They wrote to each other for thirty-one years and met four times. The letters begin in 1974, when both were postgraduate students working on the same obscure problem, and the early ones are entirely professional. He sends a proof. She finds an error in it. He concedes the error with what reads, even now, as slightly excessive grace. By 1979 the mathematics occupies roughly half of each letter. By 1983 it has become a pretext. Neither ever left the marriage they were in. This is stated plainly in the letters, repeatedly, in a tone that varies from resolve to exhaustion, and it is honoured. The correspondence contains no proposal, no arrangement, nothing that could be called a plan. What it contains instead is an extraordinarily detailed record of two people paying attention to each other. Their respective spouses knew about the letters. This was not a secret in the ordinary sense; both families exchanged cards at new year. Whether they knew what the letters contained is a different question, and the archive is silent on it, as archives generally are on precisely the things one wants. The scholarly interest is real. Two of the results in the correspondence were never published and are, according to people qualified to judge, worth publishing still. But the collection was not donated for that reason. Her daughter deposited it after both were dead, with a note saying that it seemed wrong to destroy something so carefully kept. The difficulty for a reader is deciding what one is looking at. It resists the categories on offer. Calling it an affair is inaccurate and calling it a friendship is evasive. It has the intensity of the first and the conduct of the second, sustained over three decades with a discipline that neither modern permissiveness nor traditional prohibition has a vocabulary for. The last letter is from him, dated eight weeks before his death, and it is four lines long. He does not say goodbye. He asks whether she ever resolved the third case, which had defeated them both in 1981. Her reply is in the file, unsent, in an envelope she addressed but never posted. She had resolved it. The proof is on the second page, and it is elegant, and there is nothing else in the letter at all.