Jaynes' interpretation of probability theory as an extension of logic that calculates probability of propositions conditioned on other propositions is much more straightforward that the usual set theory formulation, and the notation he uses is enormously helpful.
Alfred Korzybski, of The Map is the Territory fame, had some chapters on the concepts of differential calculus in Science in Sanity which way back when I found provided key insights (as all the General Semantics literature does, and should get more attention here.)
Judea Pearl is the main game in town for a clear notation for the mathematical analysis of causality.
David Wolpert's theoretical framework for analyzing generalization algorithms (in which he produced Stacked Generalization) is a little more obscure, but very useful for learning theory.
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?