I'm curious about the rights of ownership regarding problems presented in math textbooks. Can a math problem in general be considered intellectual property of its "inventor"? I'm assuming textual word problems can be "owned" in the same way other literature is by publishers/authors but it becomes more gray with purely numerical expressions. Is it merely a contextual ownership, for example, say no other math author can include such a problem in another textbook or is it more inclusive regarding other mediums like software or blogs etc where money is being made? An "elucidation" here would be much appreciated, thanks.
Well, I'm not so sure that this question is a math question, per-se, but it as in interesting question about mathematics nonetheless. As a matter however of full disclosure, I am not an IP expert and am really not qualified to answer this question, but will give it a go anyway.
There is no doubt that algorithms themselves can be patented. Just ask all of the software companies in the 90's that either abandoned the GIF format or started paying royalties to the LZW compression patent holder. Fractal image compression is another well-known algorithm that was patented and, most likely because of this, never really enjoyed widespread adoption.
Now, addressing the specific question, suppose that someone noted that Hatcher's Algeraic Topology text had no solutions to the exercises and decided to remedy that by working out all of the problems in the text and publishing them. Is this fair use? An argument could probably be made either way. The solution publisher could argue that only a small portion of the text was actually "copied", namely the statements of the problems, and that full attribution was given and therefore fair use of the material was made. The publisher of the text could counter, however, that wholesale reproduction of all problems goes beyond the fair use doctrine and constitutes, instead, a derivative work.
Ultimately, both sides have legitimate arguments and, if no compromise could be reached, the only way that it would really be settled is through the courts. So, I think the best answer to this question, much as someone intimated in another answer, is that the answer is currently indeterminate. I'm not aware of any cases where the specific question regarding ownership of a collection of math problems has been tested.
I asked this very question to a copywriter some years ago and he said that you can not copyright protect a formula but he also said that there are copyright protected algorithms.
Also, here is a link about plagiarism in science.
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