## Tags - Part of: - Related: - Includes: - Additional: ## Definitions - [[Mathematics]] x [[Artificial Intelligence]] x [[Machine learning]] x [[Data science]] x [[Statistics]] ## Main resources - [Artificial intelligence Mathematics section - Wikipedia](https://en.wikipedia.org/wiki/Artificial_intelligence#Mathematics) <iframe src="https://en.wikipedia.org/wiki/Artificial_intelligence#Mathematics" allow="fullscreen" allowfullscreen="" style="height:100%;width:100%; aspect-ratio: 16 / 5; "></iframe> ## Landscapes - [FunSearch: Making new discoveries in mathematical sciences using Large Language Models - Google DeepMind](https://deepmind.google/discover/blog/funsearch-making-new-discoveries-in-mathematical-sciences-using-large-language-models/) - [AI achieves silver-medal standard solving International Mathematical Olympiad problems - Google DeepMind](https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/) - [\[2404.06405\] Wu's Method can Boost Symbolic AI to Rival Silver Medalists and AlphaGeometry to Outperform Gold Medalists at IMO Geometry](https://arxiv.org/abs/2404.06405) - OpenAI [[o1]] - [8 Best AI for Math Tools (September 2024)](https://www.unite.ai/best-ai-for-math-tools/) - [GitHub - lean-dojo/LeanCopilot: LLMs as Copilots for Theorem Proving in Lean](https://github.com/lean-dojo/LeanCopilot) - [\[2312.07622\] Mathematical Language Models: A Survey](https://arxiv.org/abs/2312.07622) - WolframAlpha - [AIMO Prize](https://aimoprize.com/) - [\[2408.15240\] Generative Verifiers: Reward Modeling as Next-Token Prediction](https://arxiv.org/abs/2408.15240) [x.com/agarwl\_/status/1842609385287348712](https://x.com/agarwl_/status/1842609385287348712) ## Resources [[Links AI math]] ## Brainstorming Are humans better at math than machines? In some factors currently yes, we're better at some aspects while AI is better at some other aspects, and it might be that to get humanlike mathematics we would need to replicate the brain's algorithms much more closely. Or there might be some general mathematical engine algorithm independent of the brain. It would be lovely to have mathematical reasoning but without all these algebraic errors that humans and AIs make, errors in proofs, also with the strength of symbolic math engines and strength of human intuition tha can go out of distribution, with much more broad overview capability to connect much more dots, with even more out of distribution generalization when inventing completely novel math, than humans are capable of, that would go beyond what we can currently do and explore even more alien mathematical universes. ## Landscapes written by AI (may include factually incorrect information) Artificial Intelligence (AI) has made significant contributions to solving various mathematical problems and advancing the field in several ways: ## Problem-Solving Capabilities AI systems have demonstrated impressive abilities in tackling complex mathematical challenges: - Google DeepMind's AlphaProof and AlphaGeometry 2 recently achieved a breakthrough by solving four out of six problems from the International Mathematical Olympiad (IMO), earning the equivalent of a silver medal[6]. This is a significant accomplishment as IMO problems involve advanced reasoning and are designed to challenge top high school students globally. - AlphaGeometry 2 showed remarkable improvement over its predecessor, solving 83% of IMO geometry problems compared to 53% previously[8]. In one instance, it solved a highly complex geometry problem in just 19 seconds. - These AI systems can handle various types of mathematical problems, including geometry, algebra, and proofs, demonstrating a level of versatility previously unseen in AI math solvers[8]. ## Advancements in Mathematical Research AI is contributing to mathematical research in several ways: - AI tools are helping mathematicians discover new insights, novel algorithms, and answers to open problems[6]. - By automating the process of translating informal mathematical language into formal statements, AI is creating large libraries of formal math problems, which is a significant step forward for the mathematics community[4]. ## Educational Applications AI is revolutionizing mathematics education: - AI-powered tools like Julius offer features such as scan-and-solve capabilities for equations, step-by-step explanations, and the ability to convert and solve word problems[7]. - These tools can provide personalized instruction, adaptive assessment, and interactive learning environments, enhancing students' understanding of mathematical concepts[4]. ## Theoretical Advancements AI is also contributing to theoretical aspects of mathematics: - AI systems like DeepMind's AlphaTensor have made advancements in areas such as tensor decomposition, which has applications in numerical analysis and machine learning[3]. - AI is being used to generate new insights and relationships among mathematical concepts, offering fresh perspectives on proving theorems[1]. ## Interdisciplinary Applications The mathematical problem-solving capabilities of AI are being integrated into various fields: - AI's ability to solve complex mathematical problems is being applied in areas such as biology, physics, and engineering, leading to new insights and innovations[3]. While these advancements are impressive, it's important to note that AI still has limitations. For instance, some systems may struggle with explaining their reasoning or lack creativity in problem-solving[4]. Additionally, there are ongoing discussions about the ethical implications and potential overreliance on AI in mathematics education and research[4]. Nonetheless, the integration of AI into mathematics continues to push the boundaries of what's possible in problem-solving and mathematical discovery. Citations: [1] https://alls-academy.com/index.php/as-proceedings/article/view/248 [2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9525744/ [3] https://www.hotbot.com/answers/which-ai-can-solve-math-problems [4] https://www.ijopr.com/download/artificial-intelligence-in-mathematics-education-the-good-the-bad-and-the-ugly-14735.pdf [5] https://www.technologyreview.com/2024/07/25/1095315/google-deepminds-ai-systems-can-now-solve-complex-math-problems/ [6] https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/ [7] https://julius.ai/home/ai-math [8] https://fortune.com/2024/07/25/google-researchers-claim-new-breakthrough-in-getting-ai-to-solve-tough-high-school-math-problems/