Magical learning

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• Fermat's last theorem, the unpublished Fermat version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 = mc^2
• 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.