Math is Free as Thought - but do you get it? How?

Trust me on this one: The academic world of maths, computer science and logic is full of Great Ideas that could and should be used by practical visionaries (such as yourself and everyone else at Reboot ;-)

The problem is: Which one is it that YOU personally shouldn't have been able to live without hearing about? Binary Decision Diagrams? Linear Programming? Modal logic? Higher-order control-flow analysis? Size-change graphs? The list goes on and on. Getting familiar with just one of these could take months.

The good news: Maths is really a Free World. The patents are few and far between, the technical papers often go straight to open websites, experts take pride in writing Wikipedia articles, and free, open-source software implementing the ideas are legion. So you can get it - but only if you "get it". Because what use is all this free information if you don't understand what it can do for you? You're probably not going to spend a month learning some enigmatic topic just blindly trusting that whatever "Kripke models" are, they should be the basis of all your future projects.

How would you find out where to begin? How would you start drilling into something that is so complex? What the best way to spend six hours if you just want to get a feeling; just want to figure out whether this Idea might be what you were missing? After that, how would you spend a week to explore it further? Would you start at the local library? Play with every demo on the web? Print out 1,000 pages and read them on the couch of your favourite coffee shop? Or shower every forum and chatroom you know with questions? Of course, these questions aren't at all restricted to maths; they apply to most complex ideas, methods and fields.

I've had to climb such mountains before, and I'm doing it at the moment. This time I'm trying to observe myself and make notes while I peel off the layers of another topic I'm learning.

I'm sure that other Rebooters have similar experiences and I'd love to hear what you did, and to discuss what worked and what didn't. I don't believe that there's a silver bullet waiting for us to find, but I do think your approaches differ from mine, and that there could be some quite practical ideas to learn from each other. I volunteer to get the action going with a personal case study or two.

Post scriptum: OK, time to 'fess up. While I'm primarily a practitioner these days, I used to be a researcher and saw the other side of this problem. Research groups come up with these ideas, models, methods, algorithms, and they do everything they can to make them publicly known and freely available. They know that the idea is good and want it to be put to use, but in many cases they do not know whom to call. They built the hammer and hand it out gratis but the people with the nails don't live in the neighborhood. It's also from that frustrated perspective that I am curious to learn about how the "Idea-seekers" of 2008 go about their business.