This inspired me to compile a list:

Since, I’m not a mathematician(pure/applied) I just compiled things from the blog post combining

with the comments:

* Bayes Theorem

- Jensen’s Inequality if is a convex function and X is

a random variable. Extends convexity from sums to integrals(aka discrete to continuous)
- lto’s lemma: aka(Merton, Black and Scholes option pricing formula)
- Complex analysis.. should i disqualify this as not a theorem??
- Standard error of the mean.details link
- Jordan Curve Theorem: A closed curve has an inside and an outside. (sounds obvious in 2D

and 3D, perhaps with time as 4D, keeping options open is staying outside closed curves??)
- kullback-leibler positivity:(no clue need to look up wolfram alpha or wikipedia)
- Hahn-Banach Theorem (again needs searching)
- Pigeon-Hole principle link here
- Taylor’s theorem, (once again continuous function approximated by sum of discrete

components/expressions) Used in:
- Approximating any function with nth degree precision
- Bounding the error term of an approximation
- Decomposing functions into linear combinations of other functions
- Kolmogorovâ€™s Inequality for the maximum absolute value of the partial sums of a sequence of IID random variables.( the basis of martingale theory)
- Karush-Kuhn-Tucker optimality conditions for nonlinear programming, link

here
- Envelope Theorem — from economics
- Zorn’s lemma , also Axiom of Choice
- Fourier Transform and Fast Fourier Transform

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