A few years ago ChatGPT started babbling, Google has developed a very different kind of artificial intelligence the program is called AlphaGo learned to play the game of Go with superhuman skill through tireless practice.
Researchers at the company have now published research that combines the capabilities of a large language model (the AI behind today’s chatbots) with the ability of AlphaZero, the successor to AlphaGo that is also capable of playing chess, to solve very difficult mathematical proofs.
Their new Frankensteinian creation, called AlphaProof, has already proven its prowess by solving a number of problems from 2024. International Mathematical Olympiad (IMO), a prestigious competition for high school students.
AlphaProof uses the Gemini large language model to convert naturally expressed mathematical questions into a programming language called Tilt. This provides training data for the second algorithm to learn to find evidence that can be confirmed as true through trial and error.
Earlier this year, Google DeepMind Revealing another mathematical algorithm called AlphaGeometry, which also combines a language model with another AI approach. AlphaGeometry uses Gemini to translate geometric problems into a form that can be processed and tested by a program that processes geometric elements. Today, Google also announced a new and improved version of AlphaGeometry.
The researchers found that their two math programs could provide proofs for the IMO puzzles, as well as a possible silver medal. The programs solved two algebra problems and one number theory problem out of a total of six. It solved one problem in minutes, but took days to figure out the others. Google DeepMind did not disclose how much computing power it used to solve the problems.
Google DeepMind calls the method used for both AlphaProof and AlphaGeometry “neural symbols” because they combine pure machine learning of a artificial neural networktechnology that powers most of the recent advances in AI, with common programming languages.
“What we see here is that you can combine the approach that has been very successful and things like AlphaGo with large language models and create something that is incredibly capable,” he said. David SilverGoogle DeepMind researcher who led the AlphaZero research. Silver said the techniques demonstrated with AlphaProof could theoretically be extended to other areas of mathematics.
Indeed, this research holds out the prospect of addressing the worst tendencies of large language models by applying logic and reasoning in a more grounded way. While large language models can be magical, they often struggle to grasp even basic mathematics or reason through problems logically.
In the future, symbolic neural methods could provide a means for AI systems to translate questions or tasks into a form that can be reasoned about in a way that produces reliable results. OpenAI is also rumored to be working on such a system, codenamed “Strawberry”.
There is, however, one major limitation with the systems revealed today, as Silver acknowledges. The mathematical solutions may or may not be correct, allowing AlphaProof and AlphaGeometry to find the right answer. Many real-world problems—like figuring out the ideal route for a trip—have multiple possible solutions, and it may not be obvious which one is ideal. Silver says a solution to more ambiguous questions could be a language model that tries to determine what constitutes a “correct” answer during training. “There are a bunch of different things that could be tested,” he says.
Silver is also careful to note that Google DeepMind won’t put mathematicians out of work. “We’re aiming to deliver a system that can prove anything, but that’s not the end goal of what mathematicians do,” he says. “A big part of mathematics is posing problems and figuring out interesting questions to ask. You can think of this as another tool similar to a protractor or a calculator or a computing tool.”
