Something that's caught my attention over the past few months is that out of the strongest thinkers who I'm familiar with, a very low proportion record their informal ideas online, and discuss their thoughts in the public domain.
The domain that I'm most familiar with is pure math, so I'll focus on that, but I imagine that my remarks apply more broadly.
A very large fraction of pure mathematicians (including a large fraction of elite mathematicians) post their papers to ArXiv, a database which stores preprints of mathematical papers. The invention and widespread use of ArXiv has been very valuable, in that researchers can easily notice and access the new papers in their fields as soon as they become available.
That not withstanding, the fraction of mathematical thinking that's in the public domain is vastly smaller. Math papers generally don't include explanations of why the researchers are interested in the questions that they're writing about or how they came up with the proofs of the theorems. Even when an author does attempt to explain his or her thinking, a reader will often find parts of it opaque, and want clarification. The need to write to the author for clarification poses a trivial inconvenience which, in practice, discourages a large fraction of questions that people ask.
Informal mathematical thoughts are extremely important for doing mathematical research, and it's generally difficult to learn it without in-person contact with authors of papers.
A natural solution to these issues is for researchers to spend more time blogging about their informal thoughts, and for a commenting system to be enabled for readers to offer suggestions or request clarification.
The mathematicians who have the most to offer in the way of ideas and insight are the elite mathematicians. The fraction of them who blog is tiny. Terence Tao and Timothy Gowers do a considerable amount of blogging, but they're nearly alone in this.
- Of the 42 living Fields Medalists, Tao and Gowers are the only active bloggers who I know of, and Borcherds and Connes are the only others who I know of who have ever blogged.
- I don't know of any bloggers amongst the winners of the Cole Prize in algebra or in number theory.
- I don't know any bloggers amongst the Steele Prize winners.
- Ian Agol is the only blogger amongst winners of the Oswald Veblan Prize in Geometry who I know of.
- Many of the prize winners who don't blog are elderly, and blogging is relatively uncommon among elderly people.
- There's adverse selection coming from the best people having the least to gain from public online discourse (in light of the fact that the fraction of participants who are of similar quality being tiny).