs were accepted by a majority of one vote. His face then turned grey, hard as marble. He took a letterhead paper and simply wrote: "I have the honor to tender my resignation" then handed it to the council members and turned on his heel. The next day he didn't show up at his office, nor the day after. Paperwork began to pile up. There were letters from all over the world.
- He was a Fields Medal winner.
- His reputation was such that he attracted the greatest mathematicians on the planet to the Institute. For everyone, he was the beacon of Algebraic Geometry, illuminating the entire planet with all its light. At first, people thought it was depression or a disappearance. At IHES, he occupied an official apartment. After a week, they ended up calling a locksmith to open the door. The apartment was empty. Masses of his papers were found in a trash can. He had thrown everything away, his notes, his books, his reports, his correspondence.
- Incredible! ...
- Wait, weeks and months passed without anyone knowing where he had gone. You can't imagine the panic at the Institute. Scientists started calling from all corners of the world. They had to answer and admit that he had resigned. People wanted to know why he had acted this way, under what circumstances this had happened, where he had gone, what he was doing now. The most unbelievable rumors were circulating. At one point, they thought he had committed suicide, but as some people had met him, they had to face the facts: he was apparently still alive. We have a letter from him dated two years after his resignation from IHES addressed to a company providing organic fertilizers, where he complains that these do not meet the specified standards. It was indeed his signature and, it must be said, his style.
- And since then?
- Since then, nothing. The world's greatest mathematician simply vanished one fine day. He simply let the scientific community know that he wanted nothing more to do with this environment. He announced, through a letter he addressed to one of his former students, his decision to withdraw completely. As people had finally located him in this small village near Carpentras where he had rented a small farm, they hoped to flush him out by offering him a new prize, the Crafoord Foundation prize. This must have been in the early eighties. The amount was around forty million francs.