My name is Gabriel Wu. I am an undergrad at Harvard in Currier House. I do research and write math problems.

My academic interests include:

  • AI safety: how do we make sure that advanced AI systems do what we want?
  • theoretical computer science and math (particularly complexity theory, information theory, and combinatorics)
  • competitive programming
  • amateur philosophy (particularly consciousness, metaphysics, and morality)

The title of this blog is a reference to the Law of the Excluded Middle (LEM), a logical axiom that states \(P \vee \neg P\) for any proposition \(P\). Any time you employ “proof by contradiction”, you are implicitly invoking this law. In the words of David Hilbert, a mathematician’s dependency on the Law of the Excluded Middle is as akin to “the boxer’s use of his fists”. Yet, a competing branch of ideology called intuitionism denies this axiom, believing it to be philosophically unjustified (how can you assume that everything is either true or false from the get-go?). While I personally quite enjoy the use of my fists, I am occasionally sympathetic to the intuitionist view.