Imagine you google the word "eigenvalue". But instead of one list of search results, you automatically get a bunch of new browser tabs. In each tab, is the page about eigenvalues on each of multiple whitelisted sites. Wikipedia, nLab, Wolfram Mathworld, reddit, and LessWrong, for example.
Does this sound useful? Like it could e.g. give you multiple explanations of the same topic, all gathered together, quickly?
Turns out, this functionality exists.
Multiple browsers have extension "app stores", and one type of extension is a "multisearch" or a "multi tab search".
I found this extension for Chrome. There are almost certainly similar ones for Firefox and other browsers. The below instructions are for that specific extension.
To use it:
Install the extension.
Click the extension's icon in your browser, and go to its "Options".
Enter URLs to search, with the "%s" operator being what you'd put your query into.
An example category contains a list of sites I want to multi-tab-search about
[Google Feeling Lucky] brilliant.org %s
https://en.wikipedia.org/w/index.php?title=Special:Search&search=%22%s%22&ns0=1&fulltext=Search
[Google Feeling Lucky] ncatlab.org %s
[Google Feeling Lucky] wolfram mathworld %s
[Google Feeling Lucky] khan academy %s
[Google Feeling Lucky] proofwiki.org %srg %s
(Note: the "[Google Feeling Lucky]" option unfortunately doesn't actually open the first search-result, it just googles it for you)
Open a new tab, press "m" and then "space" before typing your query. (For this extension, you need to type "m" before you type another custom key for a different "category". So if you use "x" for a "rationality" category, you'd press m-space and then type "x orthogonality thesis" to multi-tab-search for the orthogonality thesis.)
Lots of new tabs will open, one for each site!
This is much easier to setup, but less useful/complete, than my "multi-explanation math wiki" idea. Consider it an 80/20 minimum-viable-setup for verifying the "multiple explanations = better understanding" idea.
If you find this useful, you might leave multi-site query lists that you ended up using, in the comments.