Perhaps some personal background is relevant to this question. A couple of years ago, I graduated with a master's degree in Applied Mathematics from a good Dutch university. Even though I obtained somewhat decent grades for the courses and the thesis (a 7/10 on average, maybe a B in the American system), I sensed that I probably wasn't good enough to pursue a PhD in a relevant mathematical research direction.

Therefore, I opted for a career in a different area. However, I keep coming back to mathematics over and over again. I am still drawn to some mathematical problems, and I work on them in my spare time. One day, I'd like to be a (co)author of (at least) one publication.

I've now come at a point that I think I have some interesting ideas for a certain problem. In order to flesh them out, I think it would be a good idea to collaborate with someone who has more expertise than me in the relevant domain. I've found a postdoc at my former institution, whom I suspect has the appropriate background to work on this problem with me.

I'm not quite sure, though, how to approach this person. I've never met him/her, and it seems somewhat odd or inappropriate to send him/her an e-mail out of the blue. I've thought of proposing to give a short presentation of my ideas to this person, after which s/he can decide whether the approach seems worthwhile enough to delve into more deeply.

This -- finding and approaching trustworthy fellow mathematicians who have the time and willingness to collaborate -- is one particular problem I've encountered while working as a researcher outside academia. As an “independent researcher”, if you will, I encounter all sorts of other problems, including:

- Getting access to some journals, books and research papers;
- Obtaining licenses for expensive proprietary software;

I wonder whether you have any advice to independent researchers on these matters, and whether you can perhaps give some general guidelines or nuggets of wisdom to those working outside academia.