The Paucity of Elites Online

by JonahSinick 2 min read31st May 201342 comments


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.

The opportunity cost to mathematical research here seems to be enormous. Some explanations for the phenomenon are:
  1. Many of the prize winners who don't blog are elderly, and blogging is relatively uncommon among elderly people.
  2. 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).
  3. Inertia.
Point #1 is relevant, but the fraction of young mathematicians who blog is also very small (though larger than that of the older mathematicians).

To elaborate on #2 — when I first started using MathOverflow, I found it to be a very useful resource, and learned a lot from it. In the beginning, there was a substantial number of very high quality mathematicians who answered a lot of important questions. Since then, the number has dwindled (though I would emphasize that it remains true that some of the contributors are outstanding). In more recent times, I've had the experience of asking very natural questions that I'm sure that many mathematicians have thought about, without anyone answering (here too, I would emphasize that in recent times I've gotten some helpful answers: I'm thankful to the current MathOverflow community for this). I think that the drop off in participation by high quality mathematicians can be partially attributed to [the posters who were contributing the most getting relatively little helpful feedback on their own questions and answers]. In such a situation, corresponding with one's colleagues privately starts to look more attractive than posting publicly.

It seems as though it might be possible to get around the issues #2 and #3 by simultaneously involving a substantial number of very high quality mathematicians, and having them write for and respond to each other, so that putting their thoughts into the public domain would become attractive. But doing so is beyond my pay grade :-)

I suspect that the phenomenon that I describe extends well beyond pure math, and that across fields, there's a large opportunity cost associated with high quality thinkers not putting their thoughts into the public domain. Changing the status quo here could have enormous value. I think that there might be low hanging fruit in this area, insofar as what efforts there have been seem to be few and far between, relative to the landscape of people who think about ideas.