In October 2024, Meta, the parent company of Facebook, announced a groundbreaking achievement. It unveiled an artificial intelligence (AI) model that tackled a century-old mathematical problem.
This AI focused on understanding the stability of equations tied to dynamic systems, like swinging pendulums or oscillating springs. It found what are called Lyapunov functions, crucial for predicting whether these systems would remain stable over time.
This achievement stirred excitement about the potential of AI. Some now wonder whether AI could surpass top mathematicians by solving previously deemed “unsolvable” problems.
However, mathematicians took a closer look and found the results mixed. The AI successfully determined Lyapunov functions for only 10.1% of random problems posed to it. This was a jump from the 2.1% solved by earlier algorithms, but still far from revolutionary. Plus, the AI needed considerable human guidance to yield accurate results.
Earlier in 2024, Google’s DeepMind also claimed breakthroughs in fluid dynamics. Yet, like with Meta’s AI, the technology is still far from solving the broader, unsolved issues that would win substantial recognition, such as the Millennium Prize for mathematics.
So, just how close are we to having AI rival skilled mathematicians? Experts are cautious, but most agree that AI is advancing rapidly. Many speculate that it might soon tackle complex conjectures and generate new fields of study.
Terence Tao, a leading mathematician at UCLA, believes the pace of AI development is striking. He predicts we might see algorithms solving thousands of mathematical conjectures in the coming years, some of which could be significant.
To grasp the role of AI in mathematics, it helps to look at its progress in other fields. Historically, AI first made waves in gaming. Back in the 1980s, IBM’s algorithms began challenging humans in chess. Fast forward to today, AI dominates such games, showing how fast technology evolves.
But math differs from chess and Go. While those games have clear rules and outcomes, math encompasses an infinite variety of problems. Kevin Buzzard, a mathematician at Imperial College London, notes that current AI models are mimicking human methods rather than innovating on their own.
Lack of full autonomy is a hurdle. For example, AI models attempted high-level questions from the International Mathematical Olympiad (IMO) and managed to solve several, achieving a score close to a silver medal. However, they required extensive human input to understand the questions in a form the AI could process.
This raises the question: Can we trust AI with complex math? While AI has generated hypotheses that mathematicians later prove, many still see its outputs as needing human interpretation. Neil Saunders, a mathematician at City St George’s in London, emphasizes that AI often finds results based on likelihood rather than certainty, which is essential in mathematics.
Yet, AI’s ability to draw connections between different math areas shows promise. For instance, a study led by Marc Lackenby at the University of Oxford used AI to form new conjectures in topology. The conjectures turned out to be incorrect, but the AI’s suggestions had value that went unnoticed.
As we look to the future, experts like Andrew Granville from the University of Montreal express uncertainty about the direction of mathematics in light of AI advancements. However, Granville also acknowledges that mathematics will evolve alongside AI.
In conclusion, while AI isn’t poised to render human mathematicians obsolete just yet, its role in the field is likely to grow. As technology progresses, mathematicians will adapt, leveraging AI’s potential to explore areas of mathematics previously thought unreachable.
For more on this topic, you might want to check the work by Terence Tao and his perspectives on the evolution of mathematics and AI integration. You can find his insights in various math journals and interviews.
