A significant endorsement for the practical application of artificial intelligence in advanced scientific disciplines has emerged from one of the world's leading mathematicians. Fields Medalist Terence Tao revealed he utilized OpenAI's ChatGPT to assist in solving a problem on the mathematics forum MathOverflow, a task he estimates would have otherwise consumed multiple hours of manual work. This event marks a notable milestone in the adoption of large language models (LLMs) not merely as conversational curiosities, but as functional tools in the arsenal of top-tier researchers, signaling a potential shift in how complex intellectual work is conducted. Tao's experience provides a concrete and compelling case study of the current capabilities and limitations of AI, illustrating its role as a powerful "co-pilot" that can accelerate human ingenuity by handling tedious, computational sub-tasks, even if it cannot yet replicate genuine mathematical insight.

The problem Tao tackled was not one of abstract, theoretical breakthrough, but of computational verification necessary to answer a question posed on MathOverflow.[1] Tao had already formulated a theoretical approach suggesting a specific conjecture was false and that a counterexample should exist.[1] However, proving this required identifying a set of numerical parameters that satisfied certain complex inequalities.[1] This is a common scenario in mathematics where a high-level theoretical idea needs to be grounded by concrete, often labor-intensive, calculations. His initial strategy was to use the AI to write a Python script that would search for the counterexample directly. This approach failed; the required runtime was infeasible, and the initial parameters were not well-chosen for a successful search.[1] This initial failure highlights a crucial aspect of using current AI models: they are not magic bullets and require expert guidance to navigate complex problems effectively.

Pivoting from his initial plan, Tao adopted a more interactive and conversational strategy. Instead of asking for a complete solution, he engaged the AI in a step-by-step dialogue, using it to perform heuristic calculations to narrow down the search space and identify more feasible numerical parameters.[1] This method proved highly effective. Through this extended conversation, the AI was able to locate a viable set of parameters that Tao could then independently verify.[1] The final verification step itself used a simple, 29-line Python program also supplied by the AI, which was straightforward enough for Tao to visually inspect and confirm its correctness.[1] He noted that the AI's ability to use the context of their conversation allowed it to spot and fix several mathematical mistakes in his own requests before generating code. Tao stated he would have been very unlikely to even attempt the numerical search without the AI's assistance, opting instead for a different, more theoretical analysis.[1] This successful application demonstrates the power of LLMs as interactive tools that can save valuable time on laborious calculations, freeing up human researchers to focus on higher-level strategy and creative problem-solving.

This specific success is part of Tao's broader exploration of AI's role in mathematics. He has tested newer models, such as OpenAI's GPT-o1, on a range of tasks, from identifying established theorems from vague queries to attempting challenging complex analysis problems.[2] His assessment is nuanced. While a newer model could correctly identify Cramer's theorem from a general query—a task where previous versions failed—it still struggled with more advanced research problems, requiring significant human guidance to reach a correct solution.[2] It is this experience that led to his widely cited analogy of the AI being akin to a "mediocre, but not completely incompetent" research assistant.[3][2] He later clarified this comparison, emphasizing that unlike a human student, an AI does not learn from its mistakes between sessions and lacks the multifaceted skills of a real student, such as creativity and intuition.[3][4] This lack of genuine understanding leads to what Tao calls a missing "sense of smell"—the intuition that alerts a human mathematician when an approach is fundamentally flawed, even if the surface logic appears correct.[5] Current AIs, he observes, can get stuck on a wrong path, producing proofs that look flawless but contain subtle, inhuman errors.[5][6]

The implications of Tao's experience extend far beyond this single math problem. It serves as a powerful proof of concept for the future of human-AI collaboration in science and research. He has predicted that, if used properly, AI could become a "trustworthy co-author" in mathematical research by 2026.[7][8] This future does not necessarily envision AI making groundbreaking creative leaps on its own. Instead, the primary value lies in its ability to handle the more routine and tedious aspects of research, boosting productivity and enabling larger-scale projects.[2] By integrating LLMs with other computational tools like formal proof assistants and symbolic math packages, their utility will likely increase dramatically.[3][2] However, leveraging this potential requires skill and expertise. An expert like Tao can guide the tool, break down problems, and critically evaluate the output, a skill set that will become increasingly vital.[9][10] The AI acts as a force multiplier for existing knowledge, not a replacement for it.

In conclusion, Terence Tao's use of ChatGPT to solve a computational roadblock is a landmark event, not because the AI demonstrated superhuman mathematical genius, but because it showed its utility as a practical tool for one of the world's finest minds. His detailed account demystifies the role of AI in high-level research, framing it as a powerful assistant that can perform complex, step-by-step calculations and coding tasks under expert human supervision. While the technology still lacks the intuition, creativity, and learning capabilities of a human collaborator, its ability to save hours of tedious work represents a significant advance. This incident reinforces the vision of an AI-assisted future where technology automates the laborious elements of research, allowing human intellect to focus on the conceptual breakthroughs and creative insights that remain uniquely its own. The collaboration between Tao and the machine is a glimpse into a new era of scientific discovery, where the synergy between human expertise and artificial intelligence promises to accelerate the pace of progress.