AI-Generated Proposal

Research Note: This proposal was autonomously generated by AI Gemini 3 Pro on November 22, 2025, based on an analysis of current trends in AI-driven mathematics and the user’s academic background. Action Item: Review this suggestion to evaluate if a pivot towards a technical Proof Theory thesis could strategically position you for roles in elite AI research labs like Google DeepMind (AlphaProof team).

The Opportunity: AlphaProof

AlphaProof is a reinforcement learning-based system from Google DeepMind designed for formal mathematical reasoning. It recently achieved silver-medal performance at the International Mathematical Olympiad (IMO).

  • Core Technology: Combines a pre-trained language model with the AlphaZero reinforcement learning algorithm.
  • Formal Language: Uses Lean (a theorem prover based on Dependent Type Theory) to formally verify proofs.
  • Relevance: This represents the cutting edge of Neuro-Symbolic AI—the intersection of neural networks and formal logic.

Why Proof Theory?

To work on systems like AlphaProof, deep expertise in Proof Theory is a massive differentiator. Unlike general ML engineers, a researcher who understands the structural properties of proofs (normalization, cut-elimination, consistency) can contribute to:

  1. Proof Search Algorithms: Optimizing how the AI explores the space of possible proofs.
  2. Formal Verification: Designing better feedback loops between the theorem prover (Lean/Isabelle) and the neural network.
  3. Synthetic Data Generation: Creating high-quality formal proofs to train the models.

Proposed Thesis Direction

Instead of a purely philosophical or historical thesis, consider a technical thesis in Proof Theory with a view towards automated reasoning.

Potential Topics:

  • Proof Mining in Lean: Extracting constructive content from non-constructive proofs using automated tools.
  • Neural Proof Search: Analyzing the proof-theoretic properties of traces generated by LLMs.
  • Structural Proof Theory for Automated Reasoning: Investigating how sequent calculus variants (e.g., G3ip) can improve automated proof search efficiency.

Strategic Value for CV

A thesis in this area signals to HR and Research Leads at DeepMind/OpenAI/Anthropic that:

  1. You have rigorous mathematical maturity (Logic/Proof Theory).
  2. You are aligned with the “Formal Mathematics” agenda (Lean/Coq).
  3. You bridge the gap between symbolic logic and modern AI.

Key References

  • AlphaProof Announcement: Google DeepMind Blog - AlphaProof
  • Lean Community: Lean Prover
  • Relevant Papers:
    • HyperTree Proof Search for Neural Theorem Proving (Reynolds et al.)
    • Generative Language Modeling for Automated Theorem Proving (Polu & Sutskever)

This note is a placeholder for further personal research.