Obviously mathematical research stands on its own but it is of interest how others react to it. My position has given me a unique perspective where it actually helps to try and step away from it objectively, which is something I've valued trying to do for years, and I think it worth it to talk about some conclusions.
The acceptance of the web for a particular content author can arguably be considered reflected in web search rankings. One concern is in choosing a metric simply because one is available, but I think there is substantial quantitative data that supports this metric. And in fact my own experiences give both a subjective for me reference point and potentially objective for others reference.
The benefit of this research perspective has to do with best routes to sharing research information. The 'social disruptive' nature of the web is much discussed and the potential ideal of the web is to remove gatekeepers, like math journals, or force them to re-define their role.
Specifically recently I've noted the emergence of my own mathematical research in the specialized area of number theory which considers binary quadratic Diophantine equations. That is, I have a high ranking across web search engines, with the search: reduce binary quadratic Diophantine equations
The search is important in that it is asking how to do something. That would naturally seem to reflect a demonstrated need which can be satisfied by the results of the search. To my knowledge I am the only person doing that particular search string though I have suggested it now to others.
But also importantly the actual mathematics helps solve a highly particular type of problem and absolute correctness is required, that is 100% correctness, as the mathematics has to be perfect. So it's a great example that the web can find such things.
However, I have other search results, like the name of this blog. At one point I found it necessary to change the name of this blog. My choice of the rather generic "Some Math" was not just because I thought it appropriately descriptive but also to aid in considering this kind of research as to whether or not the web would rank it highly. This social experiment was telling in that the term--some math--gave results at first not related to my content, but over time my content rose in search results. And I could easily compare across search engines.
Another contrary result has been with the search: definition of mathematical proof
That has been extremely informative as the ranking of my page where I define mathematical proof has shown a negative reaction to my discussion of it. For instance emphasizing its search ranking in the past actually lead to it dropping completely from web search across web search engines. I will note using its search position in emotional tones that are not relevant for this post, but considering what is known about web search it involves people linking to your content. So what causes people to link, or de-link is of interest.
With years of experience now in this area I think I have a very clear idea about how the web behaves with regard to certain types of content, also which content has a weaker link attribute, like my definition of mathematical proof, versus content which has a very high link attribute.
It's telling that when I changed the name of this blog to its current one, the link for the definition of mathematical proof promptly disappeared from web search, but the web switched to other research on Usenet math newsgroups with other results!
Talk about validation of a research path, when one source was removed as changing the name of this blog broke web links to it, the web first switched to an alternate source of the same information, which were posts I had made on Usenet, and then switched back, as revealed by the new link name rising in web search.
The web simply went and found the research in a dynamic process.
From a research distribution perspective it appears that math journals may be irrrelevant: people will find useful content regardless which is reflected in web search results which adjust dynamically even if where that information can be found is artificially manipulated.
Presumably if I found a way to destroy all sources that I provided, others might simply put the content up again, which is an experiment I don't see necessary. The web reflects a continuing need for information, but presumably any number of people who needed the content have copied it off the web.
Looking at this situation as objectively as I can I will admit to a subjective reality, and maybe as an independent researcher will note a certain amount of relief. An independent researcher like myself can put up content directly without gatekeepers. Web validation can come from search engine ranking, which is dynamic in nature meaning that it is a constant evaluation, which can even shift to chase the research, if one source is made unavailable, indicating a real need.
Less dynamic behavior can also be associated with content that presumably is deemed less important in the dynamic process like my definition of mathematical proof, which presumably is less of a direct need for people who might be interested in this information.
All search results considered for this evaluation were at #1 in more than one search engine at one time or another, and this position was confirmed to be global, as in, those searches would come up at #1, anywhere in the world. Though confirming that has been easier or harder at times. Primary reference has been Google, which thankfully also during the time of this research inquiry has been the dominant search engine worldwide, which it is at the time of this writing.
There was some limited checking by trying web searches in different geographic areas though I have used primarily states in the United States including Hawaii.