do I commit a copyright violation if

  1. Reuse a formula from a math book? (probably not, but why?)
  2. I give a proof from a math book, in my own words, but clearly heavily inspired?
  3. I quote from a math book?

This is mostly related to math.stackexchange.com.

Thank you.

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I Am Not A Lawyer. Nevertheless,

Ideas are not copyrightable, only particular expressions thereof. In the case of a mathematical formula, it could be argued that since there is a standardized notation for expressing mathematical concepts, the idea and the expression are inseparable, therefore copyright protection does not apply. This is known as the idea-expression divide.

A quote from a math book is another matter, since presumably that would include copyrightable descriptive text accompanying the pure math. In that case, you have a fair use right to quote a short excerpt of the larger work for educational purposes, such as posting on math.stackexchange.com. (And in that case, one would hope that the original source was credited, regardless of legal necessity.)

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    $\begingroup$ Nonetheless, it is good practice to cite your sources. $\endgroup$ – Arturo Magidin Mar 25 '11 at 19:15
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    $\begingroup$ This probably isn't what the OP is concerned with, but it's common and wasn't quite covered by the answer: sometimes people work out all the solutions to the exercises in a textbook. It's possible to do this without using the same formulas or direct quotation, but you can get into trouble if you distribute: "all the problems" is not a short excerpt of a book. Just the selection and order of problems (no solutions) is a huge part of the work of a textbook--- expression, not idea. Even though of course nobody "owns" any individual problem. $\endgroup$ – anon Mar 28 '11 at 20:57

This is just my personal opinion on the three points in particular. (Yeah, I know the other answer is already good and already accepted.)

  1. Reuse a formula from a math book? (probably not, but why?)

I would say this never constitutes a breach of copyright. But always, always cite where you found the formula.

  1. I give a proof from a math book, in my own words, but clearly heavily inspired?

Again, I would say this never, ever consitutes a breach of copyright, but always quote the math book or any other source of heavy inspiration for a proof. In a paper this means discussions with colleagues (who may be anonymous), personal communication, other papers, books, conference proceedings, and so on.

  1. I quote from a math book?

As in a large block of text taken directly from the book? Opposite to the last two points I would say never do this. I can not think of any time it would be a good idea. Also, apart from this, it may also constitute a breach of copyright. I seem to recall photocopying large portions of any book is a breach of copyright (university library mass e-mails, who reads them?) and can not really see that posting said slabs to the internet is any less 'damaging' than photocopying.

Hope that helps.

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  • $\begingroup$ There are times when it is useful and necessary to quote -- perhaps relating to a contentious matter or to highlight a nonobvious mistake relating to the particular phrasing. But this means you need to rely on fair use, and in particular the four factors: (1) the purpose and character of the use; (2) the nature of the work; (3) the proportionate amount used; and (4) the market effect of copying. Copying questions from a math book potentially runs afoul of (4); a long excerpt, especially from a short work, runs afoul of (3); etc. $\endgroup$ – Charles Aug 2 '11 at 19:01
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    $\begingroup$ Of course this is entirely distinct from the academic requirement for proper attribution. $\endgroup$ – Charles Aug 2 '11 at 19:02

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