AlphaGeometry

{{Short description|Artificial intelligence (AI) program}}

AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language model (LLM) and a rule-based symbolic engine (Deductive Database Arithmetic Reasoning). It was developed by DeepMind, a subsidiary of Google. The program solved 25 geometry problems out of 30 from the International Mathematical Olympiad (IMO) under competition time limits—a performance almost as good as the average human gold medallist. For comparison, the previous AI program, called Wu's method, managed to solve only 10 problems.{{cite web |title=AlphaGeometry: An Olympiad-level AI system for geometry |url=https://deepmind.google/discover/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/ |website=Deepmind |access-date=26 January 2024}}{{cite web |title=A.I.'s Latest Challenge: the Math Olympics |url=https://www.nytimes.com/2024/01/17/science/ai-computers-mathematics-olympiad.html |website=The New York Times |date=17 January 2024 |access-date=26 January 2024 |last1=Roberts |first1=Siobhan }}

DeepMind published a paper about AlphaGeometry in the peer-reviewed journal Nature on 17 January 2024.{{cite journal |title=Solving olympiad geometry without human demonstrations |journal=Nature |date=2024 |doi=10.1038/s41586-023-06747-5 |last1=Trinh |first1=Trieu H. |last2=Wu |first2=Yuhuai |last3=Le |first3=Quoc V. |last4=He |first4=He |last5=Luong |first5=Thang |volume=625 |issue=7995 |pages=476–482 |pmid=38233616 |pmc=10794143 |bibcode=2024Natur.625..476T }} AlphaGeometry was featured in MIT Technology Review on the same day.{{cite web |title=Google DeepMind's new AI system can solve complex geometry problems |url=https://www.technologyreview.com/2024/01/17/1086722/google-deepmind-alphageometry/|website=MIT Technology Review |access-date=26 January 2024}}

Traditional geometry programs are symbolic engines that rely exclusively on human-coded rules to generate rigorous proofs, which makes them lack flexibility in unusual situations. AlphaGeometry combines such a symbolic engine with a specialized large language model trained on synthetic data of geometrical proofs. When the symbolic engine doesn't manage to find a formal and rigorous proof on its own, it solicits the large language model, which suggests a geometrical construct to move forward. However, it is unclear how applicable this method is to other domains of mathematics or reasoning, because symbolic engines rely on domain-specific rules and because of the need for synthetic data.{{Cite web |last=Zia |first=Tehseen |date=January 24, 2024 |title=AlphaGeometry: DeepMind's AI Masters Geometry Problems at Olympiad Levels |url=https://www.unite.ai/alphageometry-how-deepminds-ai-masters-geometry-problems-at-olympian-levels/ |access-date=2024-05-03 |website=Unite.ai}}