This is a collection of succinct but wonderfully satisfying theorems. Leave a comment if you have a good one!

The punchlines are hidden; try to guess the blanks!
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• Liouville’s theorem
  A bounded complex differentiable function is constant.

• Jordan normal form
  A matrix is similar to an upper triangular matrix.

• Cauchy’s integral theorem
  The integral of a holomorphic function around a loop vanishes identically.

• Riemann Mapping Theorem
  Strict subsets of \(ℂ\) which are nonempty, open, and simply connected are related by a conformal mapping.

• A complete ordered field is the real line.

• Every field is a subfield of the surreal numbers.

• Cayley’s theorem
  All groups are permutation groups.

• Lagrange’s theorem
  The order of a finite group is divisible by the orders of its subgroups.

• Fundamental theorem of finite Abelian groups
  A finite Abelian group is a direct sum of prime-order cyclic groups.

• The \(ℤ\)-modules are exactly the Abelian groups.

• Cayley–Hamilton theorem
  A square matrix satisfies its own characteristic polynomial.

• Green–Tao theorem
  There are arbitrarily long arithmetic progressions of primes.

• Dirichlet’s Theorem
  Every proper arithmetic sequence contains infinitely many primes.

• Two random infinite graphs are isomorphic with probability one.