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.

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  • Fermat’s last theorem, the unpublished Fermat version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.

3 thoughts on “Magical learning

  1. A lot of people misunderstood the question and answered conjectures instead of theorems. Riemann’ hypotheses isn’t a theorem—it might not even be true!

  2. The vague ones, like the Reimann hypothesis, don’t bother me. Seems like fair game to want to thoroughly understand a theorem without necessarily knowing exactly what the theorem says. For example, one might wish to thoroughly understand whatever theorem most effectively resolves the P=NP question, without knowing how that would be resolved. (I’ve wondered whether it could be proven that there’s no way to prove P=NP either true or false. Possibly as some sort of outgrowth of incompleteness of the continuum.)

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