AI and Mathematics: Human-Level AI Mathematicians – is it possible?

Building computational systems that understand and practice mathematics at the level of human mathematicians has been a long-standing aspiration of artificial intelligence (AI). The rise of large language models (LLMs) has sparked imaginations that we are closer than ever to attaining, or surpassing, human-level performance on a range of tasks. Intuitively, AI and mathematics seem relatively easy to combine, but in a more in-depth analysis there are significant obstacles in the way.

Since, despite that these models are achieving tremendous performance in many realms of human expertise, such as medicine, law, and creative writing, the performance of these models on mathematics specifically lags behind.

To address this challenge, researchers are exploring ways to improve the mathematical problem-solving capabilities of LLMs. This includes adjusting the training data and feedback strategies, equipping models with expanded background knowledge, and composing LLMs with existing computational mathematics systems.

Cognitive science to train AI Mathematicians

Recent efforts to build in principles from cognitive science have also seen success. Cognitive scientists study how humans think and learn, and they have developed a wealth of knowledge about mathematical cognition that can be applied to AI.

For example, cognitive scientists have shown that humans are able to learn mathematics by abstracting away from specific examples and developing general principles. This ability to abstract is essential for solving new mathematical problems.

Cognitive scientists have also shown that humans are able to reason about mathematics in a variety of ways, including using logic, intuition, and analogy. These different ways of reasoning can be used to solve different types of mathematical problems.

By drawing on insights from cognitive science, AI researchers can develop LLM that are better able to understand and practice mathematics at the level of human mathematicians. This work has the potential to lead to the development of AI mathematicians that can help us push the frontiers of mathematical knowledge and reflect back on how we are even capable of remarkable achievements of mathematical cognition.

Prospects of AI and Mathematics

Here are some of the key takeaways from the paper from the research study on which this article is based and which can be downloaded below:

• The rise of LLMs has brought us closer than ever to achieving human-level performance on a range of tasks, including mathematics.
• However, current approaches to building AI mathematicians are still falling short.
• Cognitive science has a lot to offer in the quest towards more powerful automated mathematicians.
• By working together, cognitive scientists, AI researchers, and mathematicians can develop new approaches to building AI mathematicians that are not only capable of solving complex mathematical problems, but also of making new discoveries and pushing the frontiers of mathematical knowledge.

Download the study here in pdf-format

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