I asked two questions on twitter yesterday. The previous post summarized the results for a question about books that I asked from my personal Twitter account.

This post will summarize the results of a question I asked from @AnalysisFact.

If a genie offered to give you a thorough understanding of one theorem, what theorem would you choose? — Analysis Fact (@AnalysisFact) June 15, 2018

Here are the results by category. Some are not strictly theorems but rather topics or conjectures.

Computer science

Curry-Howard correspondence

P=NP or not

Collatz Conjecture

Logic

Cohen’s forcing theorem

Godel’s Incompleteness theorem

Continuum hypothesis

Zorn’s lemma

Algebra and number theory

The ABC conjecture (theorem?)

Prime number theorem.

Riemann hypothesis

Fundamental theorem of finite abelian groups

Classification of finite simple groups

Fermat’s last theorem, the unpublished Fermat version

Topology and differential geometry

Thurston’s geometrization conjecture

Gauss Bonnet theorem

de Rham’s theorem

Grothendieck Riemann Roch theorem

Analysis

Banach-Tarski theorem.

Stokes theorem

Carleson-Hunt theorem

The epsilon/delta definition of continuity

Universal approximation theorem

Differential equations

Navier–Stokes existence and smoothness postulate

The relativistic version of the Shrodinger equation

Atiyah-Singer index theorem

Mathematical physics

E = mc²

Noether’s theorem

Liouville’s theorem

Miscellaneous

Existence of general equilibrium prices

Farkas’ lemma

The graph minor theorem

Central limit theorem

Mischievous genie

A couple people picked up the fact that in folk stories, being granted a wish doesn’t usually turn out well.

M. Shah: uh oh. Is this one of those malicious genies that twists language used to make the wish so that you are granted some horrific wish?

Jumpy the Hat: You now understand every single thing about irrational numbers but it’s all wasted because you’re cursed to become NJ Wildberger and you don’t think they exist

M Shah: or you want to thoroughly understand some theorem about Weierstrass’s monster. But little did anyone know that Weierstrass actually did have a pet monster. And it ends up biting your head off because it doesn’t like other things that are continuous.