I’m very sorry to hear (via Michael Harris) of the death this morning in Paris of Lucien Szpiro, of heart failure. Szpiro was a faculty member here at Columbia for a few years, livening up the place at a time when the department was smaller and quieter than it is now. He then went on to a position at the CUNY Graduate Center and was often at the department here for number theory related talks. The Graduate Center has a short bio of him here, and on his website you can find more about his work, including some very nice short and lucid lecture notes on arithmetic geometry (see here and here). Some pictures of him and other mathematicians at his 70th birthday conference in 2012 can be found here.

What Szpiro is probably most famous for is the “Szpiro Conjecture” about elliptic curves which he first formulated in 1981. This is essentially equivalent to the later abc conjecture that has been the topic of recent controversy, so we really should have been all this time arguing about Szpiro, not abc. In a 2007 blog post I put out the news that Szpiro had announced a proof of abc at a talk he gave at Columbia (at Dorian Goldfeld’s 60th birthday conference). Alas, a flaw in that proof was quickly found.

**Update**: Something about Szpiro from Christian Peskine:

Lucien Szpiro est décédé d’une crise cardiaque samedi 18 avril. Ceux qui l’ont bien connu souhaitent d’abord saluer un homme d’exception. Lucien était tout à la fois un solitaire, un collaborateur passionné et un patron aimé et respecté. Un homme solitaire, intransigeant sur sa liberté, sur ses choix et sur la considération qu’il attendait. Un collaborateur passionnément ouvert au partage des idées et des projets. Un leader entrainant ses amis dans des aventures scientifiques nouvelles et enrichissantes.

Recruté au CNRS après un cours passage comme assistant à la faculté des sciences de Paris, il y est resté jusqu’à son départ à City University (New York) au début du siècle. Le séminaire qu’il a animé pendant de nombreuses années a été pour beaucoup de collègues de tous ages un lieu d’étude et de formation. Son influence et ses recherches ont fait honneur au CNRS. Ses nombreux élèves en témoigneront de leur coté. Il était heureux à New York ou il avait trouvé une forme de sérénité.

Ayant collaboré intensément avec Lucien durant de nombreuses années, je comprends que je perds un ami avec qui j’ai partagé des moments d’une intensité et d’une beauté rares. Il aimait la vie, il aimait la science et il aimait la recherche mathématique.

English translation, according to Google Translate:

Lucien Szpiro died of a heart attack on Saturday April 18. Those who have known him well would first like to greet an exceptional man. Lucien was at the same time a loner, a passionate collaborator and a loved and respected boss. A lonely man, uncompromising on his freedom, his choices and the consideration he expected. A collaborator passionately open to sharing ideas and projects. A leader taking his friends on new and enriching scientific adventures.

Recruited at the CNRS after a short course as an assistant at the Faculty of Science in Paris, he remained there until his departure from City University (New York) at the beginning of the century. For many colleagues of all ages, the seminar which he has led for many years has been a place of study and training. His influence and research have brought honor to the CNRS. Its many students will testify on their side. He was happy in New York where he had found a form of serenity.

Having collaborated intensely with Lucien for many years, I understand that I am losing a friend with whom I have shared moments of rare intensity and beauty. He loved life, he loved science and he loved mathematical research.

He was a great mentor for me and without his course at TIFR where I took notes, and all the time we discussed mathematics, I doubt I would have become a mathematician. I attended his 60th birthday in Paris and he was kind enough to attend mine in Kozhikode. Thank you for all the things you did for me and all the wonderful memories.

That is sad news.

This paper of Peskine and Szpiro is very beautiful (http://www.numdam.org/article/PMIHES_1973__42__47_0.pdf). I would argue that this work was the first to really demonstrate the Frobenius morphism as a tool of serious power and depth in commutative algebra, with relevance even to questions in characteristic zero. There is a direct line from this paper to the (ongoing) perfectoid revolution and its many amazing applications to pure commutative algebra, etc.

I’m sorry to hear that. I attended Spziro’s seminars and class many years ago at Columbia. I really learned a lot from him. I still remember his advice on how to understand the Grothendieck dualizing complex: “It doesn’t matter what it is, what matters is how it moves”, or in other words, how it transforms.

As a friend of Lucien, I must say that no account of him is complete that does not include a reference to his love for cinema, for fine dining and for music and the opera. I accompanied him to these things often and I can attest to his love of ideas and the arts.

He was a man of boundless integrity with a love of precision and an eye for the telling detail. I attended his seminars on Arakelov theory in the eighties at Columbia and on Number theory in NY (it was a joint CUNY Columbia NYU thing) when I was able to attend it. His taste was as impeccable as the precision of his grasp. He was totally dedicated to the life of the mind.

I also wish to covey my consolations to his many students and colleagues and above all to his partner of his last years, Beth Pessum.