# Mathematical Capabilities of ChatGPT

arXiv: https://arxiv.org/abs/2301.13867 · HTML: https://mlsanity.com/paper/2301.13867/

## Key facts

- Cited by 268 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 101 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Datasheets for Datasets](https://mlsanity.com/paper/1803.09010/) (2018)
- [LaMDA: Language Models for Dialog Applications](https://mlsanity.com/paper/2201.08239/) (2022)
- [Model Cards for Model Reporting](https://mlsanity.com/paper/1810.03993/) (2018)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [NaturalProofs: Mathematical Theorem Proving in Natural Language](https://mlsanity.com/paper/2104.01112/) (2021)
- [NaturalProver: Grounded Mathematical Proof Generation with Language Models](https://mlsanity.com/paper/2205.12910/) (2022)
- [Measuring and Improving BERT's Mathematical Abilities by Predicting the Order of Reasoning](https://mlsanity.com/paper/2106.03921/) (2021)
- [Mathematics, word problems, common sense, and artificial intelligence](https://mlsanity.com/paper/2301.09723/) (2023)
- [Machine Learning Class Numbers of Real Quadratic Fields](https://mlsanity.com/paper/2209.09283/) (2022)
- [Mathematical Reasoning via Self-supervised Skip-tree Training](https://mlsanity.com/paper/2006.04757/) (2020)

## Built on by (most cited first, 30 of 268)

- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [A Prompt Pattern Catalog to Enhance Prompt Engineering with ChatGPT](https://mlsanity.com/paper/2302.11382/) (2023)
- [Is ChatGPT a Good NLG Evaluator? A Preliminary Study](https://mlsanity.com/paper/2303.04048/) (2023)
- [Trustworthy LLMs: a Survey and Guideline for Evaluating Large Language Models' Alignment](https://mlsanity.com/paper/2308.05374/) (2023)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models](https://mlsanity.com/paper/2307.10635/) (2023)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [Leak, Cheat, Repeat: Data Contamination and Evaluation Malpractices in Closed-Source LLMs](https://mlsanity.com/paper/2402.03927/) (2024)
- [What can Large Language Models do in chemistry? A comprehensive benchmark on eight tasks](https://mlsanity.com/paper/2305.18365/) (2023)
- [ORION: A Holistic End-to-End Autonomous Driving Framework by Vision-Language Instructed Action Generation](https://mlsanity.com/paper/2503.19755/) (2025)
- [Senna: Bridging Large Vision-Language Models and End-to-End Autonomous Driving](https://mlsanity.com/paper/2410.22313/) (2024)
- [Summary of ChatGPT-Related Research and Perspective Towards the Future of Large Language Models](https://mlsanity.com/paper/2304.01852/) (2023)
- [Progressive-Hint Prompting Improves Reasoning in Large Language Models](https://mlsanity.com/paper/2304.09797/) (2023)
- [DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models](https://mlsanity.com/paper/2411.00836/) (2024)
- [Exploring the Reasoning Abilities of Multimodal Large Language Models (MLLMs): A Comprehensive Survey on Emerging Trends in Multimodal Reasoning](https://mlsanity.com/paper/2401.06805/) (2024)
- [Domain Specialization as the Key to Make Large Language Models Disruptive: A Comprehensive Survey](https://mlsanity.com/paper/2305.18703/) (2023)
- [MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems](https://mlsanity.com/paper/2305.14536/) (2023)
- [AugGPT: Leveraging ChatGPT for Text Data Augmentation](https://mlsanity.com/paper/2302.13007/) (2023)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [Evaluating ChatGPT's Information Extraction Capabilities: An Assessment of Performance, Explainability, Calibration, and Faithfulness](https://mlsanity.com/paper/2304.11633/) (2023)
- [A Systematic Study and Comprehensive Evaluation of ChatGPT on Benchmark Datasets](https://mlsanity.com/paper/2305.18486/) (2023)
- [A comprehensive evaluation of ChatGPT's zero-shot Text-to-SQL capability](https://mlsanity.com/paper/2303.13547/) (2023)
- [AlphaDrive: Unleashing the Power of VLMs in Autonomous Driving via Reinforcement Learning and Reasoning](https://mlsanity.com/paper/2503.07608/) (2025)
- [Is ChatGPT a Good Sentiment Analyzer? A Preliminary Study](https://mlsanity.com/paper/2304.04339/) (2023)
- [A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validation](https://mlsanity.com/paper/2305.11391/) (2023)
- [Large Language Models and Games: A Survey and Roadmap](https://mlsanity.com/paper/2402.18659/) (2024)
- [Grounded-VideoLLM: Sharpening Fine-grained Temporal Grounding in Video Large Language Models](https://mlsanity.com/paper/2410.03290/) (2024)

## Abstract (arXiv)

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, either cover only elementary mathematics or are very small. We address this by publicly releasing two new datasets: GHOSTS and miniGHOSTS. These are the first natural-language datasets curated by working researchers in mathematics that (1) aim to cover graduate-level mathematics, (2) provide a holistic overview of the mathematical capabilities of language models, and (3) distinguish multiple dimensions of mathematical reasoning. These datasets also test whether ChatGPT and GPT-4 can be helpful assistants to professional mathematicians by emulating use cases that arise in the daily professional activities of mathematicians. We benchmark the models on a range of fine-grained performance metrics. For advanced mathematics, this is the most detailed evaluation effort to date. We find that ChatGPT can be used most successfully as a mathematical assistant for querying facts, acting as a mathematical search engine and knowledge base interface. GPT-4 can additionally be used for undergraduate-level mathematics but fails on graduate-level difficulty. Contrary to many positive reports in the media about GPT-4 and ChatGPT's exam-solving abilities (a potential case of selection bias), their overall mathematical performance is well below the level of a graduate student. Hence, if your goal is to use ChatGPT to pass a graduate-level math exam, you would be better off copying from your average peer!