Tao Zhe Xuan Shows AI‑Assisted 33‑Minute Blind Proof of a Magma Equation Using Lean and GitHub Copilot

Tao Zhe Xuan, a prominent mathematician, launched a YouTube channel where his first video showcases an AI‑assisted proof of a Magma equation (E1689 ⇒ E2) completed in just 33 minutes, a task that previously required a full page of manual work.

The approach, described as a “blind proof,” involved splitting the original handwritten draft into tiny logical units, generating a code skeleton with GitHub Copilot, and then filling the details using Lean’s canonical strategies, with occasional manual edits. The resulting formal proof verifies in Lean and retains human‑readable structure.

The video also discusses the broader context: earlier attempts by Bruno Le Floch needed extensive manual effort, and prior computer‑assisted proofs relied on tools like prover9. Tao argues that AI‑generated proofs can free mathematicians from tedious details while still producing readable results.

In addition to the proof demonstration, Tao introduces a lightweight Python‑based “mathematical proof assistant” (version 2.0) that supports proposition, linear‑arithmetic, substitution, and simplification strategies, mimicking features of Lean, Isabelle, or Coq. The assistant offers two modes—assumption and strategy—with the latter as the default.

An example problem (prove x < 7z + 2 given x < 2y and y < 3z + 1 for positive reals) is formalized and solved using the assistant. The relevant code snippets are shown below:

>>> from main import *
>>> p = linarith_exercise()
Starting proof.  Current proof state:
x: pos_real
y: pos_real
z: pos_real
h1: x < 2*y
h2: y < 3*z + 1
|- x < 7*z + 2

The assistant then applies the Linarith() strategy to solve the goal, producing a linear‑arithmetic proof.

>>> p.use(Linarith())
Goal solved by linear arithmetic!
Proof complete!

For detailed tracing, the assistant can run with verbose output, showing the transformation of inequalities into a linear‑programming form and the combination that yields a contradiction (0 < 1).

>>> p.use(Linarith(verbose=true))
Checking feasibility of the following inequalities:
1*z > 0
1*x + -7*z >= 2
1*y + -3*z < 1
...
Goal solved by linear arithmetic!
Proof complete!

Tao expresses strong satisfaction with the tool and invites contributions, such as new data types, strategies, or challenging examples. Future plans include extending the assistant to handle symbolic‑function spaces, enabling automated reasoning about inequalities like Hölder’s and Sobolev embeddings using the SymPy framework.

Overall, the video illustrates the practical potential of AI‑augmented theorem proving, showing that semi‑automated methods can dramatically reduce proof time while maintaining human‑readable output.