Bringing in the Sheaves

grothIn 1958, the 30-year-old Alexandre Grothendieck stunned the International Congress of Mathematicians with his audacious proposal to remake the foundations of algebraic geometry, vastly expanding the scope of the field, subsuming all of commutative algebra and algebraic number theory, and paving the way for the solution of the elusive Weil conjectures, then considered decades or centuries out of reach. No mathematical vision had ever been more radical or more ambitious. Someday I will blog about that vision. Today’s post is about genius, eccentricity and intellectual property.

Over the next dozen years, Grothendieck and his disciples—first class mathematicians in their own right—turned the vision to reality, overcoming vast technical obstacles that might have led almost anyone else to change course—but Grothendieck was a force of nature. The completed vision was published in a series of twelve volumes totaling over 6200 pages, the Seminaire de Geometrie Algebrique, known to mathematicians simply as SGA. These in turn rested on a series of 8 foundational volumes, also sprung mostly full blown from the mind of Grothendieck, the Elements de Geometrie Algebrique, or EGA. Every one of these many thousands of pages is dense with content; I happen to have idly picked up a volume a few days ago, read two random paragraphs, and spent two days digesting them.

There is a very real sense in which all subsequent work in algebraic geometry—and much subsequent work in several related fields—consists of commentary on EGA and SGA. These are the indispensable texts. And they’re hard to get ahold of. SGA was published by the German publisher Springer-Verlag, but it has long been out of print—and as the population of algebraic geometers has mushroomed (due largely to the fertility of Grothendieck’s ideas) there haven’t been nearly enough copies to go around. There are scans available on the web, but they are hard to read (they were produced on an electric typewriter, with the mathematical symbols handwritten in), not searchable, and littered with typos.

Enter Bas Edixhoven, a Dutch mathematics professor who conceived the rather marvelous idea of organizing teams of volunteers to re-type all of SGA using modern typesetting software, correcting typos and inserting references to more recent literature where appropriate. Edixhoven secured the blessings of all of Grothendieck’s collaborators, but was unable to contact the great man himself, who has spent most of the past two decades in complete seclusion in an unknown location. (More on this below.) Confident that Grothendieck would not oppose the project, Edixhoven launched the project. After eight years, the first two of the twelve volumes of SGA—SGA1 and SGA2—are now complete and available on line.

Last month, the project crashed to a halt when a letter surfaced from the 82 year old Grothendieck, opposing any further dissemination in any form of any of his work. He asks that all such work be “removed from commerce” (which would presumably include the World Wide Web) and from all libraries. He does not threaten legal action (though as far as anyone can tell, he does seem to be the copyright holder), but he appeals to his readers’ “sense of shame”.

The Edixhoven project is now halted, with the hard work of many volunteers presumably set aside.

Why did Grothendieck send this letter? One can only guess. But in the many years since Grothendieck retired from mathematics and withdrew from society, he has periodically (though not for several years now) released long, eccentric and beautiful manuscripts containing thousands of pages of mathematics, autobigraphy, philosophy and theology, and these give some clues. The Grothendieck Revolution enabled a generation of mathematicians—including Grothendieck’s students—to solve a vast array of formerly unapproachable problems, and to formulate and solve new problems that would have been inconceiveable prior to SGA. In his long autobiography Recoltes et Semailles, Grothendieck expresses bitter disappointment about the direction of much of this research. The thrust of his objection—and I am a little hesitant to summarize the subtleties of his position in a single phrase, but here goes—is that everyone’s picking the fruit and nobody’s tending the garden. Nobody, that is, is doing the sort of deep foundational work that marked Grothendieck’s own career. That ongoing disappointment, presumably, has something to do with the letter that arrived last month.

Well, now what? Legally, it appears that Grothendieck does own the copyrights. Ethically, should those copyrights be respected? (No, I do not plan to consult Randy Cohen on this matter.) Should an embittered recluse be allowed to impede the progress of a vast scientific enterprise that he almost singlehandedly created? Does it matter that he waited eight years to object to this project? What are the issues here? Do weigh in.

Edited to add: Several commenters have asked whether Springer still has an interest in the copyright. My understanding is that the copyright has reverted from Springer to Grothendieck under the applicable European laws.


39 Responses to “Bringing in the Sheaves”

  1. 1 1 Doctor Memory

    Hm. Setting aside the ethical questions here, from a strict legal perspective Grothendieck is entirely within his rights: if he is the copyright holder (not knowing how European copyrights worked in the 50s and 60s, I have no idea if Springer-Verlag might have some claim to it as well), then any reproduction taken without his approval is without question illegal. And, of course, thanks to the ceaseless lobbying of the Walt Disney Corporation (and their many peers), we will have to wait, minimally, nearly a century until the SGA and EGA enter the public domain. Assuming, of course, that copyright is not extended again, which it of course will be the moment Steamboat Willie begins to approach the expiration date.

    A century of mathematical/scientific progress hobbled, lest Disney’s profits fall a demipercentage? It seems a fair trade.

  2. 2 2 Neverfox

    “Legally, it appears that Grothendieck does own the copyrights.”

    “any reproduction taken without his approval is without question illegal.”

    That’s simply legal positivism. The fact that it’s a law doesn’t make the law just. From my perspective, IP is unjust, as are the laws that secure his copyright. “Ethically, should those copyrights be respected?” No. If Edixhoven wishes to respect the request, however, so be it. There might be someone else less inclined to care.

  3. 3 3 JAB

    Neverfox, remember we’re at a writer’s blog! Maybe Landsburg would’ve written The Armchair Economist and Fair Play if he had no financial incentive to do so, but maybe he wouldn’t have, and my teen years would’ve been the poorer for it.

    On the other hand, I’m pretty sure I checked TAC out of the library, and didn’t manage to buy a copy for about 8 years afterward, so take that for what it’s worth…

    (On the OTHER other hands, I’ve ended up getting several copies to give other people, so maybe the library copy was a net gain.)

    On the other other other hand, as noted in Fair Play, a book worth reading is a book worth buying, in SEL’s opinion.

  4. 4 4 Harold

    What is the position re the original publisher? If they werre to bring out a new edition, does that affect the copyright? That is sidestepping the issues raised here.

    If I create a work of art, say a novel, I own the copyright of the arrangement of words in the novel. I do not own the ideas in the novel. This came up with Dan Brown I think, recently, using ideas in earlier books to construct his novel. This touches on issues perviously raised here, is mathematics created or discovered? If I write down a mathematical theory and if I have discovered it, then I cannot own the rights of it. If I have created it, then I can. It seems ridiculous that one could “own” a theory. So, how much of the theory is covered by copyright?

  5. 5 5 thedifferentphil

    If he was indeed contacted 8 years ago and said nothing, and if those first two volumes were put online and again nothing said until now, then I think that American copyright law might say that he missed his chance on those volumes, but I am no lawyer. Surely the online versions can’t be truly withdrawn, given the digital nature of things. On the remaining ones, he is fully within U.S. rights to shut it down, and he can probably will the rights to the book to a foundation that will be legally obliged to continue to stonewall the copyright for the Disney length of time into the future. The silence from Springer-Verlag may reflect an unwillingness on their part to be aggressive, because that may make potential future authors suspicious of S-V’s respect for their intellectual decisions.

  6. 6 6 Harold

    From my first post, I think he can, and perhaps should, be able to prevent people copying his work verbatim. You are considered to “own” it, so you can do what you want with it. Can we say you cannot prevent plagiarism because we don’t like your motives? It seems we must stick to it, or scrap copyright protection. However, this does not mean that you can prevent the spread of the ideas within your work. If a simple copying is not possible, then others must take these ideas and express them “in their own words” I may be wrong, but I don’t think he can own the copyright on, say, an equation. It is for others to say how much is taking ideas, and how much is plagiarism.

  7. 7 7 Peter

    The copyright clause in the constitution reads

    “To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.”

    I have doubts as to whether copyrights and patents have ever promoted science and useful arts, and with the Disneyfication of copyright law it is difficult to see how it can be argued. But this particular case is of a man who’s goal is to impede science through his ownership of copyrights. It would be interesting to see the copyright clause discussed in SCOTUS, but given what Grothendieck has said it is doubtful this will happen.

  8. 8 8 jambarama

    Grothendieck’s letter opposes: any further dissemination in any form of any of his work, including that all such work be “removed from commerce” and from all libraries.

    Assuming he is the full & recognized copyright holder of a legitimate copyright, then he has several rights. One is the right of reproduction – he has the legal right to stop people from creating new copies of his works. But he doesn’t have any rights regarding copies that were made legitimately, such as printed versions purchased by libraries – his rights were extinguished regarding those volumes.

    Should he have the right to stop unauthorized duplication? I think so. If you give yourself the ability to appropriate others work when it suits the better good – you undermine the incentives copyright provides (whether they’re needed for creative expression is another question).

    In addition, you’ll always appropriate because free dissemination of ideas is always more valuable than the payments to the copyright holder (assuming any imperfection in markets). This is a slippery slope argument, but I can’t think of a reasonable line to draw (e.g. research v. non-research?).

    Should he have the right to remove writings which were legitimately created from libraries and bookshelves? Absolutely not.

    Of course I think copyright protection is vastly overreaching, lasts far too long, and has terrible problems [e.g. orphaned works, double protection problem with DRM & (C)]. And waiting 8 years, assuming you can show he knew about the project earlier, smacks of laches, so he may have forfeited his right to stop the digitization project.

    But unauthorized duplication, even in the name of science, is a bad idea if we’re going to continue using copyright to benefit authors.

  9. 9 9 Michael

    Is there something like intellectual eminent domain? Granted, it would be difficult to come up with a fair market value for intellectual property.

  10. 10 10 Paul Grayson

    Nobody has said this yet, which is surprising for a Landsburg blog: when Edixhoven types up a copy and sends it to you, that is a transaction between consenting adults which does not involve Grothendieck. Therefore, the government has no business making a law against copying. (No more so than it does, say, requiring FDIC insurance, banning polygamy, or imposing a minimum wage.)

    Let him keep his work secret, release it with a shrink-wrap license (and see if any library would buy it), or show it to only a few influential reviewers until a sufficient bounty is paid, if he likes. He does not need a “right” to endless control over other people’s computer keyboards.

  11. 11 11 Neil

    I am not a lawyer, but I was involved in a case once, and I recall the principle that a copyright protects the *expression* of ideas, but not the ideas themselves. Which makes sense because ideas should be and properly are the property of human kind so that we can build on them (even if that building on them could be interpreted, in some cases, as the gathering of fruit rather than the tending of the garden.) Presumably, Grothendieck’s request, eccentric as it is, which is always to be expected from great mathematicians, concerns only his peculiar expression (EGA and SGA). Will that really hold back progress in mathematics?

  12. 12 12 Harold

    I said plagiarism before – this was incorrect as no-one was attempting to pass of this work as their own. Neil makes just about the same point as myself

  13. 13 13 Bennett Haselton

    As several people have pointed out, Grothendieck would not have the right to demand that legal copies of his work be removed from libraries, however the original text of his letter at actually says:

    “I will ask the person responsible for such pirated editions… to remove from commerce these books; and librarians holding such books to remove these books from those libraries.”

    That is, he’s only asking for *pirated* copies to be removed from libraries, not legitimate copies. (Perhaps the original post should be edited to clarify that? Since several people pounced on it.)

    Is there any legal precedent explicitly saying that even if you can’t duplicate a mathematical paper without the copyright holder’s permission, you can rewrite it in your own words, since facts are not copyrightable? It would be interesting to see how quickly a person could get really good at rewriting content on the fly to transform it into a new expression of the same ideas, to remove the copyright protection. “It was the best possible time period, while simultaneously being the worst possible one.” “Heaven and Earth were created by God at time t=0.”

    Fascinating story. I didn’t know mathematics had Salingers.

  14. 14 14 Doctor Memory

    thedifferentphil: copyright expressly and explicitly does not work that way. Trademarks can be lost if they are not defended frequently, but the 1,000,000th illegal copy of a work, a decade later, is just as illegal as the first.

  15. 15 15 Roger Schlafly

    You act as if owning the copyright ends the legal analysis. It does not. Grothendieck does not have the right to prohibit “fair use” copies. Noncommercial and educational reproduction of out-of-print books is usually considered fair use.

  16. 16 16 Benkyou Burito

    Roger- fair-use protects reproductions of copyright material for certain very limited purposes. One can copy a few pages to hand out to a class. And that would hold in this case if one were copying the original publications, and not using them en whole to create a new publication against the rights-holders intentions.

    I have competing sensibilities about IP law. Is Brazil doing the wrong thing by producing AIDS drugs that its people can’t afford? Does Brittany really need $16 bucks from me just because I like that ONE DAMN SONG on her album? (toxic)

    In this particular case I would go Coaseian and suggest someone find a way to sit face to face with the man. Offer to endow an award that encourages the kind of work the man wants to see in return for the rights to re-master his books. Maybe Make hardcopies available for sale that fund the endowment.

  17. 17 17 Philip

    My take on this is…

    * Gothendieck apparently holds the copyright.

    * Irrespective of the utility for society of violating his copyright, it would clearly be illegal to do so.

    * Nevertheless, he effectively waives his IP rights if he fails to act to protect it once it has been violated. I understand this to be establish legal doctrine, but I could be wrong. I do not know what period of time he has to take such action before his right is assumed to be waived.

    * Considering the societal value that publishing his work would have, I’d urge an act of “civil disobedience” and proceeding with publication, forcing him to take action to protect his property rights.

    * If he does, then I’d recommend backing off.

  18. 18 18 Neverfox

    JAB, I haven’t forgotten. And yes, without the incentive of the state-granted privilege to control other people’s physical property (e.g. their copy of the book), he might not have written it. I can imagine lots of spiffy laws that would incentive me – perhaps one that forces everyone to buy by book, for example. But why should that be the basis of justice? If your business model requires using violence against people for doing what they want with their mind and property, so much the worse for your business model. That said, the anti-IP literature as done, I think, and excellent job of debunking the “IP is necessary for innovation and art” myth. So if he didn’t write it because it assumed he couldn’t make money, I would first charge him with a deficiency in creativity and historical knowledge. I’m sure no one created things or shared ideas before copyright law and no one made a living as an author (friendly sarcasm). However, I do not wish to get into the whole IP debate here. I’ll leave others to read the arguments of my more loquacious colleagues at the resource link above.

  19. 19 19 Philip

    Here are some factors to consider in evaluating the merit of his copyright claim:

    * Under the US legal doctrine of sovereign immunity, he has no copy rights, if during the production of his work, government “time, material[s], or facilities” were used to support the work. I think this applies broadly and covers work done by govt employees, contractors, and those whose work is supported by government grants or loans. It’s possible that Germany has similar provisions of law.

    * From Wikipedia: “Copyright does not prohibit all copying or replication. In the United States, the fair use doctrine, codified by the Copyright Act of 1976 as 17 U.S.C. § 107, permits some copying and distribution without permission of the copyright holder or payment to same. The statute does not clearly define fair use, but instead gives four non-exclusive factors to consider in a fair use analysis. Those factors are:

    1.the purpose and character of the use;
    2.the nature of the copyrighted work;
    3.the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
    4.the effect of the use upon the potential market for or value of the copyrighted work.[47]”

    Similar “fair use” provisions are including in many European countries.

    Since Grothendieck has made no attempt to sell his work and appears to have no plans to do so, (4) may be applicable. (1) and (2) may apply as well.

    * Here’s another “fair use” exemption from Wiki that may apply:

    “Educational use is regarded as “fair use” in most jurisdictions, but the restrictions vary wildly from nation to nation.[48]“

  20. 20 20 Jonathan Kariv

    My knee jerk reaction is that I don’t want to be the one telling Grothedick he’s being silly, and he might have reasons I’m not managing to think about. Steve could you give any elaboration on exactly why groendick onsiders it shameful to reproduce SGA and EGA?

  21. 21 21 Steve Landsburg

    Jonathan: I know nothing beyond what’s in the post.

  22. 22 22 David Grayson

    I like Neverfox’s point: just because a law encourages some activity that is good (such as creative works), doesn’t justify creating a law.

    It’s probably true that more movies, songs and books get written because of IP laws. That’s a nice benefit from IP laws. But it costs us a lot of money to enforce and to obey these laws, and we are less free because of it. So maybe it’s not worth it for the U.S. government to be in the business of enforcing copyrights.

    Morally though, it’s wrong to hurt another person. You are hurting Britney if you sell bootlegged copies of her album (although I’m sure Paul will disagree), so that’s wrong. In contrast, you are *not* hurting Groethendick when you try to sell copies of his book (because he’s not trying to make money on it), so that’s morally okay.

    In general, I think it’s only right to violate the copyright of works where the copyright owner is not actively trying to make money from it.

  23. 23 23 Harold

    It seems you are hurting Groethendick – thats why he wrote the letter. You are not hurting him financially.

    One purpose of copyright is to encourage creation and publication of creative works. This is done partly through a financial incentive. Usually, most peoples’ interest is roughly in alignment. The author wants to spread his works as widely as possible and also maximise income. The publisher wants to maximise income. This is done by providing as many copies as people want to read, so more or less everyone is happy. In this case there is a breakdown because the author seems to want neither to maximise income nor spread his work – in fact the opposite. Is he acting rationally? He presumably values something above the money he could gain, the kudos and the rosy glow of sharing. As Benkyou said, if someone could find out what this is and offer it in exchange, perhaps a foundation, everyones desires could be re-aligned. This may not be possible.

    It seems the copyright is now acting exactly opposite to its intended purpose. Instead of encouraging dissemination, it is allowing the opposite. However, artists have a vision which they value very highly – that is what motivates them to do art. (Some also value money). They are reluctant to allow their vision to be corrupted, so may not release their work unless they can control its use. As well as the financial incentive, copyright also does this. An author may not want a poem used in an advertisement for a machine gun. If he owns the copyright he can prevent this. It is this purpose that copyright is now serving.
    But we are getting into difficult terrain. If we are to take the creative ownership part too far, then copyright would be eternal. It seems we have perhaps gone too far down this road already. It is debatable how much work would not be released if this protection were not available.

    In this case, it seems there is a “public interest” argument for overriding the copyright. Should we allow such a defence? The fair use rules already provide a limited version, should we extend these to cover the situation here? I am a bit reluctant to advocate welding fiddly bits on to our slegehammer of a law to try to turn it into a screwdriver. Perhaps better to go backwards, and simplify. Acknowledge that copyright has good and bad aspects, so compromise to try to maximise benefits. Stick to a 25 year time limit to satisfy nearly all authors, then it is public domain. How much work would not get published with these rules?

  24. 24 24 Milton Recht

    It is not about copyright or IP. It is about controlling the research consequences of one’s own intellectual efforts through the means available. He is not the first and certainly will not be the last to regret the outcomes from his intellectual endeavors. Society (governments, legal system) gave him the power to control his published works.

    Furthermore, there will always be cases of unpublished brilliant mathematical works, manuscripts, journals, etc. in hiding until the death of the writer. In these cases, we do not get to taste the fruits of labor until the mathematician’s death.

    We are lucky he made the ideas in the documents available during his lifetime. Without IP laws he may have waited until his death to release the original copies of the texts.

    Upon his death, the estate can grant rights to publish the texts, correct typos and to make them searchable. I presume eventually that the printed text will enter the public domain.

    He has the rights, which means he has the right to exercise and enforce his rights. Our selfish needs, beyond what society has legally incorporated (such as fair use), do not factor into his rights.

    It is difficult to wait when one is hungry and tasted the delicious food, but the knowledge will not be lost. The derivative, proven mathematics will not disappear. Current research will not come to a halt. Progress maybe inconvenienced by the limited number of uncorrected copies, but it will not be stopped. He put the works out into the public. It is not about access. It is about convenience. There is no right to convenient access.

  25. 25 25 Philip

    (1) A point of fact re: copyright expiration: US, French and German copyright holders’ rights do not expire until 70 years after the author’s death. This is current law. For works that were created several decades ago, the period after death could be longer or shorter.

    In other words, we have a long wait unless there’s a way to employ the fair use provisions or Grothendieck fails to act to protect his copyright. Reading more about G, I think it’s possible he would not protect the copyright because of the publc exposure a suit would entail. He’s 82 now and his tolerance for any type of public exposure has declined rapidly in recent years.

    * Here’s a rough translation from the French of G’s letter. Note that he appeals to conscience and does not threaten legal action or even claim copyright protection on unpublished works. Also note that there is an implied threat to detroy his works before his death:

    “Declaration of intent of non-publication

    “I do not intend to publish or republish any work or text of which I am the author, in any form whatsoever, printed or electronic, whether in full or in excerpts, texts of personal nature, of scientific character, or otherwise, or letters addressed to anybody, and any translation of texts of which I am the author. Any edition or dissemination of such texts which have been made in the past without my consent, or which will be made in the future and as long as I live, is against my will expressly specified here and is unlawful in my eyes. As I learn of these, I will ask the person responsible for such pirated editions, or of any other publication containing without permission texts from my hand (beyond possible citations of a few lines each), to remove from commerce these books; and librarians holding such books to remove these books from those libraries.

    “If my intentions, clearly expressed here, should go unheeded, then the shame of it falls on those responsible for the illegal editions, and those responsible for the libraries concerned (as soon as they have been informed of my intention).

    “Written at my home, January 3, 2010,

    Alexandre Grothendieck”

    * Re: G’s motives for trying to restrict or end public access to his works, it’s pretty clear his efforts are driven by intense pascifism and a conclusion that his work has been used in ways that violate his convictions and are likely to be used so in the future.

    Here are two links that addresses this and provides a rich trove of other links to explore:

    Good luck getting anyone in to sit down with G face-to-face and persuading him to change his mind.

    Re: Grothendieck’s

  26. 26 26 Doctor Memory

    Nevertheless, he effectively waives his IP rights if he fails to act to protect it once it has been violated. I understand this to be establish legal doctrine, but I could be wrong.

    No no no no no no no. Folks, please do a little research before making claims like this. You are describing how trademarks work. There is no such requirement to enforce copyright.

  27. 27 27 Tom Temple

    I think you guys are missing the easy fix here. The “ideas” are the important part and are not under copyright. Someone can publish a series of properly cited “surveys” that reproduce all of the ideas. The work is old enough that I imagine that many if not most of the important theorems have already been reproduced in other work.

    The ideas will not be lost just because the original work is no longer published. This is an interesting story, but in terms of the “human progress” angle, just a bump.

  28. 28 28 Philip


    The ideas themselves are protected as IP, not just his writings.

  29. 29 29 Neil

    You are right, Tom, but if you read back you will see that that is the point of an earlier post [mine, of course :)]. You are wrong, Philip. You cannot protect ideas. If you could, every textbook in the country would be in trouble.

  30. 30 30 Philip

    Tom and Neil-

    Re: “failure to defend”; would suit be brought under US law, French law or some international IP treaty? It makes a difference.

    I was insufficiently precise re: the protection of ideas. Ideas, in and of themselves are not protected under copyright law (but they can be under patents).

    But when ideas are expressed in tangible form, such as 10 volumes of highly creative work that is immediately identifiable as Grothendieck’s by an audience of specialists, then yes, his ideas are protected by copyright.

  31. 31 31 Philip

    Here’s a concise explication of how copyright law protects ideas. It even has a textbook example for Neil.

    “Section 102(b) of the Copyright Act states clearly what most writers have heard: “In no case does copyright protection for an original work of authorship extend to any idea, procedure, process, system, method of operation, concept, principle or discovery …”

    “But this leaves undone a tricky task: drawing the line between a work of authorship and the ideas embodied in that work. That may sound easy, but it has plagued copyright lawyers for centuries and produces a surprising array of copyrightable works that one might have assumed were unprotected ideas. The key is understanding that copyright doesn’t stop at your words, but protects any original expression in your work, including detailed outlines, plots and characters.

    “Copyright: Detailed Outlines

    “In the 1960s, Harper & Row published an extremely popular child development textbook. Meredith Corp. created a competitive textbook using the Harper & Row book as the model by distributing detailed chapter outlines to freelancers, who worked from these outlines without seeing the original. When Harper & Row sued, the court found Meredith Corp. guilty of infringement, due in part to “an extensive taking of the entire structure and topical sequence” of the original.

    “Similarly, from 1989 to 1992, Jerome and Laurie Metcalf developed a series of works about the African-American staff of a county hospital in inner-city Los Angeles. They pitched the idea to producer Steven Bochco and were told he liked it but was too busy to handle it. When Bochco’s “City of Angels” premiered on CBS in 2000, the Metcalfs were disturbed by the similarities to their proposals and sued. The court would not dismiss the copyright claim, finding “articulable similarities between the plot, themes, dialogue, mood, setting, pace, characters and sequence of events.”

  32. 32 32 Neil

    Yes I agree, Philip, that copyright protection goes beyond verbatim copying. I guess that is why there is a grey area where, when presenting the ideas of others, it is expected that we give attribution. Of course, with ideas, sometimes attribution is arbitrary. I can think of many cases where attribution for an idea is conventionally given to a relative late comer.

    It seems that we have gotten stricker about this than in the past. I was surprised to see, when reading Einstein’s 1905 paper for another topic, that Einstein made exactly zero references to other work, which was surely out there.

  33. 33 33 Jon Shea

    It seems to me that there are only two lawful recourses.

    1) Convince Grothendieck to change his mind.

    2) Republish the content in a sufficiently modified form. Instead of transliterating the SGA directly, interested parties would have to understand, digest, and restate the work in their own words. It’s not obvious exactly how different a rewrite would have to be to avoid legal challenge, but it’s likely that the project could have a very similar structure to the SGA as long as the text itself was materially different. I haven’t read the SGA, so I don’t know how much important information is encoded in Grothendieck’s particular phrasing or diction, but that would be lost.

    The situation does present an opportunity for anyone who is skilled at summarizing or explaining the SGA on their own, assuming they can find a copy.

  34. 34 34 Harold

    Since Grothendiek is appealing to shame rather than law, the question is possibly wider than the only legal recourse. If it could be guaranteed that there would be no legal redress, should the project be stopped?

  35. 35 35 Philip

    John Shea-

    I think it’s clear that your option #2 violates the copyright. I outline why in my previous post one post above yours.

  36. 36 36 Neil


    I don’t see why. You simply avoid “extensive taking of entire structure and topical sequence”. That is what the art of textbook writing is all about.

  37. 37 37 Jon Shea


    There is some level of modification and restatement that is sufficient to avoid violating copyright protection. As your excerpt states, it’s not clearly exactly where the line is. Maybe you couldn’t copy the exact structure and topical sequence of the SGA, but it would be easy enough to shuffle those around. Whatever level of rearrangement and rewriting is necessary, that’s what I suggest.

    I think the bigger problem with my suggestion 2 is that it’s probably pretty much impossible for almost anyone to actually digest and restate the SGA. Let me quote a mathematically inclined friend of mine:

    All I have to contribute on this subject is that I know from personal experience that when reading mathematics this sophisticated when your own intelligence is, well, ordinary, classifying something as either a typo or a stunningly brilliant insight is nigh on impossible.

    I still have nightmares about the “textbook” in homological algebra that turned out to be (roughly) transcribed lecture notes. :shudder: I wasted weeks decyphering that crap, and it was just “regular” hard algebra.

  38. 38 38 Philip


    I think G’s work is so unique, creative and complex that it will be impossible to disguise any re-creation as anything other than a copyright infringement.

  39. 39 39 Benkyou Burito

    I just finished a seminar thesis on the globalization of Intellectual Property Rights. My central case was the criminal and then civil trials of was an online music store in Russia that sold western owned music for about a nickel a track. Russian law allowed something call compulsory licensing, which let government agencies approve the license to reproduce and sell entertainment and literature even against the wishes of the works’ creator. was found acquitted in Russian criminal court. And the RIAA dropped all charges against it (the owner) in U.S. Federal court.

    The US Trade Rep. and the Russian gov worked out a deal to shut the business down as a condition of Russia’s WTO accession, but the owner opened up a new store the next day,, which sells the same songs just as cheep and has been operating “legally” since 2007.

    Anyway, in a state with such laws, it would be legal to reproduce the books and sell them or distribute them as long as a portion of the profits were given to the author.

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