Mathematical proofs and copyright

[Quartz]

In this thread I suggest the use of the Dot Conjecture, without detailing it, because that would be doing his homework. However, I’m not sure what the copyright situation would be if I had cause to detail it. Reproducing a proof with an author’s commentary would clearly raise copyright issues, but what about the proof itself? What if I commented on it myself?

[Chronos]

I believe that facts are not copyrightable, but the presentation of them is. So if you copied an English-language proof directly out of a book, that’d be a violation. If you restated the proof in your own words, that would be OK. I’m not sure, though, if it would be a violation if you exactly copied a formal symbolic representation of a proof.

[Gfactor]

The Supreme Court considered this issue a long time ago:

The copyright of a work on mathematical science cannot give to the author an exclusive right to the methods of operation which he propounds, or to the diagrams which he employs to explain them, so as to prevent an engineer from using them whenever occasion requires. The very object of publishing a book on science or the useful arts is to communicate to the world the useful knowledge which it contains. But this object would be frustrated if the knowledge could not be used without incurring the guilt of piracy of the book. And where the art it teaches cannot be used without employing the methods and diagrams used to illustrate the book, or such as are similar to them, such methods and diagrams are to be considered as necessary incidents to the art, and given therewith to the public; not given for the purpose of publication in other works explanatory of the art, but for the purpose of practical application.

FindLaw's United States Supreme Court case and opinions.

[TubaDiva]

Thanks, interesting point there; by the nature of the beast, it’s different than our usual Fair Use guidelines, but of course it would be. The ruling even makes sense.

TubaDiva

[Quartz]

Right. Thanks chaps.