"I began to worry that, by focusing on exposition, I was failing to do the best work I could. Often, my work felt illegitimate in some way"
This could be worthy of discussion and how the author has responded to it is commendable.
This could be worthy of discussion and how the author has responded to it is commendable.
Talking to others in the space, I think a number of people share my experience, and often stopped doing this kind of work. While there's extremely positive feedback from some people, it's kind of "you have a cool hobby" and it's kind of iffy how much it helps professionally.
In some cases, I know people who have had well-intentioned senior researchers, or their advisor, encourage them to switch to focusing on traditional papers. In a smaller number of cases, I know people have received explicitly negative feedback. Sort of, "those who can, do research; those who can not, explain research."
My career has worked out really well, but it's unclear how much of that is luck. I think we can support people better.
Luminaries in a field (Einstein, Feynman, Tao) have "post-rigorous" understanding (https://terrytao.wordpress.com/career-advice/there%E2%80%99s...). Pure research without sufficient explanation doesn't help others build this level of depth and leaves the findings as a black box.
For what its worth, having dabbled in some visualizations of concepts, its really difficult, and I didn't find that the available tools were well suited for mathematical visualization. Its really unfortunate that to be able to present something intuitively, there's a very high technical skill floor as well as a relatively high artistic floor.
On similar lines, the fact that each of his posts takes 50-200 hours of work is another reality check. I always thought he was writing these on the side in 2-3 hours. This made me believe I could not with years of practice produce such great work. I am still not sure if I would be able to but at least I can now set realistic expectations for myself. Also, knowing it took so much work on his end has made me respect him even more.
Of course, that layout only becomes clear only after the area has developed a little, but IMHO the most important education that can be imparted to newcomers in a field is that "context". It pains me to see that good expository material that share insight seem to be hard to find, particularly on front-line research. Broadly, I feel that research communities ought to do a better job of writing accessible review material -- otherwise they inevitably fracture into sub-communities which start talking past each other.
I've rewritten this comment maybe 10 times because I'm struggling to capture how completely myopic this idea is. But here's a quote from Feynman's 5th messenger lecture [1] that I really enjoy, he's talking about the graph of all possible human endeavors:
[The graph] is a series of concepts that we use to understand things at an ever higher level. And going on, we come to things like evil and beauty and hope. Now, which end is nearer to the ultimate creator or the ultimate or, if I make a religious metaphor, which end is nearer to God? Beauty and hope, or the fundamental laws? I think that the right way, of course, is to say that the whole structural interconnections of the thing is the thing that we have to look at. And that all the sciences and all the efforts-- not just the sciences but all the efforts of intellectual kind-- are to see the connections of the hierarchies is to connect beauty to history, to connect history to man's psychology, the man's psychology to the working of the brain, the brain to the neural impulse, the neural impulse to the chemistry, and so forth, up and down, both ways. And today, we cannot-- and there's no use making believe we can-- draw carefully a line all the way from one end of this thing to the other. In fact, we've just begun to see that there is this relative hierarchy. And so I don't think either end is nearest to God. And to stand at either end and to look out off the end of the pier only, hoping out in that direction is the complete understanding, is a mistake. And to stand with evil and beauty and hope, or the stand with the fundamental laws, hoping that way to get a deep understanding of the whole world with that aspect alone is a mistake. And it is not sensible, either, for the ones who specialize at one end and the ones who specialize at the other end to have such disregard for each other. They don't, actually. But the people say they do. Sorry. [LAUGHTER] But actually, the great mass of workers in between, connecting one step to another, are improving all the time our understanding of the world, both from working at the ends and working in the middle. And in that way, we are gradually understanding this connection, this tremendous world of interconnecting hierarchies. Thank you.
[1] http://www.cornell.edu/video/richard-feynman-messenger-lectu...