{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hardmath-a-benchmark-dataset-for-challenging","title":"HARDMath: A Benchmark Dataset for Challenging Problems in Applied Mathematics","arxiv_id":"2410.09988","date":"2024-10-13","proceeding":null,"authors":["Jingxuan Fan","Sarah Martinson","Erik Y. Wang","Kaylie Hausknecht","Jonah Brenner","Danxian Liu","Nianli Peng","Corey Wang","Michael P. Brenner"],"abstract":"Advanced applied mathematics problems are underrepresented in existing Large Language Model (LLM) benchmark datasets. To address this, we introduce HARDMath, a dataset inspired by a graduate course on asymptotic methods, featuring challenging applied mathematics problems that require analytical approximation techniques. These problems demand a combination of mathematical reasoning, computational tools, and subjective judgment, making them difficult for LLMs. Our framework auto-generates a large number of problems with solutions validated against numerical ground truths. We evaluate both open- and closed-source LLMs on HARDMath-mini, a sub-sampled test set of 366 problems, as well as on 40 word problems formulated in applied science contexts. Even leading closed-source models like GPT-4 achieve only 43.8% overall accuracy with few-shot Chain-of-Thought prompting, and all models demonstrate significantly lower performance compared to results on existing mathematics benchmark datasets. We additionally conduct a detailed error analysis to gain insights into the failure cases of LLMs. These results demonstrate limitations of current LLM performance on advanced graduate-level applied math problems and underscore the importance of datasets like HARDMath to advance mathematical abilities of LLMs.","url_abs":"https://arxiv.org/abs/2410.09988v2","url_pdf":"https://arxiv.org/pdf/2410.09988v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"hardmath-a-benchmark-dataset-for-challenging","repo_url":"https://github.com/sarahmart/hardmath","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"language-modeling","task_name":"Language Modeling"},{"task_slug":"language-modelling","task_name":"Language Modelling"},{"task_slug":"large-language-model","task_name":"Large Language Model"},{"task_slug":"math","task_name":"Math"},{"task_slug":"mathematical-reasoning","task_name":"Mathematical Reasoning"}],"methods":[{"method_slug":"absolute-position-encodings","method_name":"Absolute Position Encodings"},{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"gpt-4","method_name":"GPT-4"},{"method_slug":"label-smoothing","method_name":"Label Smoothing"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"position-wise-feed-forward-layer","method_name":"Position-Wise Feed-Forward Layer"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"set","method_name":"SET"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"transformer","method_name":"Transformer"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2410.09988","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}