Why GPT-4 Struggles with Maths: Exploring the Limitations of AI Language Models

This article was co-written with ChatGPT-4 and the graphics by DALL-E.

Artificial Intelligence (AI) has made impressive strides in recent years, and one of its most notable achievements is the development of advanced natural language processing models such as GPT-4. While GPT-4 excels at understanding and generating human-like text, it struggles when it comes to tackling more complex mathematical problems. In this article, we delve into the reasons behind GPT-4's limitations in mathematics and discuss the implications for the AI community.

Training Data: A Text-heavy Foundation

GPT-4 is trained on an extensive corpus of text, encompassing a vast range of topics and linguistic styles. However, the proportion of mathematical content within this training data is relatively small. Consequently, GPT-4 may not have encountered sufficient mathematical concepts and problems to develop a deep understanding of them. This lack of exposure to mathematical content in the training data hinders GPT-4's ability to solve complex mathematical problems effectively.

Sequential Processing: Hindered by Linear Thinking

Another reason behind GPT-4's mathematical limitations is its sequential processing approach. The model processes text one token at a time, which may not be the most efficient method for handling intricate mathematical expressions that require manipulation of symbols or equations. As a result, GPT-4 can struggle when confronted with problems that demand non-linear thinking and manipulation of variables.

Limited Working Memory: The Struggle to Keep Track

GPT-4 operates within a fixed-size context window, meaning that it can only consider a specific number of tokens at a time. Complex mathematical problems often require tracking multiple variables, constants, and equations simultaneously. Unfortunately, GPT-4's limited working memory can be a significant constraint when addressing these types of problems, leading to inaccuracies or incomplete solutions.

Symbolic vs. Numerical Reasoning: A Language Model's Achilles Heel

GPT-4's primary strength lies in its ability to reason with natural language. However, when it comes to solving mathematical problems that require manipulation of equations or formulas, GPT-4's proficiency in symbolic reasoning falls short. This shortfall is particularly evident when the model encounters abstract symbols that must be manipulated to arrive at a solution.

The Path Forward for AI and Mathematics

Despite its limitations in solving complex mathematical problems, GPT-4 remains an impressive AI model with numerous applications across various domains. However, its struggles with mathematics serve as a reminder that AI models are not universally adept at all tasks.

To advance the field of AI, it is crucial to develop models that can excel in specific domains, such as mathematics. This will likely involve a combination of improved training data, enhanced processing techniques, and more focused model architectures. By understanding and addressing GPT-4's limitations, the AI community can work towards creating AI models that are better equipped to tackle the challenges of mathematics and other specialised fields.