Terence Tao, in a public lecture at the International Congress of Mathematicians 2026, warned that mathematics is facing a new crisis, not in its foundations, but in its relationship with AI. He described how AI’s growing ability to perform research-level mathematical tasks challenges the community to rethink its values, practices, and role in a rapidly changing world. You need to understand what this means for the future of mathematical work and how to navigate the shift without losing the depth and rigor that define the field.

A Crisis in Mathematical Foundations in the Age of AI

Mathematics once faced a foundational crisis in the early 20th century, when paradoxes and incompleteness forced a reexamination of its core assumptions. Today, AI is creating a new kind of crisis, one that doesn’t challenge the logic of math itself, but the values and practices that define how it is done. Terence Tao warns that the rise of AI tools capable of performing research-level mathematical tasks is already reshaping the field. This shift demands a critical look at what mathematics should prioritize: human insight, rigor, or efficiency? The answer will shape the future of the discipline.

The Evolving Role of AI in Mathematical Research

AI’s current capabilities in mathematical problem-solving

AI is already demonstrating the ability to perform specific mathematical tasks, from solving complex equations to identifying patterns in large datasets. These tools are not yet replacing human mathematicians, but they are assisting in areas that require brute-force computation or data analysis. Terence Tao acknowledged this in his lecture, noting that AI tools can accomplish some research-level mathematical tasks with some level of correctness and quality, though always under human supervision.

The potential of AI in accelerating mathematical discovery

AI has the potential to significantly speed up mathematical discovery by handling routine calculations and exploring vast problem spaces that would be impractical for humans alone. This can free up researchers to focus on higher-level conceptual work and innovation. The key is to integrate AI as a tool that enhances, rather than replaces, human insight and creativity in mathematical research.

Limitations and ethical considerations of AI in mathematics

Despite its promise, AI in mathematics is not without limitations. Current tools struggle with abstract reasoning, intuition, and the formulation of new mathematical concepts. Ethical concerns also arise, such as the potential for bias in AI-generated results and the need for transparency in how these systems arrive at conclusions. Mathematicians must remain vigilant in ensuring that AI supports rigorous and ethical practices in their field.

The AI Capability Conjecture: What Can AI Really Do?

Understanding the conjecture’s key variables

The AI Capability Conjecture is not a single claim but a framework for understanding what AI can do. It hinges on several variables: the level of human supervision, the expense involved, the success rate, and the quality of output. These variables define the boundaries of AI’s current and future capabilities in mathematics.

Terence Tao’s formulation highlights that AI is not yet a full replacement for human mathematicians. Instead, it operates within limits, performing specific tasks with specific conditions. This framework helps the mathematical community assess what is possible and what remains out of reach.

Examples of AI’s success in mathematical fields

AI has already shown success in areas like solving complex equations and identifying patterns in large datasets. For instance, AI tools have been used to assist in proving theorems and exploring conjectures in number theory and combinatorics.

These successes are not trivial. They demonstrate that AI can contribute to research-level mathematics, though always in partnership with human insight. The tools are not perfect, but they are useful in ways that were not previously possible.

The role of human oversight in AI-assisted research

Human oversight remains critical. AI may perform tasks with some level of correctness, but it is the human mathematician who ensures that the results are meaningful, rigorous, and aligned with mathematical values.

Without human guidance, AI’s output can be misleading or incomplete. The role of the mathematician is not to be replaced, but to evolve, using AI as a tool to extend their reach and deepen their understanding.

How the Mathematical Community Can Respond to AI

Updating mathematical education for an AI-driven future

Mathematical education must evolve to include AI literacy. Future mathematicians need to understand how AI tools function, when to trust them, and how to integrate them into research. This doesn’t mean replacing rigorous training with shortcuts, it means equipping students with the ability to collaborate with AI effectively. Universities and institutions should begin incorporating AI tools into curricula, ensuring students are not just passive users but informed participants in the evolving mathematical landscape.

Collaborative approaches between mathematicians and AI developers

Mathematicians and AI developers must work together to define the boundaries and potential of AI in mathematical research. This collaboration should be practical and goal-oriented, focusing on real-world applications rather than theoretical speculation. By engaging directly with developers, mathematicians can ensure AI tools are designed with mathematical rigor in mind, avoiding the pitfalls of overreliance on unverified outputs. This partnership will help shape AI that complements, rather than replaces, human insight.

Establishing ethical and cultural frameworks for AI use

The mathematical community must take the lead in defining ethical standards for AI use. This includes addressing issues like transparency, bias, and the role of human oversight in AI-assisted research. A cultural shift is needed to ensure that AI is used responsibly and that the value of human judgment is preserved. Establishing these frameworks early will help maintain the integrity of mathematical practice while embracing the benefits AI can offer.

As mathematics in the age of AI continues to evolve, tools like DeepMind’s AlphaMath are already demonstrating the potential for AI to assist in complex problem-solving, offering new insights into long-standing conjectures and accelerating the pace of discovery in fields such as number theory and topology.

The integration of AI into mathematical research may not replace human intuition, but it can significantly enhance it, allowing mathematicians to explore vast problem spaces more efficiently and identify patterns that might otherwise remain hidden in the intricate landscape of mathematics in the age of AI.

With over 10,000 research papers published annually in mathematics, AI-driven platforms are beginning to play a crucial role in organizing, analyzing, and even generating hypotheses, marking a transformative shift in how mathematics in the age of AI is practiced and taught globally.

What This Means for the Future of Mathematics

The potential for AI to expand mathematical frontiers

AI has the potential to push mathematical research into new areas by handling complex computations and pattern recognition at a scale no human can match. Terence Tao noted that AI tools are already capable of accomplishing research-level mathematical tasks with some level of correctness and quality. This opens the door for exploration in fields that were previously too computationally intensive to pursue.

The importance of preserving human insight and creativity

While AI can process data and perform calculations, it cannot replace the human ability to formulate new problems, see connections between disparate ideas, or think creatively. The value of human insight remains irreplaceable. Mathematical progress will depend on maintaining a balance between AI’s computational power and human intuition.

Building a resilient mathematical community in the age of AI

The mathematical community must adapt to ensure that AI is used as a tool, not a replacement. This means updating education, fostering collaboration between AI developers and mathematicians, and setting ethical guidelines. A resilient community will not only integrate AI but also define how it should be used to enhance, not diminish, the depth and rigor of mathematical practice.

Source: teorth.github.io