This comment is insightful!
The areas where strong evidence is common are largely those areas we don’t intuitively think of as governed by probability theory and where classic logic performs well.
I’m pretty sure that statistics (as mathematics) all assume ‘logic’ (first-order logic at least), so I think this is also technically correct!
Gathering enough evidence sometimes allows reasoning to be performed using propositional logic with acceptable results.
Yes! Being able to use logic can be a fantastic super-power (when it works). Sometimes the universe really is like a Sudoku puzzle!
Being able to use both probabilities and logical statements, and appropriately, is a significant part of what I think David Chapman is gesturing at with what he calls ‘meta-rationality’. And beyond both of those formal rational systems, there’s an entire Platonic universe of alternative ontologies that can also be useful in some contexts (and for some purposes).
What kinds of advice or ideas do you think would be helpful that’s specific to mathematicians? Any (hypothetical) examples? Are there things that are currently ‘painful’ or that you expect to be, that you don’t think your (hypothetical) workflow/productivity system addresses?
Possibly helpful: I use GitLab for all of my projects; not just software. I find GitLab issues work very well for all but the biggest/longest projects (and even then it’s easy enough to split up a project into ‘sub-projects’ with separate GitLab issues). One reason I like GitLab is that it has a very nice Markdown dialect and it includes pretty good (for me) ‘math’ support. (My favorite part of it’s Markdown is todo lists, i.e. checklists. I find that very useful for, first, outlining what I want to do, and then, later, recording that I’ve done all of those things.)