# Machine learning and information theory concepts towards an AI Mathematician

arXiv: https://arxiv.org/abs/2403.04571 · HTML: https://mlsanity.com/paper/2403.04571/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 7 Mar 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)
- [Proof Artifact Co-training for Theorem Proving with Language Models](https://mlsanity.com/paper/2102.06203/) (2021)
- [The Consciousness Prior](https://mlsanity.com/paper/1709.08568/) (2017)
- [A Survey of Exploration Methods in Reinforcement Learning](https://mlsanity.com/paper/2109.00157/) (2021)
- [Landmark-Guided Subgoal Generation in Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2110.13625/) (2021)
- [Sources of Richness and Ineffability for Phenomenally Conscious States](https://mlsanity.com/paper/2302.06403/) (2023)

## Built on by (most cited first, 20 of 20)

- [Formal Mathematical Reasoning: A New Frontier in AI](https://mlsanity.com/paper/2412.16075/) (2024)
- [A Survey on Deep Learning for Theorem Proving](https://mlsanity.com/paper/2404.09939/) (2024)
- [Knowledge Mechanisms in Large Language Models: A Survey and Perspective](https://mlsanity.com/paper/2407.15017/) (2024)
- [Learning Formal Mathematics From Intrinsic Motivation](https://mlsanity.com/paper/2407.00695/) (2024)
- [Out-of-distribution generalization via composition: a lens through induction heads in Transformers](https://mlsanity.com/paper/2408.09503/) (2024)
- [Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning](https://mlsanity.com/paper/2412.15184/) (2024)
- [Autonomous Research Agents: A Survey of AI Scientists and the Verification Gap](https://mlsanity.com/paper/2608.05179/) (2026)
- [ATG: Benchmarking Automated Theorem Generation for Generative Language Models](https://mlsanity.com/paper/2405.06677/) (2024)
- [A Triumvirate of AI Driven Theoretical Discovery](https://mlsanity.com/paper/2405.19973/) (2024)
- [Library Learning Doesn't: The Curious Case of the Single-Use "Library"](https://mlsanity.com/paper/2410.20274/) (2024)
- [Artificial Intelligence and the Structure of Mathematics](https://mlsanity.com/paper/2604.06107/) (2026)
- [Beyond "Hallucinations": A Framework for Stable Human-AI Reasoning](https://mlsanity.com/paper/2510.14665/) (2025)
- [Benchmarking graph construction by large language models for coherence-driven inference](https://mlsanity.com/paper/2502.13953/) (2025)
- [The Information-Theoretic Imperative: Compression and the Epistemic Foundations of Intelligence](https://mlsanity.com/paper/2510.25883/) (2025)
- [Discovering mathematical concepts through a multi-agent system](https://mlsanity.com/paper/2603.04528/) (2026)
- [Governing Reflective Human-AI Collaboration: A Framework for Epistemic Scaffolding and Traceable Reasoning](https://mlsanity.com/paper/2604.14898/) (2026)
- [Coherence-driven inference for cybersecurity](https://mlsanity.com/paper/2509.18520/) (2025)
- [Math Takes Two: A test for emergent mathematical reasoning in communication](https://mlsanity.com/paper/2604.21935/) (2026)
- [From Consumption to Reflection: Designing Human-AI Relations for Stable Reasoning](https://mlsanity.com/paper/2606.11195/) (2026)
- [Learning to Discover Interesting Mathematics](https://mlsanity.com/paper/2609.28603/) (2026)

## Abstract (arXiv)

The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities -- which correspond to our intuition and habitual behaviors -- but still lacks something important regarding system 2 abilities -- which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.