Mathematics Stack Exchange (MSE) is the most unusual blog or wiki I came across. It is frequented by professional mathematicians. The standard is a lot higher than Wikipedia. What makes them willing to spend their effort there? Why MSE is attractive to them? I ask these questions as a layman.
Academics have a lot of unstructured time (I do not mean "free" time), which is definitely a part of it. This does not explain why the math should be different from other subject-specific-and-academia-adjacent SEs.
Mathematicians don't need to know where a problem comes from in order to care about it. That makes math unusually amenable to Internet forums. In many fields, something is only interesting if a lot of people are talking about it, or if the people talking about it are "important." If I come up with a question or proposal about how to change a law, for example, who cares; if a retired head of government has the same proposal, it's interesting - because of where it's coming from. Yet if some important person has a position on X, it's well ventilated elsewhere, and an Internet forum is kind of redundant. There are better outlets. This might explain why political scientists and heads of state are not browsing the Politics SE for things to respond to. Which is not to say that professional mathematicians browse Math.SE for research ideas, but you get the point.
Math has less nexus to things people see in headlines, or hold as personal beliefs. Random people aren't going to jump into math forums and demand debate (most of the time). There are people who want their homework done, but that's about it. In many fields, random people form strong opinions about issues after watching TV. Not in math. (People complain about a lack of mathematical literacy in the public, but it's part of what keeps a site like this a place where professionals may still appear.)
I'd further note math is not an IP-intensive area. Many of my friends in biology, chemistry, etc. have ties to commercial concerns that either forbid them from publicly sharing anything resembling what they're working on (or might work on). Many lab sciences folks absorb (rightly or wrongly) a norm that many things are a competition and knowledge is to be shared at most in publications and at conferences. Not math (although should you work for a government that employs mathematicians, I do not recommend bringing insights or problems from work to Math.SE or indeed anywhere on the Internet).
Math more than many other fields is close to childhood play. Very few people write long essays or lines of code at the behest of other people (or whatever else) as children. But many have fond memories of figuring math things out at an early age. For many this site is a bit like time traveling. And nostalgia aside, math produces problems capable of being understood and posed by very young people that remain of interest to professionals. I can't think of another field like that.
To add to the already excellent answers here, there are two reasons why I personally have contributed to MSE:
- MSE is an endless source of interesting mathematical problems. I find problem solving fun, and after one moves beyond things like math competitions, it can be hard to find random math problems to solve on a daily basis. MSE provides that. I even have published some stuff that originated from MSE questions.
- The way the rep and bounty system is structured on MSE make it advantageous to contribute answers to the site even if all you really want is to have a question of your own answered. The reason I first started contributing answers was to gain rep so I could offer a bounty on a question of mine. (I am now well past the point where I need rep to offer bounties, so this point doesn't really apply to me any more. But the bounty system can offer an incentive for people to begin contributing in the first place.)
Similar to a coach of a nationally ranked football team having a recruiting advantage. For a variety of reasons, mathSE attracted high quality queries and high quality answers, perhaps partly as a result of mathSE prioritizing this metaMath article.
Anyway, math professionals start flocking and giving high quality contributions, which attracts more math professionals. These additional professionals do the same, which creates an avalanche effect.
It has gotten to the point that it is very common for a mathSE reviewer with a 30+k reputation to leave a comment that has more insight/elegance than an answer that I would have left.
I'm not a professional but I've been on this site for a year now and I think my long stay boils down to five points and I can imagine a similar experience would be for someone who is a professional:
- There is a minimum standard kept on questions and answers
- Once written posts can be referenced many times later on another posts, so you kinda build links between concepts in your mind
- There is no other worthy competitor to this site that I know of
- Addiction. This is a point I don't like bringing up but it is indeed true, there is a motivation to hit an X point bench mark on the site, right now I wish to get at least 4000 points.
- Though the site has some addictive nature with the points and all, it is a 'good' addiction as I have learned a lot of things from spending time here. So, it's time well spent.
However, there are negative points about this site too. I think there is a lot more potential for growth and improvement.
I started using math.se as an undergrad when I was just starting to explore research-level material that I had noone to ask about. There wasn't really anywhere else where people with expertise would humor me, and what I wanted to know about wasn't in books. I became connected to the community, and after a while, I learned enough that I could start answering questions within my niche. That eventually lead me down a pipeline to math grad school.
I think this experience is unique to math.se and I like the idea that others could have it too. I stick around because I like supporting that.