Speaking selfishly, personally, I would be more engaged with the content if you tackled some specific mathematical problem or set of ideas and used it as an example to make a broader point about learning math. This could be done, perhaps, by talking about some concept that gave you a lot of trouble until you finally found the right perspective that made the issue "click"? Not just as a hollow example, make it so that we too are puzzled by the oddity or frustrated by the difficult situation, and give us the actual answer and the process necessary for finding it. Or if that's not an accurate understanding of how you actually go about learning new mathematical concepts, then talk about that issue instead, maybe even while addressing the "click" misunderstanding. Be more specific and involve more applied knowledge please. Give us a strongly flavored taste of what it is like to experience high level mathematical understanding and to work with the nitty gritty of mathematical issues.
You linked to a "visualizing machine intelligence" post a few days ago, I really enjoyed that, although I didn't understand too much and am still processing some of its ideas. Do more things like that please and thank you.
Thanks for the suggestion.
The actual situation is that over the past 3 months I've had a cluster of insights that's extended far beyond math education as typically conceived, and I think that I've finally uncovered a road forward for people in our reference class to (as a group) increase our productivity by ~100x+. (As a point of reference, Bill Gates makes ~$10 billion a year: that should make the factor of 100x less far fetched.)
There are so many things to say that it's difficult to know where to start. I have ~500 unpublished pages on the subject, but a...
At age 17, my future looked very promising. I had overcome a crippling learning disability, and discovered how to do research level math on my own. I knew that the entire K-12 infrastructure had failed to figure out how to teach the skills that I developed, and so I felt empowered to help others learn how to think about the world mathematically.
Things didn't go as I had been hoping they would. My years between 18 and 28 consisted of a long string of failed attempts to help people learn math, and to promote effective altruism. I learned a lot along the way, but I didn't have the outsized impact that I aspired to. On the contrary, I was only marginally functional, and I alienated most of the people who I tried to help. I found this profoundly demoralizing, and struggled with chronic depression. If I had died at age 28, my life would have been a tragedy.
Fortunately, at age 29, I'm still alive, and after spending a decade wandering in a wilderness, I've gotten my act together, and am back on my feet.
What I finally realized out is that my failures had come from me having very poor communication skills, something that I had been oblivious to until very recently. Recognizing the problem was just the first step. It's still the case that most of what I try to communicate is lost in translation. I know that the issue is not going to go away overnight, or even over the next 6 months. Sometimes it's frustrating, because my self-image is so closely tied with my desire to help people, and even now, in practice, most of my efforts are fruitless.
But I'm not concerned about that. I probably still have 30 or 40 productive years ahead of me. I'm ok with the fact that no matter how hard I try, I fail most of the time. Y-Combinator founder Paul Graham emphasizes the importance of relentless resourcefulness. Every failure is a learning opportunity. I know that if I keep experimenting and learning, eventually I'll succeed. Figuratively speaking, I know that even if I lose dozens of battles over the next four decades, in the end, I'll win the war. And that's enough to keep me going.
Something analogous is true of everyone who has a strong passion, and is willing and able to learn from failure. Steve Jobs expressed a similar view in his 2005 Stanford commencement address (transcript | video):