Wayback Machine for mathematics? I have had a couple of experiences recently which have made me wonder whether the mathematics community should try to establish and maintain something like the Wayback Machine, but specifically focused on mathematics.
In a paper that I wrote back in 1999, I cited a webpage with the title "Is elementary?" and provided the following URL:
http://www.apmaths.uwo.ca/~rcorless/AM563/NOTES/Nov_23_95/Nov_23_95.html
As you might guess, that URL is no longer functioning. I tried the Wayback Machine and I was lucky that it had indeed archived a copy of the relevant part of the page.  Unfortunately, crucial parts of the page were not preserved; the original page used LaTeX2HTML, whose results were not satisfactorily archived.
The above example is not so important from a mathematical point of view because there is now a much better reference available for the mathematical fact in question, but it is a good illustration of the sort of thing I am concerned about—there's a considerable amount of material on the web that is of mathematical value but that is disappearing because it is not being formally published or archived.
My second example is more (ahem) consequential, and is something that the mathematical community might be able to do something about if we act now.  For years there has been a useful web resource at Purdue for researching Consequences of the Axiom of Choice.  Unfortunately, the page is no longer functioning, as you will quickly discover if you try submitting a form number.  The URLs have changed.  I suspect that Purdue redesigned its website at some point, changing the URLs, and that since Herman Rubin died a couple of years ago, there is now nobody responsible for maintaining the Axiom of Choice page.  I tried emailing a couple of random people in the Purdue mathematics department to find out if something could be done to revive the page, but have received no response.
The ideal solution for the Axiom of Choice page may be for some researchers with an active interest in the area to create a wiki, whose survival will not depend on the survival of a single person.  That is the route that the OEIS took and it seems to have worked out well.  One would like to have not just a snapshot of the contents frozen at a single point in time, but a dynamic resource that is continually updated.  Failing that, though, a snapshot would be better than nothing.  However, according to my understanding, the Wayback Machine is not well designed for something like this where you're supposed to access the content by querying a form.
These two examples are of course only the tip of an iceberg.  Scattered across the Internet are all kinds of lecture notes, computer code, databases, blog posts, etc., that are of long-term mathematical interest but that are at risk of disappearing when people retire or die.  Even something like MathOverflow should perhaps be archived from time to time in some independent location in case something goes awry with the corporation in charge of it.

Would it be feasible to set up something like the Wayback Machine but specifically targeted at mathematics, so that we could ensure higher quality preservation than the actual Wayback Machine is able to provide?  If so, which organizations are best equipped to create and maintain such a resource?

 A: In general, I love the Wayback Machine, so when I read your question, I was very in-favor of it. But, we should also think about unintended consequences. If every random mathematical note one uploads to a personal webpage (including notes for students) gets archived somewhere, then that might have a chilling effect on peoples' willingness to upload such notes. I know that in grad school I uploaded a lot of lectures notes for talks I was giving, and when I looked back later I realized they had errors, incorrect citations, etc. I was glad to have the option to take them down.
A good middle ground, between archiving nothing and archiving everything, would be to archive things that have been cited. This is part of the reason I joined the editorial board of the Graduate Journal of Mathematics, because I think this journal can be a good place for useful notes to get published. When I find an unpublished note that has citations, I often write to the author to encourage them to submit it to our journal. If there was a "Wayback Machine for math" then maybe it could reach out to the authors of such notes and archive the pdf unless the author requests that they not do so. I think once something has been cited, it's important for the community that it be accessible.
A: In my previous answer, I focused on unintended consequences of creating a Wayback Machine for math. But I'm worried that answer is preventing us from answering the actual question.

Would it be feasible to set up something like the Wayback Machine but specifically targeted at mathematics, so that we could ensure higher quality preservation than the actual Wayback Machine is able to provide? If so, which organizations are best equipped to create and maintain such a resource?

The Wayback Machine works via web crawlers, and it would be somewhat difficult to replicate what they do just for math. You'd have to help the algorithm decide which pages to archive, and I don't see any clean way to do that. For example, if you only crawled pages with a .edu endpoint, and with math in the URL, you'd miss personal web pages. You could crawl pages where the index page has mathematician in the text, but you'd miss pages about software, paper repositories not tied to a personal web page, etc.
I think a better solution, in the short term, would be to get journals to keep a copy of any web page that is cited when a paper is published, just in case that page goes down in the future. In case the journal can't be convinced, authors could also keep copies of web pages they cite. For every paper I've published, I have a folder with the tex file. I can just make a subfolder where I keep a copy of web pages I cited as of the day I submitted the paper. This would also be a good idea for citing online lecture notes (e.g., Stefan Schwede's notes on symmetric spectra or equivariant homotopy theory) which have many different version and where the theorem numbering might eventually change from what it was when you cited it.
Keeping these folders is very little extra work for us (or for the journals) and feels important to the enterprise of mathematics. To me, it's analogous to how other scientific fields are combating the Replication Crisis, by keeping track of what they did to their data, keeping a copy of the data as it was when the paper was written, and keeping their R code, so that a future researcher could replicate what they had done. I want people to be able to see the same documents I saw when I wrote my paper, so for any that lack a permanent home, I should keep a copy just in case they vanish. If they do vanish, at least I'll have a copy I can share in case someone asks, or potentially host if I have permission (like the Wayback Machine does).
