Google DeepMind has utilized artificial intelligence to nearly replicate the geometry problem-solving abilities of the brightest students globally, pushing forward the coveted endeavor to apply this rapidly evolving technology to intricate mathematics.
AlphaGeometry, the innovative system developed by the tech giant, accurately responded to 25 out of 30 questions from the high school International Mathematical Olympiad, as detailed in a paper released in Nature on Wednesday.
The system’s performance, closely approaching the level of excellence required to secure a gold medal among human competitors, underscores the increasing proficiency of AI in mathematical tasks while also highlighting the existing challenges. The complexities of reasoning and learning inherent in advanced mathematics serve as a crucial benchmark in the pursuit of developing an artificial general intelligence (AGI) capable of matching or surpassing human capabilities.
Quoc V Le, a researcher at DeepMind, remarked, “This marks a pivotal advancement towards constructing an AGI. It serves as yet another illustration of how AI can propel scientific progress and enhance our comprehension of the fundamental mechanisms governing the functioning of the world.”
AlphaGeometry operates as a neuro-symbolic system that leverages a fusion of language acquisition and deductive reasoning. DeepMind likens this hybrid approach to the concept of “Thinking, Fast and Slow,” coined by psychologist Daniel Kahneman to elucidate the potency of combining rapid pattern recognition with more contemplative logical thinking.
This method epitomizes what Trieu H Trinh, another member of the DeepMind research team, refers to as “the best of both worlds” in tackling geometry problems. While the field of geometry is familiar to us on a daily basis through observations of shapes and spatial relationships, it is underpinned by a sophisticated framework of mathematical principles.
To train the system, researchers curated a vast repository of 100 million instances of synthetic geometry data. The system’s achievement of answering 25 out of 30 questions closely trailed the average score of 25.9 attained by human champions in mathematical Olympiads spanning from 2000 to 2022, surpassing the previous state-of-the-art automated system’s score of 10.
Despite its commendable performance, AlphaGeometry encountered certain problems that it found arduous or perplexing. For instance, it struggled to resolve a complex problem involving intersecting circles that was successfully tackled by Vietnamese mathematician Lê Bá Khánh Trình during the 1979 Olympiad — a figure who served as an inspiration to some of the researchers.
The ultimate objective for DeepMind and other experts in the field is to develop AI systems capable of addressing mathematical challenges that have thus far surpassed human comprehension.
Mikhail Burtsev, a Landau AI Fellow at the London Institute for Mathematical Sciences, lauded the progress made by DeepMind but emphasized that it operates within the confines of the challenges it has set for itself.
He remarked, “The true test lies ahead, which is to ascertain whether an AI can uncover novel mathematical solutions for questions that have remained unanswered to date.”
While the vision of witnessing an AI-powered mathematical system engaging in and triumphing over a human counterpart — akin to the victory of the chess computer Deep Blue over world champion Garry Kasparov in 1997 — remains aspirational, it is yet to be realized.
DeepMind has indicated that there are currently no plans to participate in the International Mathematical Olympiad. However, the company has not ruled out the possibility as it continues to venture deeper into the demanding domain of mathematics.
