One of the quirks of professional mathematics is that researchers are discouraged from speculating too far beyond the range of what they can actually prove. To quote Minhyong Kim (from https://mathoverflow.net/a/38694/766): "it's almost as though definite mathematical results are money in the bank. After you've built up some savings, you can afford to spend a bit by philosophizing. But then, you can't let the balance get too low because people will start looking at you in funny, suspicious ways."
It can take some conscious effort for junior mathematicians, once they actually have earned enough "theorem credits" to afford to speculate, to actually venture opinions and make broader conclusions. Easier to play it safe and only stick to what their theorems and results can objectively verify. While this does cut down on a lot of nonsense, I sometimes wonder if we should have more spaces to encourage mathematical speculation.
We do have the mechanisms of posing open problems and formuating conjectures, which work well enough, but we don't really have a culture of throwing out less precise, but still informed, speculation on where a subject might be headed. (Except perhaps during conference teas and dinners. Which is one good reason to attend such conferences...)
@tao - One "safe space" for airing less precisely formulated speculations seems to be blog articles. But blogging seems to have declined in popularity with young mathematicians.
Another is Twitter, though I've mainly seen category theorists speculating there, not so much other kinds of mathematicians.
I hope Mathstodon will become another place for informed speculation!
@johncarlosbaez @tao It is interesting to contrast the tone of what counts as informed speculation among mathematicians compared to scientists in other fields. Mathematicians seem to be less comfortable getting out of the comfort zone of what they can (at least conceivably) prove. Chemists, Astronomers, Physicists, Biologists and Statisticians all seem able to engage with others in their discipline more broadly outside of their immediate areas of expertise. The culture of rigor/proof seems to stifle many mathematicians from voicing their insights in a broader context. IMHO this is a loss for the entire scientific community,
