Deep0Thinking

Deep0Thinking

Louis Liu

Louis Liu

Mathematics at Carnegie Mellon.

My interests center on logic, the metatheory of science, and formalized mathematics.

Current work

Axiomatization of classical mechanics

In progress
What I think about

Research interests

In classical first-order logic, soundness connects derivability T proves phi to semantic consequence T entails phi; completeness gives the converse. T ⊢ φ T ⊨ φ soundnesscompleteness FINITE DERIVATIONSALL MODELS OF T Classical first-order logic

Proof and meaning

Soundness and completeness connect formal derivations with truth in every model. They do not imply that a theory decides every sentence.

On syntax, truth, and completeness
Across
  • Mathematics
  • Physics
  • Computer science
  • Neuroscience
What I'm working on

Research & projects

Research in progress

Axiomatizing classical mechanics

Making the assumptions of a physical theory explicit.

 Co-authored preprint · 2026

ReuF2F

Evaluating coding agents on proving or refuting open research problems.
Personal project

Two-Do

A couples' planning app, built with my partner, Grace Tian.

From my notes

  1. Logic & metatheory

    Why Mathematical Logic Textbooks Look Circular

  2. Foundations of physics

    A Mathematical Exploration of Norton's Dome and Determinism in Classical Mechanics

  3. History · series

    History of Logic