At 63, Israeli immigrant solves 38-year-old math riddle
usatoday.com
usatoday.com
First: Because both math and software don't require expensive equipment, credentials, or direct access to one's mentors (like Ramanujan, you can learn from books!) you can start your training as a mathematician at a very early age and be doing professional-grade work before you graduate high school. As I said the last time this came up, "software is one of the few fields where a seventeen-year-old can have ten years of pro-level experience".
Second: Mathematicians who want to get jobs in academia have large incentives to do good work when they're young: Until they make a splash, they're poorly paid grad students and postdocs. This is also true for other scientists, but in physics or biology you have to be in grad school before you can even get a long-term job in the lab where you can start learning to do great experimental work -- and then you still have to take reams of data, do multiple postdocs, etc.
By the time they hit age fifty, most talented mathematicians have already accomplished some math. They have jobs, and possibly tenure. They have children, they have committee meetings, they have books to write. They have already proven themselves. Even if they do accomplish some great math papers, you won't see headlines about "astoundingly old mathematicians". They'll be billed as "veteran math professors", whom everyone expects to do great work, since they've been doing great work ever since they were twenty!
But then there's this poor guy, who somehow arrived in his forties and fifties without tenure or even a job. That was unpleasant for him, of course, but it gave him a lot of incentive to do some great mathematics in order to get and keep a new academic job. And, what do you know, he rose to the occasion. Perhaps if more sixty-year-olds had good reason to do great math, we would see more of them doing so.
If I were younger and looking for a job in sociology, maybe I would have done some of that formal research instead of posting half-assed speculation on news.yc. :)
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi...
It isn't exactly as mechanical_fish says, but it's along the same lines, and critically, it tries to explain why scientific contributions fade dramatically after marriage.
Another interesting article, while doesn't count as research, likely because there isn't much of a sample size, and probably wouldn't be one anymore, is the Richard Hamming talk pg posted here: http://www.paulgraham.com/hamming.html
After these inputs, a valid hypothesis is "monotony kills creativity." There are studies that show this idea is generally correct; if you ask, the ones I would cite to support this hypothesis would be ones about education, where stimulating environments correlate to achievement. Research in this area should be easy to find.
This also applies for the software industry (especially mid-to-large size companies). Youthful programmers want to learn the latest hot/cool/interesting technology. After several projects and as they gain pratical experience, youthful programmers start to realize that it's not about what technology is used, there are common problem parameters, regardless of technology. As they start to realize this, they might start settling down (getting married, having a family) and their priorities shift from pounding out interesting code to developing a life. I see this unspoken everyday in the happy-where-I-am-and-just-doing-my-job-nothing-more actions of some people in their 40+s (and shockingly 30s and yes some 20s) in my broader development org. So, the people with the most experience are those who probably delegate to those with the least experience.
It's just 9 pages long, including an intro and bibliography.
http://en.wikipedia.org/wiki/Road_coloring_problem
You can't "point" nodes at each other to communicate the directions to the destination. Instead, you must communicate by coloring each edge with one of k colors (k is the out-degree of every node). Then, for any chosen destination node, you give a sequence of colors; the recipient of the directions starts in any node (even the destination node) and simply follows the sequence of colors, ending up at the destination. The fact that such a coloring always exists is somewhat surprising.