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    I started, half-expecting it to be closed very quickly. I decided I didn't care if it got closed though, because it was a good way to raise awareness of an issue that is currently important to me. I finished my post with something of the form "if this gets closed then just email me".

    To my genuine surprise, (1) the post got lots of upvotes (17 at last count) and (2) I've collected a huge set of errata for this book that someone else had but hadn't as far as I know made public until I asked. On the other hand I still feel that this is sort-of an abuse of the system. I used MO because I know there are lots of number theorists reading and I thought I'd get some useful errata for CUP and for me. This seems to me to be a very narrow-interest thread: it's about 1 book, and anyone who doesn't own that book will surely not be particularly interested. It's a classic book though, and for those that do own the book, the thread is doing them a great service. Also, the authors/editors aren't going to compile their own typos: most if not all the contributors are retired and some are dead, including Froehlich, and Cassels is now very old and no longer active.

    I am sort-of bewildered by this. I would far rather be seeing fun problems on MO in general, but on the other hand I am loving this thread because a typo in a hard book can sometimes kill a graduate student, and the fewer typos the better.
    • CommentAuthorAnweshi
    • CommentTimeJan 11th 2010 edited

    This is not surprising at all, considering the importance of the book for algebraic number theory and classfield theory. We all who were interested in the subject, worshipped the book at some point of time.

    I suggest that you even make a page for this book in your homepage, and make a page for errata, so that there is no duplication of work in reporting errata.

    Of course, the MO page will do fine as the errata page, if MO moderators are ok with the idea. The merit of the project is unquestionable. The only sticking point is how much may be highlighted within MO. This page might keep returning to the front with each editing/reporting, and some people might find it irritating!

    It depends on the MO crowd and the moderators. As for myself, I am totally excited at the possibility to have a "clean" Cassels-Frohlich in hand.

    @Anweshi: I agree. My copy of Cassels-Froehlich is one of my most well-thumbed books. I lectured a course on Tate's thesis in 2008 and it's still really the best reference. My graduate students did a study group on it last term. It's clearly still a relevant book. The issue is exactly what you say though: do we want MO to become the Cassels-Froehlich erratum repository? (and, by extension, repository for other errata?)

    I think you might be right in that they might merit a mention on another website. Now all I have to do is persuade someone to check them all and TeX them up...
    • CommentAuthorAnweshi
    • CommentTimeJan 11th 2010 edited

    @Buzzard. MO becoming an erratum repository may be not within the stated guidelines. However Cassels and Frochlich has a special place among books. It is a bible in a certain subject, and given the number of authors and age of the book, it is hard to organize an erratum in a normal way. One can hope that there are no other books occupying the same curiously important place as C-F does.

    I compare your effort to the much larger effort by French mathematicians(but started by Edixhoven) to typeset the SGA. That had a webpage for each volume and lots of people were involved. However here the work put in by each person is infinitely less, only an understanding of the book is needed to contribute errors. No huge typesetting task is involved. For a person who did work through the book, the effort involved in making a contribution is exactly the same as that of typing a short answer to a familiar question MO, one which he already knows the answer to. If there are enough algebraic number theorists in MO, the errata will build up quickly. Also anyone who wants to check can straight come here and have a verification.

    I say, let the MO moderators speak. It is their headache to control this or any similar future threads, after all. If they are ok with it, why not go ahead? On the other hand it is not good to force them to accept something which they really don't want to. They may face similar problems in future too and it may snowball out of control.

    I note that if the forum were only for algebraic number theory, then this question wouldn't even have surfaced. Not a single person would have ever dreamed of closing the thread. The issue here is that this forum is for all topics in mathematics and others may not appreciate so much attention on one particular book. The overall view of the populace might depend on the number of algebraic number theory enthusiasts here. I myself strongly vote for letting the thread stay.

    I agree that C-F is a special case. In particular, doing things that may help in getting C-F republished is clearly a good deed. I think if there were lots of questions like this we'd rethink whether they were appropriate, but we're not at that point yet.

    There were many opinions by different people about what questions are allows and many people suggested guidelines. I think your post is within all guidelines that FAQ ever contained; it may not be within what some vocal members suggested on meta, but that makes them misguided, not you.

    I must say I don't see anything "special" about C-F compared to Hartshorne, Mumford, Silverman, or other classical well-read texts other than the (rather technical) fact that this is more a collection of essays than a single book. So I'd be fine with seeing errata to other books. The usual guidelines apply though: a person should be "actively working on a problem", so I would object to a person asking 10 questions about the books he/she just happens to have.

    For the question, though, I would select a slightly different form: a question + single community wiki answer.

    Yes Ilya---the "special"ness of C-F is I guess that it's (a) very old (b) still actively used by current grad students and (c) written by lots of people. Serre's "Galois cohomology" probably also satisfies (a) and (b), but Serre occasionally corrects and updates this book when Springer reprint it! Hartshorne has also been reprinted several times, and Hartshorne will no doubt have fixed various errors that came up along the way. Cassels-Froehlich was published in 1967, reprinted in 69, and then again in paperback in the late 80s, so it has been far less active when it comes to reprinting, and the fact that there are many authors means it's much harder to get a coherent list of errata from everyone.

    Let me say that I don't intend on making such questions a habit!

    Another interesting thing is that I've heard nothing from the "youth of today". All the comments I've had so far are from people of my generation or above, who have emailed me, and I suspect that they heard about my mission on a number theory mailing list or on sci.math.research rather than here.

    Finally, I agree with Harry that it's annoying that every time I post the article gets bumped up to the top. However I'm not expecting too many more corrections to come in now. I am still waiting on Conrad and Lenstra, both of whom promised me something, but I made the mailing list/newsgroup crowd aware of the page on this site and I suspect I won't hear from too many more people now.
    • CommentAuthorAnweshi
    • CommentTimeJan 12th 2010 edited

    @Buzzard. The youth of today needs the erratum. It is not that they should contribute it. However working groups of grad students in algebraic number theory such as the group of your students, would be capable of contributing more compared to isolated grad students like me with other subjects to do as well.

    @Ilya. I suggest that you spend some time with this book. Then you will see what is special with it. But, what are the guidelines as stated, and what are the twists made by the vocal people in meta? Could you please explain? It might help me out..


    "guidelines as stated" are what is currently in the FAQ. "community opinion" would be, I guess, more authoritative, but harder to formalize. "twists made by vocal people in meta" are personal opinions that matter if they are close to community opinion, and should be politely ignored if they significantly deviate (but if in doubt, err on the side of not disturbing people and ask on meta).

    That was my personal opinion :)

    @buzzard: The youth of today have a hard time getting their hands on Cassels and Froehlich, since it has been out of print for about 20 years. When I was a grad student, the math library at Harvard usually didn't have it, since people (presumably young people) would keep walking off with it. I myself would pay any reasonable price for a copy.
    It was very difficult for me to find Cassels and Frohlich, and I had to borrow it (a rather old copy) from a faculty member. Via outofprintmath I hear that the AMS is working on reprinting it though.

    The question seemed entirely appropriate to me (though I'm only saying this because someone asked for a younger member to comment).
    You'd pay any reasonable price, Pete, but would you type "Cassels Frohlich djvu" into Google, follow the trail, and download a free copy of dubious provenance?
    @Tom: What I said stands independently of whether or not I may have a free electronic copy of dubious provenance (and for which the reproduction is merely adequate). And if I did have such a thing, I would only have had it for about a year or so, rather than the adult lifetime that mathematicians of a previous generation have been able to spend with it.
    Pete, indeed. A persuasive argument that internet "piracy" will not kill the publishing industry.
    @Harry: You're certainly correct in spirit, and on average. I'll bet the amount of money that Lang made from his books was more than nominal, for instance. By all accounts, he wrote fast enough so that his hourly revenue might have approached minimum wage.

    Also you make more by writing lower level books, which can be used by a wider audience. My colleague Ted Shifrin has written several books at the intermediate undergraduate level, at least two of which are among the standard texts used by American colleges and universities for these courses. I asked him once what kind of yearly revenue he gets, and if I remember correctly it's in the low four figures -- i.e., somewhat more than nominal, but not really significant.

    At the other extreme, James Stewart is famous for having an architecturally notable $24 million house that he bought with (one presumes) the sales of his calculus book.

    I wonder if I am the only one who has thought of bypassing the publishing industry entirely and attempting to sell mathematical writing directly over the internet, for a fee which would be nominal for the buyer -- say 1 cent per page -- but for which all profit would go directly to the author.
    For what it's worth, my two cents are that this is exactly what a community project for mathematicians can and should be used for. This is a reference that takes advantage of what many of us want (accurate references) and what some people have (corrections to those references).

    Personally, I think that having a repository of erratum would not be out of order as it would be of interest to many, and I think that so long as people have erratum of a book to post, that is an indication that there are people interested in reading them and having access to them.

    I certainly don't think that it fits the template for what kinds of questions should normally be on MO, but it worked well. I think one very important factor was the organizational effort Kevin put into the problem. Crowd-sourcing doesn't work well from the ground up; some particular person (or small group of people) has to bring a project to a point where it's useful to others, and then the people who find it useful will improve it while using it. Within a few hours of posting the question, he'd posted lots of errata. If he hadn't, I think the question would have been a flop, upvotes and specialness of C-F notwithstanding. I assume the early upvotes were largely based on the assumption that Kevin wouldn't post such a question lightly, not just on the fanciful hope that somebody would come along with a long list if there was enough demand in the form of votes.

    If somebody posted "It'd be good to collect errata from Hartshorne, but I only know this one," I think it would be a poor thread unless somebody else picked up the ball and turned the thread into an actually useful reference by posting lots of errata. Having somebody post one every now and then wouldn't work because nobody would use a list with only 3 errata as a reference, so the list would be buried in obscurity. Nobody would ever tell a colleague, "you should really check out this list of 3 errata online." A crowd-sourced project that nobody ever has much reason to look at will fail.

    I agree with Ilya that a single answer, sorted by page number, is clearly the way to go. It makes the post much more usable. I assume Kevin posted them as separate answers because they were coming from different sources and he wanted to get them up as soon as possible. But it would be really nice if somebody edited everything into a single post. Merging the posts one at a time, with edit comments like "added Eric Bach's errata," will make it easy to determine the source of each erratum through the revision history.

    @Harry: for me, morals don't come into it. I would definitely prefer a book to a pdf/djvu or a bunch of photocopies. I have some photocopied books in my office, but these are only books that I seriously tried to get hold of and failed. When Amazon sends me the email saying "we are sorry but, despite repeated efforts, we have not been able to get hold of X" I don't feel guilty about "stealing", because I have no other options left. When Springer made all their old LNMs available again recently I instantly bought seven of them despite having all seven photocopied in my office already! Aah, the joys of grant money ;-) A book is much easier to read on the tube than a big pile of photocopied pages, and if you've ever travelled in the rush hour in London you'll know that looking at a laptop isn't a viable option either.
    OK, back on topic. I was expecting comments by at least one Conrad and precisely one Lenstra, and I've now got them, and I suspect that there won't be many more coming in now. I just posted everything I got over the last 2 days in one burst so as not to bump the thread any more than I could help.

    So let me summarise what has happened regarding this project. I didn't just ask for errata here, I asked on an internet newsgroup, a number theory mailing list, and I also approached several people individually by email. As it happens, most of the people who provided non-trivial lists were not regulars to this site so I had to post a lot of answers myself. I was expecting people to chime in but that didn't happen. Why did I keep posting answers? The answer to that is simple. Lenstra emailed me saying "I have oodles of corrections but not much time; which ones do you know already?". From that I realised that if I kept the list here up to date I would save people a lot of work because I wouldn't have 7 people emailing me about 1 typo and so on. I posted links to the thread on the mailing list and newsgroup and to the individuals, so in fact this site will have got some "free advertising" (indeed I see that one question today was answered by a KConrad, and I wonder whether this is anything to do with the Keith Conrad I emailed the other day asking him if he had any corrections and pointing him to the ones I had so far). Perhaps I should also say that one thing MO did was to alert me to the fact that Keith might have had corrections. I knew his brother Brian would be likely to have corrections, but someone who saw the thread at MO emailed me telling me to get in touch with Keith.

    In practice though, ultimately I see that I did not have to use MO to do this job. I could have just set up a blog/wiki to do it and posted there. Doing that would of course have stopped the annoying thing of this thread continually being bumped to the top of the list every time I posted to it. What MO did for this thread was that it advertised it well---arguably it advertised it to "many younger professional mathematicians" (and I've already mentioned one advantage of this: I heard that Keith might be a good person to approach because of MO). I know it's a crude generalisation, but I wonder whether the number theory mailing list I posted to (which has been going for decades now) is more likely to be read by older professional mathematicians. For example I know Cassels saw what I was doing because I posted to the email list, not because I posted here. What this thread might have done for MO was that it gave me an excuse to plug MO on the mailing list, which can't be a bad thing really.

    So there you go. In summary, this would have worked pretty much just as well on some random blog, e.g. I could have put it on the London Number Theory blog I just started a couple of months ago, but perhaps the site itself gained from having the thread, although it probably lost out a little when the thread kept getting bumped in that crucial period in the first few days.

    Kevin, I share your ambivalence over whether this was an appropriate question. I think I share Harry's feeling that it's OK to trust high-reputation users (e.g. you) to bend the rules, or go slightly beyond the guidelines, or however you like to say it. On the other hand, I don't like the idea of one rule for regulars, one for newbies. That way cliqueyness lies.

    What I don't share is your oft-expressed worry over the question sitting near the top of the front page for a few days. I can see why it might worry you, but I for one haven't found it bothersome.

    A brand new user (SpecR) just opened a new errata question, on Principles of Algebraic Geometry. I just wanted to give everyone a heads up on this.

    I encouraged him, via the comments, to get in touch. I think that without the enormous effort Kevin Buzzard put into his question, it would have been a flop. I'd like to ascertain what's going to happen here.

    An example of a book that would fill up the front page for weeks with errata is Lang's Algebra book. George Bergman has a 20 or so page errata document, and that's only on the chapters he uses for teaching (only about half of the book). Also, Gelfand and Manin's first edition would cause the same problems. I don't know about this PAG (PGA ;)) book, but it could very well be full of errors.
    • CommentAuthorsparr
    • CommentTimeJan 27th 2010
    How is "fill up the front page for weeks" a possibility? Even if the question gets an answer every day, keeping it at the top of the front page, it still only occupies a single slot.

    That said, if Errata questions become commonplace, I think it would be handy to have some semi-standard guidelines for them. As a new user here, but not of other Overflow sites, it seems like one erratum per answer would be ideal, as it would allow individual errata to be ranked, refuted, censored, removed, etc.

    +1 Harry. I hope this wiki takes off.

    • CommentAuthorMariano
    • CommentTimeJan 27th 2010

    An 'errata' tag would not hurt.


    @Harry. Was your comment "I mean, if you'd feel more comfortable, I'm sure the guys over at nLab would be willing to make something similar." directed at me? If so I don't follow.


    @Harry. Ok that makes more sense ;)

    Harry: FWIW, tomorrow (Fri) and/or Mon 1st, I'm going to put all the Cassels-Froehlich comments into one pdf file, and stick it on my web page. You're welcome to link to it or host/mirror it on the Errata Wiki if you want. I would have just emailed you this comment but have no other way of contacting you other than posting on fora like this.
    • CommentAuthorWillieWong
    • CommentTimeOct 15th 2010

    Another Errata question was opened today.

    Was there ever a decision about whether such questions are suitable for MO? And if yes, what should be the guidelines?

    • CommentAuthorquid
    • CommentTimeSep 3rd 2011 edited

    In a possibly somewhat similar spirit a new question:

    It's not quite the same idea it seems. In any case, it seemed a sufficiently uncommon type of question to make me wonder whether it is or is not on-topic. I knew there were some similar things, searched around a bit and found this thread. Or perhaps I even misunderstand the intent, of that new question.

    Any opnions?

    ADDED: question was edited by Francois Dorais. Now gone.


    Hi, I posted the question. When I posted the question I had thought that since errata questions seemed to be well received and consistently voted highly, they had become part of the MO landscape.

    I came here to post a defense of my question with this in mind, but in doing so I realized that the question could be posed in a way that's both more focused and less provocative. Normally I would edit the question to reflect this, but the url/question title uses the e-word and will therefore always be a little more provocative than is needed or wanted. So I deleted it. I'll ask the revised question some time later.


    If you edit the title, the url will change too. Actually, the last part of the url is completely irrelevant, e.g., links to your deleted question.


    A fresh start is better anyways.