I just heard that mathematician Serge Lang passed away this past Monday. Lang was a well-known number theorist and algebraist, a member of Bourbaki and recipient of the 1960 AMS Cole Prize. He was a professor here in the Columbia math department for fifteen years, leaving in 1972 for Yale, where he spent the rest of his career. Lang was an amazingly prolific author of mathematics textbooks, and famous for his outspoken views and “files” on various controversies. In recent years some of these had become increasingly cranky, especially on the topic of AIDS. He was truly one of the most remarkable characters of the mathematics research community.

**Update:** There’s an obituary at the Yale Daily News (thanks to David Goss for pointing this out).

**Update:** The New York Times ran an obituary of Lang today.

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Oh boo…he was quite a character. His algebra book is, like, the best algebra book in the world ever (reading one of his differential geometry books at the moment as well, it’s quite nice).

When I was a postdoc at Yale sometimes I would stay up late working in my office. Serge Lang was the only person I’d see, regularly working past 2 am, sometimes rushing off to the copier room to print out copies of his “files” to send to people.

He was quirky but fascinating – incredibly energetic, too.

When I was his TA for calculus he insisted that derivatives could be taught in 15 minutes: explain the idea, give the definition, show how to compute some examples… done.

I heard he would take a trans-Atlantic cruise each summer and produce a book during this time. I’m not sure that’s true, but it would help explain his prolific writings.

It’s a pity he’s gone.

I thought myself Linear Algebra, Complex Analysis and some Differential Geometry from Lang’s books.

As an undergrad, S. Lang, M. Spivak and T. Apostol were my “mathematical icons”!

It’s really sad to know that he’s gone…

This is sad. I’ve been spending a bit of time lately looking at some of his books, and he was on my mind a lot. I remember one time when I was a grad student, I was standing next to him at tea while he was explaining to a first-year that analysis is just “number theory at infinity”. I said Come on, that’s not true. He immediately turned up the volume, challenging me to stop bullshitting and give an example. I said OK, p-adic analysis, and then walked away. But I’ve always wished I had stayed to see what his reaction would have been. We need more trouble makers like him.

I guess that I’m in a minority here, in that I hated most of his books. I thought his Real Analysis was okay, but his Algebra is by and large a horrible book (it does have a few good chapters). I’m told his Differentiable Manifolds book has a truly outstanding number of mistakes in it.

I’m sorry to hear that he has passed, though.

He told me that when he read about a subject, he would write down everything he could find out about it. At the end, this could be made into a book. When he saw that you were impressed by how quick he was, he said that he did not have the gift of physicists who could watch an experiment and immediately visualise the equations that explained it. His was an uncompromising mind, and in non-mathematical conversation, he often asked you to define the words you used, or to perform a calculation in the field in the middle of a pop science explanation he was giving at a dinner. I have to thank him for the gift of a lifetime passion for mathematics he gave me, and I miss him and to know that I shall never stumble upon a new book by him in a bookshop makes me sad.

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Lang used to spend every summer at Berkeley. Arguing with him at tea time was enormous fun. I’m going to miss him.

I was an undergraduate at Yale. I never had Lang for a prof., but I knew him through the math club, of which he was an advisor. He was a tireless advocate of precision and rigor even in every day speaking. While I think that sometimes went too far, it was good that there was someone pushing things in that direction in a world in which people were losing rigor in their everyday speech more and more. I used to argue with him all the time. His defense of Shafarevich when Shafarevich was repressed by the Soviets and a second time, when the NAS to its discredit, decided to expel him for his views was highly laudable. I think that he was a bit unfair to Sam Huntington, and I sometimes disagreed with his views on pedagogy (he thought that his way to understand a subject is the only correct way). But surely, he will be missed by everyone who knew him (save for Sam Huntington, perhaps).

He was at Berkeley this summer, too, and gave a lecture on analysis to undergraduates before he left. He was in good spirits and was cheerfully dismayed by our ignorance. I was honored to meet him.

This past year, Professor Lang gave a wonderful presentation to the San Jose Mathematics Circle at San Jose State University.

He led the circle in an inspiring discussion of the numerical constant Pi. He opened new avenues of thought on this very old topic. In his leading the Circle, we could feel the presence of his greatness.

While Professor Lang was one of the world’s great mathematicians, he was also at ease in working with the youngest students in the Circle. He had a natural sense of humor that immediately caught the attention of young people.

A student that I mentor, Bowei Liu (who was then a gifted sixth grader), was influnced by his gentle nature and fine-tuned art of using a version of the Socratic Method to gain understanding of a deep mathematical topic. Bowei went on to win the Mu Alpha Theta Achievement Award at the Synopsis Silicon Valley Science and Technology Championship, across all grade levels 6-12, for his researched-based project on Pi entitled “Experimental Mathematics: The Relative Efficience of Estimating Pi.”

Whether it was Bowei, or someone like myself, who struggled to understand his “Algebra” textbook, we have all benefitted by his remarkable lifetime of achievement in mathematics. He was a “magister.”

My life has been enriched by having had the opportunity learn both about mathematics and dissent in a free society from the late Professor Serge Lang.

Serge was my advisor as an undergrad back in the early 1980’s. He was a tremendous moral, intellectual and musical influence. I’ll never forget that after we first met over dinner at the Law School, upon hearing that I knew no Baroque lute music, he walked me over to Cutlers records on Broadway and bought me an album of Julian Bream and Peter Pears.

Sadly, I was out of touch with him for many years, although I tried to get in touch with him at the beginning of the Summer. I will really miss him.

One of my favorite of his rejoinders: “that is a true statement that happens not to be relevant.”

Some ill-informed and ignorant person sated above: “In recent years some of these had become increasingly cranky, especially on the topic of AIDS.” Lang did not become cranky: he just asked questions concerning the anomalies amd contradictions regarding the redundant and unproven ‘HIV/AIDS’ hypothesis. Richard Horton of The Lancet could never answer any of Lang’s questions regarding the ‘HIV’ fraud: Horton, as well as Robert Gallo, Luc Montagnier and David Ho have never proven that ‘HIV’ exists or causes ‘AIDS’. In fact no one has: all the theories on ‘HIV’ are bassed assumptions and suppositions which have never been scientifically proven. Lang will be remebered for ‘Challenging’ the current ‘HIV’ myth making mathematical models!

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I suspect that I am the only person who had Professor Lang wait on the telephone. Early in the 90s our Departmental secretary left me a message Professor Lang wanted me to call him. We never met and I was excited that he knew me to call me! At that time making a long distance call from my office was a little hassle. I went to the secretary and told her that I wanted make a long distance call and gave her the number. I thought that she would inform me when she was making the call. A little after she called me in my office to tell me that Professor Lang was on the phone in her office. I was stunned that I had him waiting on the phone. I think he was a little annoyed with me but his attitude changed right away and he asked me for a reprint of one of my articles.

Later I received an e-mail from one of his students stating that Professor Lang received the reprint I sent him and wanted me to send him other reprints as well. Professor Lang, I think, immediately had the student e-mail me again that he wanted preprints as well as reprints. I will always remember and be appreciative of his interest in my work.

I got my B.A. at Columbia in 1955 and went to Princeton for graduate study in math. In my first year I studied with Lang’s thesis advisor Artin (among others). Artin returned to Germany after that year and asked Lang, who was then on the Columbia faculty, to commute to Princeton to continue teaching algebraic geometry, which Artin had introduced to a few of us – an extraordinary request by Artin and an extraordinary acceptance by Lang.

At that time algebraic geometry was not yet fashionable. and after a while, I was Lang’s only student in that subject, which he continued to teach. Two years later, I wrote a Ph.D. thesis under his direction, proving a conjecture he had made. He was a perfect advisor for me, sensing exactly when to be nice and when to yell at me, inspiring me with his passion for the subject and his uncompromising intellectual honesty.

I will forever be grateful to him.