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Keynote 2: Mathematics Education in the Age of AI

Junaid Mubeen (Parallel) began his keynote on the second morning of the workshop by clarifying what he termed the “why” of mathematics. As the centerpiece of every education system, it is worth asking why learn math in the first place. There are a range of possible answers, he said, beginning

with a utility argument: Math is useful in many practical applications. As the Greek mathematician Euclid said, “The laws of nature are but the mathematical thoughts of God.” But, he stressed, math is not a static entity. It continually evolves according to the tools and technologies of the time. It was once about facts and figures—the language of commerce and trade. In recognition that humans are not predisposed to perform calculations with speed and accuracy, this cognitive burden was moved away from humans with such tools as sliderules and pocket calculators. It no longer makes sense to employ humans to perform these calculations. This journey has continued with more sophisticated tools like Wolfram|Alpha and other computer modeling tools. The optimistic view is that the journey of empowerment will continue with advances such as large language models (LLMs) and generative artificial intelligence (AI), and the arc of human–machine collaboration will expand.

To fulfill that promise, there is an urgent need to upgrade school mathematics, Mubeen said. What mathematics curricula have in common around the world is that they exist as if these technologies do not exist. School mathematics emphasize students memorizing formulas and procedures to be able to recall at will. To Mubeen, this is a very outdated version of what mathematics should be. While the need for an upgrade already existed, the era of generative AI makes it especially urgent.

THE REASON TO STUDY MATH

What would an upgrade of a mathematics curriculum fit for the 21st century look like? Mubeen posed. It was easier to answer a few years ago when it was easier to delineate between human and machine intelligence. We could have said that computers do routine calculations and computation, and humans handle the more creative aspects, he said. With LLMs, that question is harder to answer, as LLMs are becoming capable as mathematicians. As one example, Gemini (the chatbot from Google) can solve International Olympiad problems that the vast majority of high school students cannot solve.¹

This could produce anxiety about what humans’ role will be, but Mubeen said he takes encouragement from the fact that for all their capabilities, LLMs are built fundamentally differently than humans. A child learns about what a cat is, for example, and can distinguish second and subsequent cats quickly and efficiently. In marked contrast, LLMs must be

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¹ Thang Luong and Edward Lockhart. 2025. Advanced version of Gemini with Deep Think officially achieves gold-medal standard at the International Mathematical Olympiad. https://deepmind.google/blog/advanced-version-of-gemini-with-deep-think-officially-achieves-goldmedal-standard-at-the-international-mathematical-olympiad/

trained on hundreds of thousands of images to distinguish a cat. This puts their performance in a different light. As another example, he imagined two students who can solve the International Olympiad problem. The first can apply knowledge creatively to solve it. The second solves it because they have absorbed and memorized every problem ever published. Both are impressive, but the first student is impressive because of their ability to solve a new and novel problem not seen before, while the second is impressive for their ability to store information. Similarly, LLMs fall short when faced with problems that fall outside their training distribution. He pointed to a paper from Apple Research that looked at the limits of LLMs’ mathematical reasoning.²

Other examples of limitations include higher failure rates when a LLM is given an atypical chessboard configuration or when it is faced with what the field calls a “reversal curse.” LLMs skew on what they have been trained on. In mathematics, systems that have shown capability with very sophisticated problems may have difficulty with rudimentary problems that humans can solve. LLMs can produce hallucinations, fabricated facts, and an inability to distinguish between truth and falsehood.

Thus, Mubeen commented, AI is smart, but also capable of producing “stupid” outputs that humans would not produce, nor can it recognize its error. AI is “smart, stupid, and confident,” which must be taken into account when relying on a chatbot for an output. Humans can be, too, he acknowledged, but the difference is that humans can regulate their way of thinking. Humans can apply filters between truth and falsehood, and that is the purpose of education. Mubeen continued, “To me, this is the raison d’être of mathematics. It is a system that helps humans think better, navigate outputs, identify spurious ones, and identify truth from falsehood at a time that truth is under attack.”

SEVEN COMPETENCIES OF MATHEMATICAL INTELLIGENCE

In books and other outputs, Mubeen advocates a version of mathematics that is not easily automated, deemphasizes calculation, complements machine intelligence, and plays to natural human strengths.³ He delineates seven competencies of mathematical intelligence: (1) estimation (having a sense of what is plausible), (2) representations (how to bring ideas to life in vivid ways), (3) reasoning (how to develop arguments with clarity

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² Iman Mirzadeh et al. 2024. GSM-Symbolic: Understanding the limitations of mathematical reasoning in large language models. https://arxiv.org/abs/2410.05229

³ Junaid Mubeen. 2022. Mathematical Intelligence. Cambridge, UK: Pegasus; Junaid Mubeen. 2026. Think Like a Mathematician: Simple Tools for Complex Everyday Problems. Cambridge, UK: Pegasus.

and rigor), (4) imagination (tinkering with rules and examining the consequences), (5) questioning (using curiosity to find problems worth solving), (6) temperament (thinking at different speeds, coping with struggle to develop resilience), and (7) collaboration (noting the value of the diversity of intelligences to tackle problems in the collective). As an example, he offered a puzzle with a pattern that departs from expectations. Extrapolating from the example, mathematics is the study of patterns and provides tools to distinguish meaningful from meaningless or misleading solutions.

At the practical level, Mubeen’s organization, Parallel, promotes these competencies through resources and an academy for high school students.⁴ The goal is to foster independent learning and problem solving beyond the school curriculum, but Mubeen said Parallel shares the challenge of “any place with an Internet connection.” LLMs can short-circuit the path from problem to solution. It has been an issue since the advent of the Internet, but previously there was some friction in turning to online answers. LLMs can deprive students of the opportunity to think for themselves. One response is to seize upon AI and use chatbots as coaches or guides. That is the hope, but the reality is that LLMs are designed to spoon-feed. The offerings to date are not equipped to take on the role of a human tutor, in Mubeen’s view.

NOT AN AI BAN BUT A RATIONALE

While he may wish that students do not turn to AI, Mubeen posed the question about why students turn to LLMs. He suggested two reasons. First, “we need to acknowledge that school mathematics problems are often very dull. These problems do not arouse their curiosity.” Second, grading results in the alignment of perverse incentives. Students are told it is wrong to make mistakes, which is the wrong way to think about a subject like math. He posited about the opportunities if subjects like math were driven by intrinsic drive, not extrinsic motivators. Learning would be an end in itself. This is something that Parallel Academy is grappling with now.

Mubeen recognizes that, against pressures and constraints, students will access these tools, and bans are short sighted. Rather, he advocated a policy that explicitly outlines a rationale for why students should be wary of using these tools. One compelling argument is that these tools are being designed to take away their future jobs, as many AI executives have acknowledged. Students need to be made aware of these threats when they engage with these tools. Other use cases to understand the limitations of AI include assignments in which students are given AI output and their task is to debunk it and show the hallucination.

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⁴ For more information, see parallel.org.uk

“One way or another, we need to adapt,” he said. “But when we do, we cannot resort to knee-jerk reactions.” It is not just about teaching students about data and machine learning, similar to when students were taught to code for the job market. Given LLMs, coding is not a path of employment for most students. Another pitch, he suggested, is that math is fun, stimulating, and helps condition the mind, among other intrinsically driven reasons. The real reason to do mathematics ought to be intrinsic, he concluded. Beyond the practical applications, math should strengthen students’ sensibilities to thrive in the 21st century and will stand the test of time.

DISCUSSION

Padhu Seshaiyer asked Mubeen about how to measure mathematical intelligence. Mubeen pointed to the concept of multiple intelligences articulated by Howard Gardner in the 1980s, which contested the previous one-dimensional view of what constitutes intelligence. Mubeen said the notion of dimensionality in mathematics is an area of research. People try to neatly sort and categorize many concepts in day-to-day life, including mathematical ability. Mathematical ability and intelligence are multifold, as he described above. Standardized testing is hopelessly narrow and is more about memorizing facts than intelligence. It is hard to pin down intelligence.

David Manderscheid referred to the LLMs that solved International Olympiad questions, but, he said, they are artificial questions. He asked about the work of First Proof, an organization trying to pose real mathematical questions to AI. Mubeen concurred that a key question of AI is whether it can produce original thought. They can do mimicry; while impressive, the skeptical view is that it only matches things seen before. Math researchers are looking to see if AI can be the first, before humans, to establish proofs for certain theorems. He urged keeping an eye on their progress. It is not that LLMs will never get there, he observed, but to date they have been shaped by training data. His view is that further innovations are needed. If successful, this will present a whole new paradigm in how to do mathematics.

Ben Galluzzo reflected that workshop attendees all agree on the beauty of mathematics, but he questioned how to popularize this approach with teachers and students. Mathematicians have not been good marketers of the “math is beautiful” concept, and asked what success would look like. Mubeen said there are no easy answers, but he pointed to politicized incentives around keeping the curricula and testing as they are. Speaking about the beauty of math is a hard sell when people’s perception of math is shaped by what they have been subject to in the classroom. When Parallel Academy was set up, it was realized that many excellent initiatives exist, but most are in parallel to the school curriculum. For example, he proposed the idea of

a Puzzling 101 course, leaning into people’s love of puzzles of all kinds. It would be proximate to the vision of the mathematics he is describing but is distant to the math that most people are exposed to.

David Weintrop asked about the role of math educators to unpack the “black box” of AI. Mubeen said this is a fundamental part of digital literacy. Everyone should have a rudimentary understanding of how LLMs work. They do not need to know the details, but there are principles that every educator should understand and teach. All need to experience issuing a prompt and being stunned by the speed of the answer, but also to see where it may be “going off the rails a bit.” A fruitful assignment for students is see what LLMs are capable of, but also their incapability of escaping hallucinations. Students need to learn how to use but also second-guess these tools.

Conrad Wolfram commented on the value of puzzles and other hooking points for students. Mubeen agreed that there is space for multiple applications to address real-world phenomena. School mathematics makes a hopeless attempt to do this, but he called for a curriculum with both real-world problem solving and more abstract concepts to strengthen competencies common to all spheres.

An online questioner, who is a high school math computer science teacher, commented that the joy of math and programming often gets lost amidst the pressures of college admissions and measurement at the policy-making level. Mubeen said he sounds harsh on school math, but he directs the blame at policy makers for allowing misaligned incentives to occur. Parallel Academy was developed with this in mind. They realized, with all the constraints in the schedule, it could only exist in parallel with the school curriculum. The content does not have a dependency on what is done in school and students meet in the evening and on weekends. Schools identify students who might benefit but do not have to do anything else. Flexibility is built in when students have competing demands such as high-stakes exams. One silver lining to AI is that it injects a sense of urgency in that the current curriculum is out of date.

Seshaiyer closed by thanking Mubeen for his comments on how to prepare students to go beyond being consumers to becoming producers of information and to help them be students for life, not just for tests.