Langlands on Langlands

In a forthcoming issue of the AMS Bulletin, there will be a long review by Robert Langlands of the book p-adic Automorphic Forms on Shimura Varieties by Haruzo Hida. The book itself is on a very technical subject, but the review includes long sections by Langlands that are much more generally about the current state of the so-called “Langlands Program”. While this inspired the “Geometric Langlands Program” that I’ve written about here recently, it’s a quite different subject, one that is very much central to research in number theory. Basically it deals with number fields (extensions of the field of rational numbers), and the function fields of geometric Langlands involve very different issues.

At the same time as making available his review, Langlands also made available commented copies of his correspondence with various experts in the subject about a draft of the review that he had sent them. Much of the review itself is likely to only be accessible to experts, and this is even more true of the correspondence. Casselman comments:

I also have the impression that you have edited this review for the pleasure of experts, and that therefore the cutting-room floor is filled with the sort of stuff The Naive Reader might appreciate.

The response to this from Langlands is:

I had in mind explaining more, but the editing was not a matter of choice but of necessity. I did not understand enough to say more.

I suspect few people will be able to follow the discussion here, but it gives a good idea of what is going on in an active but very difficult area of mathematics.

Both of these documents are from a fantastic resource, a web-site set up by Bill Casselman which contains pretty much the complete works of Langlands on-line. If you want to know more about the Langlands program and where it comes from, there’s lots of material worth reading on the site. One of the more readable sources for a beginner is the 1989 Gibbs symposium lecture on Representation theory- its rise and its role in number theory.

For a lower form of entertainment, there’s another book review, of Leonard Mlodinow’s Euclid’s Window, which appeared in the AMS Notices. The review is pretty much completely over the top, beginning with the sentence:

This is a shallow book on deep matters, about which the author knows next to nothing.

Update: I should also have mentioned that last month there was a small conference at the IAS on The L-group at 40, in honor Langlands’ 70th birthday.

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24 Responses to Langlands on Langlands

  1. Peter Orland says:

    Since I haven’t read Lenny Mlodinow’s book, I don’t know
    if the review is a fair one. Apropos of nothing, I took classes
    with Lenny at Berkeley before he turned into a writer for “Star
    Trek” and author of pop-science books. The review reminds
    me of the proverbial referee report, “This paper fills a
    much needed gap in the literature.” (attributed, no doubt
    falsely, to Paul Halmos).

    But at any rate, I was impressed by Langland’s breadth of
    knowledge of the classics of mathematics and of the history of
    science in general.

  2. I haven’t read Mlodinow’s book either, but I feel certain that if I disliked it, it wouldn’t be for the reasons given by Langlands. Lewd and tawdry jokes? Cartoon caricatures of complicated historical narratives? A relentlessly late-20th-century perspective? Sounds pretty good to me…

  3. luny says:

    On a somewhat unrelated note, check out the closing talk of the Quark Matter conference,
    slide 19 onwards.
    The slides do not convey the extremely caustic sarcasm the speaker presented them.
    Considering the extremely political nature of this conference, this is interesting.

  4. fh says:

    “Sounds pretty good to me…”

    You are joking, right?

  5. Gumbi says:

    Langlands ironically characterizes his own review as “the pedantry of… one priggish mathematician” and I have to say that is pretty accurate. I have seldom seen a more blatant or arrogant display of a reviewer showing off his superior knowledge and mastery of every aspect of the subject covered by a book.

    I suggest that Langlands put a tiny part of his amazing mind to the study of what economists call “comparative advantage”. He will learn that even if he is better than everyone at everything, there is still a role for the lesser minds of the world to make their own efforts, poor though they might be compared to what the great Langlands would have done if he had condescended to devote time to such matters.

  6. Kea says:

    When I met him, I thought Langlands was very nice.

  7. You are joking, right?

    Yes, but I also had a serious point. When we talk about the history of science (or anything else), I don’t agree that we’re forbidden from generalizing, making moral judgments, telling stories with heroes and villains, cracking jokes, or asking questions that wouldn’t have seemed pertinent at the time but do seem so now.

    So for example, anyone who’s not a total philistine “knows” that Bertrand Russell’s History of Western Philosophy and E. T. Bell’s Men of Mathematics are worthless as intellectual history: “biased,” “simplistic,” “reductive,” “romanticized,” and so on. In other words, the trouble with these books is that they’re not dry as dust.

    Wherever Russell and Bell get their facts wrong, one can and should take them to task for it. But beyond that, they’re every bit as entitled to their romantic visions of history as their critics are to their own.

  8. Mark Hillery says:

    When Robert Langlands’s review of Leonard Mlodinow’s book came out, the two opinions I heard most frequently expressed, which coincided with my own, were that a review that is this over the top says more about the reviewer than the book, and that the AMS Notices should never have published it. Since I have known Leonard for 30 years and enjoyed his books, I wrote to the then editor, Harold Boas (who, weirdly enough, went to high school with Leonard Mlodinow – six degrees of separation anyone?), criticizing the decision to publish the review. Much to my surprise, I received a rather lengthy response. The main thing I remember about it is that I was accused of making an ad hominem attack on Robert Langlands. Why? I had suggested that in order to see what people who want to write popular accounts of mathematics and physics are up against, it might do Prof. Langlands some good to take a little time off from the Institute for Advanced Study and teach a precalculus course at a large state university. It’s a tough audience out there and capturing and keeping their interest is not easy.

    Writing about science, and especially mathematics, for a popular audience is a very different task than doing research in mathematics or writing scholarly accounts of it. Doing it well takes hard work and a great deal of writing skill. I have read several books by very good scientists, meant for a popular audience, that were quite dull, because the writing was flat. Those of us who work in science benefit from the efforts of those who work to make the public interested in our subject.

  9. fh says:

    “But beyond that, they’re every bit as entitled to their romantic visions of history as their critics are to their own.”

    Whatever became of “Everyone is entitled to their own opinion, but not their own facts.”?

    Now we all are entitled to have our own mythologies, but just basic scholary and intellectual ethics/honesty forbid the kind of trivializing and falsifying of history for the purpose of entertaining.

    Russel no doubt was very aware of the perspectives of the respective times he writes about. This does not mean that we can not or should not analyze them through a modern perspective, but to actually provide anything with any sort of valuable insight one needs to understand first. Their internal consistency and perspectives (as far as possible).

    Something which by all appearances the author failed spectacularly at.

    Russel uses western philosophy as a canvas to communicate certain insights and structures in philosophy. That is, the book tells us (to some degree at least) about Russell’s philosophy not about the historical philosophies. Therein lies (one of) it’s value(s).

    Also there is a difference between “biased,” “simplistic,” “reductive,” “romanticized,” and “flat out wrong,” “ahistorical,” “without any understanding of the matter” etc… In so far as Langlands review is accurate the author also committed errors in terms of scholary precision that are unforgivable.

    Then just as Russels use of a mythizised but essentially insightfull analysis of history is remarkable and praiseworthy, this use of an essentially wrong mangled and disfigured history for the sake of cheap entertaining is abhorrable.

  10. lostsoul Ph. D. says:

    The Langlands assessment of Euclid’s Window is renowned as an example of OTT and sarcastic review – it must be (in)famous because even I have heard of it. It owes its celebrity to its acerbic style (which other AMS reviewers have cultivated in the past), and not to whatever it may convey about the book in question (which I have not read, but have heard people speak quite highly of). How different is it from some of the ordure heaped on Peter’s book of late? Professional competence and, still less, genius do not guarantee civility and self awareness; just because a fellow is an ass-hole, it doesn’t mean he’s wrong. But, then again, it doesn’t mean he’s right either. The perils of popularisation, I suppose.

  11. Mlodinow wrote a PhD dissertation on how QM would work in a universe with an infinite number of spatial dimensions. This dazzled Gell-Mann, who had him appointed to a major faculty position at Caltech. Then the story gets interesting.

    Mlodinow has had successful teleplay writing during and after his tenured Physics professorship at Caltech, a marvelous biographical book (Feynman’s Rainbow), and collaboration with Steven Hawking, that will yield a new movie next year. Might there not be a sour grapes effect here? I admire Langlands’ math very much, so far as I understand it. But this reminds me of Carl Sagan being blackballed from the National Academy of Sciences by those jealous of his popular success in books, TV, and film.

  12. L group says:

    It’s great that AMS published the review. It will have no impact on the popularity of the book, as the readership of the Notices can form their own opinions and are a drop in the ocean compared to the mass market. More exacting viewpoints, such as Langlands’ or that of Weil in earlier times, are much less visible, and it is good that they are represented from time to time.

  13. JC says:

    Jonathan Vos Post,

    Was Mlodinow a postdoc or tenured faculty at Caltech? From reading his book, I got the impression he was only a postdoc. What was amusing were Feynman’s anti-string tirades, he wrote about.

  14. Peter Woit says:

    The talk mentioned by “luny” seems to be stirring up trouble, see


    where there’s the usual Lubos attack on anyone who points out that string theory is being over hyped.


    I also think the Langlands review of the Mlodinow book has more to say about Langlands than about the book, and I think the AMS Notices should not have published it.

    Reading the many reviews of my book has provided a new perspective on book reviews, and why they often have little to do with reality. While many reviewers misunderstood what I had to say in the book, I can’t complain, since on the whole, their misunderstandings led them more often to write positive things than negative things. The one time I tried to contact a publication about whether they were willing to correct something completely factually untrue that a reviewer had written (KC Cole in the LA Times) was an eye-opening experience. The people there made clear to me that their policy (and presumably the policy of many places) is that:

    1. While in the rest of the newspaper they care about factual accuracy, reviews are opinion pieces and thus they have no problem with factually inaccurate statements appearing in them.

    2. The only standard for these reviews is whether the reviewer has some sort of argument, no matter how irrational and crazy, for what they wrote.

  15. D R Lunsford says:

    Langlands says about his thesis

    Examining again, after forty years, the verification of the basic estimates of the second part, I found a large number of misprints, so that it would have been difficult if not impossible to follow my arguments line by line. I have tried in the present version to correct the misprints, but cannot be certain to have fully succeeded.

    The thesis remains, to my regret, my only active encounter with partial differential equations, a subject to which I had always hoped to return but in a different vein.

    That is remarkable in a way. I wonder what he meant?


  16. D R Lunsford says:

    Mlodinow was apparently a writer on the Picard version of Star Trek. I think that is the harshest review I’ve ever seen, of anything! Well no, Ebert’s 0-star movie reviews are a lot like this..

    I can’t say a word about Langlands as a mathematician but he is certainly an entertaining writer. The review leaves one with an uneasy feeling for some reason, as if culture itself, and not just mathematical culture, were in decline, and he is lamenting the passing of it.


  17. JC:

    From the Preface to “Feynman’s Rainbow: A Search for Beauty in Physics and in Life” [Warner Books, May 2003):

    “… this book is about my time just after graduation in 1981, when I was on the faculty of the Calfornia Institute of Technology….”

    “I had been given my fellowship…. Did I really fit in here, with two Nobel prize winners down the hall….”

    “This book tells the story of my first year on the Caltech faculty”

    I admit to the ambiguity: does he mean that “faculty” includes “postdocs”?

    I don’t think that Caltech had adjuncts, but they also had Instructors, such as my friend Dr. Thomas McDonough. Instructores teach classes, so I suppose are faculty, but not tenure track.

    I’d ask Mlodinow directly, but he is sufficiently busy that he answered an email of mine when I invited to speak on a track of an international conference where I chaired 3 sessions, but explained why he had to decline the attractive offer due to how busy he was.

    Good question. I’m still not sure.

    Do you agree with the possibility of my Carl Sgan / sour grapes analogy? Amusingly, Brian Green had a bit part in the science fiction film “Frequency” and now seems to have been an executive consultant or the like on the big-budget feature “Dej Vu.”

    Here we go again with Esquire Physics, or People Magazine Physics.

  18. Heavy Ion Guy says:

    Dear all,

    At quark matter this year Larry did make some strong statements about string theory. This was a response to one paragraph in Brian-Greenes Op-Ed piece in the New York Times.

    The full paragraph which makes reference to the heavy ion work is here “And in a recent, particularly intriguing development, data now emerging from the Relativistic Heavy Ion Collider at the Brookhaven National Laboratory appear to be more accurately described using string theory methods than with more traditional approaches. ”

    This statement in the public press should be called for what it is — a wild exaggeration of the state of the theory in the heavy ion community. Larry’s main point was that if such claims are to be made in the public press they should be held to the same standards of scientific scrutiny as the “more traditional approaches”. Larry was correct to sharply criticize this remark.

    That being said, a number of people (who normally think about heavy ion collisions) have recently been calculating transport coefficients with AdS which they really wanted to know in QCD. These transport coefficients have been inferred from hydro and kinetic models of the heavy ion reaction and generally are smaller than what would be expected from a weakly coupled plasma. It is important to emphasize that each of hydro/kinetic models have a number assumptions that can certainly be challenged. Nevertheless to reproduce these small transport coefficients with perturbation theory consistently requires an extrapolation outside the domain of validity into the strong couplign regime. The AdS/CFT provides a useful foil to extrapolations based on perturburation theory into this regime. Many aspects of the strongly coupled N=4 plasma are markedly different from the qualitative features of perturbation theory. It would be nice to determine a relatively clean observable which would probe these qualitative differences. I think that AdS/CFT is a phenomenological long shot, but it is good (and relatively easy) fun.

  19. JC says:

    Jonathan Vos Post,

    The Sagan/sour grapes analogy sounds a bit like what happens in many fields and/or niches. “Serious” folks who find success in the popular media/culture, are seen as “sell outs”.

    Do you think it is related to how people like to “compare” themselves to others? Many “serious” people see popular culture as something “low brow”.

  20. Juan R. says:

    This statement in the public press should be called for what it is — a wild exaggeration of the state of the theory in the heavy ion community. Larry’s main point was that if such claims are to be made in the public press they should be held to the same standards of scientific scrutiny as the “more traditional approaches”. Larry was correct to sharply criticize this remark.

    Ok, but would be remarked that calls for holding to the same standards of scientific scrutiny in public press are not new. They are part of well-known scientific ethics guidelines in other communities.

    About stringers reactions, Clifford is right when states that there is nothing wrong with being publicly excited by the possibility, though.

    In the same vein, there is nothing wrong being publicly excited by the possibility string theory leave us nowhere in main goals.

    Still, Clifford fail to understand that Greene was critized not because claimed possibilities but because claimed more accuracy becoming from the string part when even there is not qualitative agreement with experimental data.

    About Motl comments, i would cite

    But physics is not just about the fundamental Lagrangians as some of the idealized theorists could think. It is about the understanding of all possible phenomena and about predicting of the outcomes of experiments in a wide variety of physical situations.

    That is just the reason because string theory is in trouble.

    Unfortunately, Motl presents the same class of disturbed reasoning about string theory that Greene. For instance Motl writes

    The most far-reaching new technique in the research of strongly coupled gauge theories is undoubtedly the AdS/CFT correspondence.

    Just a few words after you discover that by most far-reaching technique means that many people have very good reasons to expect that this tool will be the most efficient one to understand questions about the strong force. But nobody proved this, just again, like in last 40 years, we receive good hopes from stringers.

  21. Cynthia says:

    I somewhat agree with Prof. Langlands’ criticism of Leonard Mlodinow’s “Euclid’s Window”. Unquestionably, Mlodinow is considerably sloppy at conveying “this math/physics pathway towards strings” to the lay public. He’s especially bad at explaining this connection between Non-Euclidean geometry and Einstein’s geodesics of spacetime.

    Needless to say though, I’m still rather in shock to discover that Mlodinow holds a PhD in physics. Yet I’m in ever greater shock to find out that he has a specialized degree in perturbation theory, no less! I’d surmise, however, the poor-quality of Mlodinow’s work is perhaps more of a reflection of his sub-optimal skills as a pop-physics writer, and less of an intrinsic indicator of his physics know-how.

    Just think about it for a moment though, being a writer for “Star Trek” films, Mlodinow isn’t required to compose meaty, substantive material; he simply needs to create a script with lots of golly-gee-whiz wizardry.

  22. foo says:

    Why is the review of Mlodinows book by Langlands over the top? Is it factually wrong?

    If a book is as badly written as Mlodinows book seems to be, then a slamming is appropriate, I’d say.

  23. Bob says:

    Nice discussion – very enlightening.

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