An understanding of the insights behind math is essential. But I wonder: To improve your rationality, how often do you really solve an equation, arithmetically (as opposed to just going by feel) calculate probabilities from Bayes Rule, or derive a formal proof?
The concrete practice is an indispensable way of arriving at the insight. ("No royal road to geometry" etc.)
Achieving facility with the concrete work is evidence that you have the insight. Evidence to yourself, the one person you need to prove it to.
To be avoided is gaining a mere feeling of understandishness. Anyone can learn to say "light travels along geodesics in curved space", but if you can't calculate the precession of Mercury, you don't know general relativity.
I have started to put together a sort of curriculum for learning the subjects that lend themselves to rationality. It includes things like experimental methodology and cognitive psychology (obviously), along with "support disciplines" like computer science and economics. I think (though maybe I'm wrong) that mathematics is one of the most important things to understand.
Eliezer said in the simple math of everything:
I want to have access to outlook-changing insights. So, what math do I need to know? What are the generally applicable mathematical principles that are most worth learning? The above quote seems to indicate at least calculus, and everyone is a fan of Bayesian statistics (which I know little about).
Secondarily, what are some of the most important of that "drop-dead basic fundamental embarrassingly simple mathematics" from different fields? What fields are mathematically based, other than physics and evolutionary biology, and economics?
What is the most important math for an educated person to be familiar with?
As someone who took an honors calculus class in high school, liked it, and did alright in the class, but who has probably forgotten most of it by now and needs to relearn it, how should I go about learning that math?