My document of life-lessons spits out this (it has a focus on teaching children, but it aims high):
Key math insights of general value:
What is a number really - Peano's sentence
Equality (do the same to both sides, equivalence classes)
Negation and inversion (reversing any relationship in general)
Variables, functions, domains
Continuous functions
Limits, infinities (leads e.g. to real analysis)
Postponing operations (fractions, 'primitive functions', lazy evaluation)
Probability (enumerating paths that can are taken fractionally, Bayes rule)
Tracking errors (dealing with two or more functions/results at the same time)
Induction, proofs
Transformation into another space (Fourier, dual spaces, radix sort)
Representations of sequences and trees and graphs
Decomposition of plans and algorithms (O-notation)
Encoding of plans as numbers (Turing, Curry, Gödel)
The idea is to see the patterns behind the patterns (link in Einsteins Speed).
This is really good and impressive. Do you have such a list for statistics?
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?