Yes! I would guess that your usage of the post in your video will come under "fair use", and hence it will be sufficient to leave a link back to the question on Math.SE.
Even if what you do does not come under "fair use" or "fair dealing", all you need to do is* give proper attribution, and license your work under a compatible license. Most likely, you can simply add a link in the video description, and release your video under a "ShareAlike" compatible license, e.g. CC BY-SA, which Youtube conveniently lets you choose during the upload process.
*-this is the interpretation of someone who has never seriously dealt with legalese before.
Quoting from the Human-readable summary of CC BY-SA 4.0 on the official creativecommons.org site:
You are free to:
Share — copy and redistribute the material in any medium or format
Adapt — remix, transform, and build upon the material for any purpose, even commercially.
The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original. No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation.
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
The link is a better version of the above text-only quote, as it has tooltips, links to more information, and will likely be kept up-to-date.
As in the Meta.SE post An Update On Creative Commons Licensing , older posts are licensed under the 3.0 version of the license. It seems to me that the distinction isn't important for making videos; just give attribution and release under CC BY-SA. there might be complications if you are making say, a book, video game, or other more complicated product.
To find out the particular version of CC BY-SA that a Question or Answer is using, click on the clock symbol to the left of the post:
Then the current license is displayed under the title. Also, each edit to the post will update the post to the newest license (in particular, older posts that were recently edited are under CC BY-SA 4.0.)
the ShareAlike (SA) part of the license and the options Youtube provides you mean that if you must a compatible license, then your only choice is CC BY-SA. This means you might have issues if you e.g. try to use copyrighted music, or music expressly licensed as NonCommercial (NC) in your video. I would guess similar issues would arise if you say, gave a compass and straight edge construction of some famous companies' logos (spitballing here.)
Here are the examples that Sarvesh found - A way to find this shaded area without calculus? , Area Problem from Math Stackexchange, A Beautiful Problem (IIT Test). More can be found by searching for math.stackexchange on Youtube.
Other links I found that may be helpful:
- ShareAlike compatability on the CC Wiki
- On Gamedev.SE: Is it legal to use Creative Commons art in a commercial game?
- On Quora: Is it possible to use "CC-BY-SA" content in YouTube video?
- On Video.SE: Cannot mark my video with CC SA licence because Youtube Content ID found 3rd party soundtrack which itself is CC SA licensed
- On Open.Ed from the Uni. of Edinburgh: Applying a CC licence on YouTube With instructions on how to apply the CC license to your Youtube video)
Personal remark - I love when personality and individuality is mixed with mathematics, be it in a lecture or a video (I'm still making my way through 3b1b's SoME), so I hope you find this helpful and make the video!
In addition to Calvin Khor's excellent post, I would like to make a couple of additional points.
Under US law, and the laws of most other countries, ideas, concepts, principles, discoveries, and the like are not subject to copyright at all. If the only thing in common between your YouTube video and your source is a bunch of ideas and concepts, and you never exactly copy or closely paraphrase existing content, then you can very likely ignore the CC-BY-SA license altogether and release the video under whatever license you like. Furthermore, this applies to any source, not just Stack Exchange. If you want to adapt an argument which you found in some textbook, the same rule applies. This is because nobody is allowed to claim ownership of the underlying mathematical facts and principles. They belong to everyone, and so anyone can make a video about them.
From an ethical perspective, you should properly cite and attribute your sources, so that your viewers can understand where your ideas came from. There is no legal requirement, but if you have anything to do with academia, failing to cite sources may be considered plagiarism, which can have serious academic consequences in some cases. I would strongly recommend that you cite any source which you use or rely on to any significant degree.
You must abide by the license to the extent that you actually copy (or closely paraphrase/imitate) someone else's words or images. Briefly displaying a question, as in this video, may be fair use under US law (and may even be fair dealing under the more restrictive UK law), but fair use is a notoriously gray area and you do so at your own risk. There is no reliable means to determine whether a specific use is actually fair without seeing the inside of a courtroom. Furthermore, these defenses are largely nonexistent outside of US and UK law, but some countries' laws may provide more specific exceptions under the right circumstances.
On the other hand, if there is no reasonable way of explaining something aside from using a specific visualization, then that visualization may be exempt under the scènes à faire and/or merger doctrines, but this is again a gray area. For example, if you want to explain Cantor's diagonal argument, it is extremely difficult to do so without, at some point, showing a tableau of real numbers alongside their associated natural numbers, and highlighting the digits along the main diagonal; the proof just isn't going to make any sense unless you show that specific image. As a result, the visualization as a whole is probably not subject to copyright protection. But it is safer to build this visualization from scratch than to copy it from someone else's presentation of the argument, because they may still have copyright protection on design elements such as the choice of colors and formatting. Similar arguments apply to most other mathematical diagrams.
For US caselaw on this and related issues, see primarily Baker v. Selden (in which Baker was accused of copying Selden's bookkeeping system, but prevailed because the Supreme Court ruled that you can't copyright such a thing), and secondarily Feist v. Rural (in which Feist was accused of copying Rural's telephone book, but prevailed because the Supreme Court ruled that the book was not subject to copyright due to its lack of original creative or artistic content - it was just an alphabetical list of phone numbers).