How does one handle books without errata?

Question

My situation:

My book is Differential Forms in Algebraic Topology by Loring W. Tu and Raoul Bott of which An Introduction to Manifolds by Loring W. Tu is a prequel. Neither of which appears to have an official errata list. However, the prequel has an unofficial errata list, and the few errors I've found in the prequel (like this) don't appear to have been asked about before.

Now the book appears to have some errors that are asked about on stackexchange already. Twice now I've typed up questions that turn out to have been asked about already. One of which is a confirmed error. There could be a lot more here https://math.stackexchange.com/search?q=bott+tu (like this), but there's no specific order, and I don't imagine I can search only for the ones in a particular Chapter or Section.

Recently, I tried to come up with an errata on stackexchange, but my question Errata for Bott Tu Differential Forms was put on hold even though Errata for Atiyah-Macdonald on overflow is just fine. I'm assuming there isn't a difference between stackexchange and overflow for this case because so far no one suggested for me to ask on overflow instead.

In general:

It seems like wasting a lot of thousands of readers' time that to try to understand something in a textbook that

1. turns out to be an error

2. is apparently asked about somewhere on stackexchange or physicsforums.

There's nothing really one can do about

1. errors one realizes but no one has asked so far (like this)

2. errors that one doesn't even realize until 17 sections later (like this)

3. possible errors one suspects but which one thinks is kind of obvious, in which case I think we can kind of apply this Why do so many textbooks have so much technical detail and so little enlightenment? to think "It's not really worth typing it up on stackexchange, so I'll assume it's an error until there's evidence otherwise"

The question:

But for errors that people have already spent so much time inventing a wheel for, how does one avoid reinventing the wheel i.e. avoid spending time asking questions about something that turns out to be an error already asked about on stackexchange?

• Some notes and guide questions to address the main question in the preceding paragraph.

• Does one really look up every single question on that mentions the book like this https://math.stackexchange.com/search?q=bott+tu? So far we don't have an "error" tag for questions where it turns out that the book has made an error.

• Should we study only books that have either official errata and an errata on stackexchange or overflow?

  • Could be relevant: (I didn't have much of a problem with An Introduction to Manifolds by Loring W. Tu, but I did with From Calculus to Cohomology by Ib Madsen and Jørgen Tornehave such as with the term "positively oriented".

    If you are having so many issues with the definitions in a given textbook, it might be a good time to pick up another book. There are so many introductory smooth manifold texts to choose from. The world is your oyster. – AnonymousCoward May 10 at 13:35

  • I guess we apply the concept from "definitions" to "errors".

• My recent question: Errata for Bott Tu Differential Forms in Algebraic Topology

• Note: I'm not asking "Why don't authors have an official errata?" or "Why doesn't stackexchange/overflow allow this?" I'm asking what one should do given that compiling isn't allowed and there is no official errata in the situations where there will definitely be an error that is already asked about but is not readily accessible in some arranged or at least compiled format.

• Imagine thousands of readers all having the same question as I did here, where I spent 2.5 hours trying to understand it and 1 hour typing it up. This would be 3,500 hours of time wasted.

Answer 1

There's a lot that could be said here, but I'll try to answer the actual questions. I'm not entirely sure that they're on topic for meta, but I feel that an answer would nonetheless be useful here.

The questions: (copied and pasted from the question for clarity)

But for errors that people have already spent so much time inventing a wheel for, how does one [avoid reinventing the wheel][5] i.e. avoid spending time asking questions about something that turns out to be an error already asked about on stackexchange?

Response: I'll address this one at the end.

• Does one really look up every single question on that mentions the book like this https://math.stackexchange.com/search?q=bott+tu? So far we don't have an "error" tag for questions where it turns out that the book has made an error.

Response: YES. I'm sorry, I do hope that the bold caps wasn't rude, but yes of course when you encounter what seems to be an error in a book you should first google it or search for it on math stack exchange. This should be one of the first steps in this process.

Even if you don't find anyone discussing that particular part of your particular text, you should search for what's confusing you. Perhaps someone else has had the same confusion, but with a different text, or perhaps you can find the correct statement somewhere else. Don't spend two hours agonizing over something (that you're not supposed to agonize over), that's not a good use of your time. If you find something unclear in a textbook, look it up immediately.

• Should we study only books that have either official errata and an errata on stackexchange or overflow?

Response: No of course not. To be honest, this comes across as if you're very frustrated. While I can understand your frustration, it's a bit rude.

• Could be relevant: (I didn't have much of a problem with An Introduction to Manifolds by Loring W. Tu, but I did with From Calculus to Cohomology by Ib Madsen and Jørgen Tornehave such as [with the term "positively oriented"][6].

  If you are having so many issues with the definitions in a given textbook, it might be a good time to pick up another book. There are so many introductory smooth manifold texts to choose from. The world is your oyster. – AnonymousCoward [May 10 at 13:35][7]

  • I guess we apply the concept from "definitions" to "errors".

Response: This isn't a question, but I do want to comment on this comment.

Yes, this is very good advice. If you don't like the style of a textbook, for whatever reason, pick up a different textbook.

• Note: I'm not asking "Why don't authors have an official errata?" or "Why doesn't stackexchange/overflow allow this?" I'm asking what one should do given that compiling isn't allowed and there is no official errata in the situations where there will definitely be an error that is already asked about but is not readily accessible in some arranged or at least compiled format.

Response: It's good that you're not asking the first question, since that would be wildly off topic on this site. The second question however might be more valuable to consider, and would certainly be on topic. Additionally, your question really comes off as if you're actually asking about why compiling an errata is not allowed.

• Imagine thousands of readers all having the same question as I did here, where I spent 2.5 hours trying to understand it and 1 hour typing it up. This would be 3,500 hours of time wasted.

Response:

Again I can understand your frustration, but this is off topic, particularly since you're explicitly not asking about whether or not we should allow errata.

An option and suggestion.

I suspect the answer so far won't be very useful to you, and I suspect most people will give you the same answer I did, which was basically, "Yes, of course you should Google things when you get confused."

As a suggestion then, consider writing a proposal as a question on meta.

I've been thinking about this, so I'll get you started.

Proposal: Use questions to compile errata for textbooks.

Reason for proposal: Many people already come on here to ask about errors or perceived errors in textbooks. It would be useful to collect all this information in one place. Moreover, while MSE may not have the ideal format to collect such information (since ideally errata would be formatted in an ordered list), it has the benefit of having a large community around it that would be able to more easily maintain such a list.

Guidelines for such questions

Naturally, since there should be only one such question per book, it had better be of high quality, and intended for the purpose of collecting errata. Thus it should follow the guidelines established in this proposal.

1. All such questions should be tagged with a tag to be created for this purpose. Perhaps (errata). This allows people to ignore this tag if they want to avoid seeing it.

2. One question per book, not per version.

3. The question and all answers to it should be community wiki. (I realize that this would require flagging a moderator to make the question CW, but I think that's probably the correct course of action).

4. All errors belong as answers.

5. Each error must contain the following information

   • Version number, page number, and textual location (e.g. 1 ed, pg 143, proof of Prop 10.1)
   • Importance of the error: (major/minor/typo)
     • A major error invalidates the proof of a lemma, proposition, or theorem. No simple fix.
     • A minor error is a logical error in a proof, but where a fix is available.
     • A typo is an error where the intent is clear to an expert, but the wrong symbol was used, or there was a misstatement.
   • Errors must be justified. Justification is either a link to another MSE question, where the error was discussed at length, or it is one of the following.
     • For a major error: A counterexample to the claim that is supposed to be proved.
     • For a minor error: A counterexample, showing that the claim is in fact an error, as well as how it should be fixed.
     • For a typo: The correct statement or symbol.

6. Errata are not for discussion. Answers should not address each other. If there is a problem with one of the answers, either the comments or another question may be used to resolve the issue.

7. Errata questions should direct people to the guidelines in the proposal, so that answers are of appropriate quality. Low quality answers should be downvoted.

Answer 2

There is a related discussion about this kind of idea here. (Also look at the discussions referenced therein. For instance, there was the proposal of a tag regarding erratas.)

Let me answer the implicit question of whether/why erratas should or should not be allowed, which is more tangible and on-topic.

While definitely a good and noble endeavor, establishing erratas goes against the core design around which SE is built, which is the Q&A format. For one specific issue about the idea (though there are many), it would probably result in somewhat frequent anachronistic bumpings, particularly if there were a significant amount of erratas. Another issue is the necessity of many guidelines for such a thing to have a chance of working (see jgon's answer.) For instance, the errata in MO that is mentioned seems not very well organized to me, precisely due to the fact that the software is not intended for that. There are a lot of separated answers, organized by no real useful metric for an errata. It looks to be essentially a place to dump errors. To settle for that would be a misuse of both SE and a disservice to the potential of a better place for making an errata.

Again, surely online erratas should exist somewhere, perhaps even have an website devoted to that. But I don't think here is an appropriate place. Even a public git repository could be more appropriate, I think.

Bottom line is: I think that the idea of making MSE to allows erratas is an idea that is unconsciously based on the popularity of MSE, not based on its properness to handle that sort of thing.

As a last note, the fact that a similar question is open/closed in MO should not be used as an argument for its status in MSE. (Not to mention that the question is over 8 years old, which is relevant to keep in mind.) Both sites are considerably different regarding which questions are appropriate or not.