# AI for Mathematics: A Cognitive Science Perspective

arXiv: https://arxiv.org/abs/2310.13021 · HTML: https://mlsanity.com/paper/2310.13021/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 115 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 30 of 32)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Augmented Language Models: a Survey](https://mlsanity.com/paper/2302.07842/) (2023)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [Baldur: Whole-Proof Generation and Repair with Large Language Models](https://mlsanity.com/paper/2303.04910/) (2023)
- [From Word Models to World Models: Translating from Natural Language to the Probabilistic Language of Thought](https://mlsanity.com/paper/2306.12672/) (2023)
- [Abstraction and Analogy-Making in Artificial Intelligence](https://mlsanity.com/paper/2102.10717/) (2021)
- [Thor: Wielding Hammers to Integrate Language Models and Automated Theorem Provers](https://mlsanity.com/paper/2205.10893/) (2022)
- [NaturalProver: Grounded Mathematical Proof Generation with Language Models](https://mlsanity.com/paper/2205.12910/) (2022)
- [Evaluating Language Models for Mathematics through Interactions](https://mlsanity.com/paper/2306.01694/) (2023)
- [MathChat: Converse to Tackle Challenging Math Problems with LLM Agents](https://mlsanity.com/paper/2306.01337/) (2023)
- [Word meaning in minds and machines](https://mlsanity.com/paper/2008.01766/) (2020)
- [People construct simplified mental representations to plan](https://mlsanity.com/paper/2105.06948/) (2021)
- [Understanding Human Intelligence through Human Limitations](https://mlsanity.com/paper/2009.14050/) (2020)
- [Humans decompose tasks by trading off utility and computational cost](https://mlsanity.com/paper/2211.03890/) (2022)
- [Peano: Learning Formal Mathematical Reasoning](https://mlsanity.com/paper/2211.15864/) (2022)
- [Testing GPT-4 with Wolfram Alpha and Code Interpreter plug-ins on math and science problems](https://mlsanity.com/paper/2308.05713/) (2023)

## Built on by (most cited first, 10 of 10)

- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Building Machines that Learn and Think with People](https://mlsanity.com/paper/2408.03943/) (2024)
- [VisionGraph: Leveraging Large Multimodal Models for Graph Theory Problems in Visual Context](https://mlsanity.com/paper/2405.04950/) (2024)
- [Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning](https://mlsanity.com/paper/2412.15184/) (2024)
- [AutoMathKG: The automated mathematical knowledge graph based on LLM and vector database](https://mlsanity.com/paper/2505.13406/) (2025)
- [A Triumvirate of AI Driven Theoretical Discovery](https://mlsanity.com/paper/2405.19973/) (2024)
- [WirelessMathBench: A Mathematical Modeling Benchmark for LLMs in Wireless Communications](https://mlsanity.com/paper/2505.14354/) (2025)
- [Models Can and Should Embrace the Communicative Nature of Human-Generated Math](https://mlsanity.com/paper/2409.17005/) (2024)
- [From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier](https://mlsanity.com/paper/2607.07779/) (2026)
- [Understanding the Countably Infinite: Neural Network Models of the Successor Function and its Acquisition](https://mlsanity.com/paper/2311.15194/) (2023)

## Abstract (arXiv)

Mathematics is one of the most powerful conceptual systems developed and used by the human species. Dreams of automated mathematicians have a storied history in artificial intelligence (AI). Rapid progress in AI, particularly propelled by advances in large language models (LLMs), has sparked renewed, widespread interest in building such systems. In this work, we reflect on these goals from a textitcognitive science perspective. We call attention to several classical and ongoing research directions from cognitive science, which we believe are valuable for AI practitioners to consider when seeking to build truly human (or superhuman)-level mathematical systems. We close with open discussions and questions that we believe necessitate a multi-disciplinary perspective -- cognitive scientists working in tandem with AI researchers and mathematicians -- as we move toward better mathematical AI systems which not only help us push the frontier of the mathematics, but also offer glimpses into how we as humans are even capable of such great cognitive feats.