The first full releases will include:

  • Foundational papers formalizing Burns Law and its analytic implications for prime structure.
  • A reproducible research pipeline connecting LaTeX papers, GitHub repositories, and AI-assisted verification.

These are not just results — they’re part of a new method of doing mathematics: transparent, iterative, and structurally integrated.

How to Follow the Work

  • This site will publish updates, preprints, and conceptual notes as the research develops.
  • All formal proofs and reproducible builds will be archived at
    github.com/jtpmath/research
  • For a more conversational look at the process, the Videos page will feature overviews and behind-the-scenes explanations of the mathematics as it evolves.

Methodology

Expert-Prompted AI Mathematics: A Framework for Research-Level Reasoning

1. Motivation

Language-based AI models are now able to perform algebraic manipulation, formal translation, and pattern detection at speeds that would have been unimaginable even a few years ago. Yet in research mathematics, correctness depends on the logical framing of a problem, not just on computation. Without explicit human control over definitions, hypotheses, and inference rules, an AI system can reproduce false reasoning at scale. The future of AI in mathematics therefore requires a hybrid workflow in which mathematicians remain the source of logic while the AI provides acceleration and search power.

2. The Expert-Prompted Workflow

Step 1 – Human-Defined Framework.
The mathematician defines the categorical setting, variables, and constraints. The AI is never asked to invent the problem but to operate strictly within a well-typed structure.

Step 2 – AI-Assisted Derivation.
The AI executes symbolic computations, expands series, runs simulations, and searches for counterexamples or conjectural patterns. Its outputs are provisional data, not results.

Step 3 – Expert Verification and Refinement.
The human expert inspects each derivation for logical soundness and reformulates prompts where inconsistencies appear. In this stage the AI becomes a feedback instrument for discovering where reasoning breaks.

Step 4 – Peer and Formal Validation.
Verified outputs are checked independently—either by colleagues or by proof-verification software—to ensure that all conclusions can be reconstructed without the AI.

3. Educational and Research Impact

This framework transforms AI from a proof generator into a proof accelerator. It models how advanced researchers and graduate students can collaborate responsibly with computational systems, maintaining human oversight while exploiting machine speed. The workflow is domain-independent: it applies to analytic number theory, dynamical systems, algebraic geometry, and beyond. It also provides a reproducible standard for documenting AI involvement in mathematical publications, promoting transparency and trust in the era of automated reasoning.

4. Future Work

My next objective is to formalize evaluation metrics for AI-assisted reasoning—measures of logical fidelity, error propagation, and human-AI interaction efficiency—and to pilot this workflow in open research problems where symbolic and numerical components intersect. The goal is to create a sustainable methodology through which AI augments mathematical discovery without compromising rigor.