“Whatever your view on AI in mathematics, enabling high school students to push the frontier of mathematical research is something worth celebrating.” – Quanquan Gu – UCLA Professor
The underlying tension in contemporary mathematics education is no longer simply about access to high-quality teaching, but about who is able to participate in frontier-level problem solving and under what conditions that participation is considered legitimate. When secondary students can use advanced artificial intelligence systems to explore conjectures, test structures and traverse research literature, the traditional apprenticeship pathway into mathematical research is disrupted. The resulting opportunity is profound: pupils who previously would have been confined to routine exercises can now probe open questions, but the risk is equally stark, as educators and researchers debate whether AI-augmented contributions count as genuine mathematical insight or merely sophisticated pattern matching supported by machines 1,3,13.
From selective pipelines to broadened participation
For much of the twentieth century, entry into mathematical research followed a narrow pipeline: strong performance in school, competitive undergraduate training, and rigorous doctoral supervision. High school students appeared at the research frontier primarily through exceptional competition performance or rare mentorship arrangements. AI systems capable of generating proofs, suggesting structures and navigating formal libraries change that dynamic. Work on benchmarks for automated theorem reasoning indicates that large language models now solve competition-style problems and construct candidate proofs at levels once reserved for advanced undergraduates 4,14. When such capabilities are freely accessible, motivated secondary students can experiment with research-style tasks, shifting the frontier from a remote horizon into something that can be explored in the classroom or at home. This broadening of participation raises questions about what counts as authorship and how the community should recognise early contributions that rely heavily on computational support 5,13.
The role of researchers and laboratories
Quanquan Gu is known primarily for work at the intersection of non-convex optimisation, deep learning, reinforcement learning and large language models, with a stated interest in using AI to accelerate scientific discovery across domains such as biology, medicine and public health 1. Within this agenda, mathematics is both a methodological foundation and a potential application area. The emerging picture from AI research labs is that mathematical reasoning tasks serve as stringent tests for general-purpose models: success on formal proofs, competition problems and synthetic benchmarks is taken as evidence that systems are developing more systematic reasoning capabilities 4,14. When a researcher in this environment draws attention to high school students pushing mathematical frontiers with AI, it is not simply a pedagogical remark; it reflects a shift in how AI and mathematical creativity are co-evolving, and how new generations are being drawn directly into that co-evolution as co-experimenters rather than passive beneficiaries 1,9.
AI as scaffold rather than substitute
Empirical work in mathematics education consistently shows that AI tools are most effective when they function as scaffolds within structured instructional designs rather than wholesale substitutes for teacher expertise. Studies on AI-supported think-pair-share activities in algebra, for example, find that integrating AI prompts and feedback into each phase of collaborative problem solving significantly improves pupils problem-solving skills and motivation relative to traditional instruction, while leaving the human teacher in charge of conceptual explanation and classroom norms 6. Systematic reviews emphasise similar patterns: generative models excel at procedural guidance, multi-perspective explanations and personalised feedback, but they are less reliable on complex reasoning and proof construction, and they can generate plausible yet incorrect mathematics if used without verification 5,13. This dual character of AI as both enabler and potential source of error shapes how frontier experiences unfold for young learners: the same system that lets a pupil explore non-trivial conjectures can also mislead them about validity unless embedded in robust verification routines and dialogic teaching 4,5.
Frontier exploration and verification bottlenecks
Recent work on benchmarks for mathematical reasoning highlights a subtle but crucial shift: models are increasingly able to generate candidate solutions and proofs for upper-undergraduate problems, but reliably verifying those proofs remains an open challenge 4. In quantitative terms, one can think of a model proposing sequences of statements that resemble formal derivations, while evaluators attempt to determine whether the logical entailment holds at each step. In more formal language, if a student-model pair attempts to solve a problem in stochastic calculus, they might work with a process S_t and consider increments dS_t/S_t; the model can suggest manipulations, but ensuring that each transformation adheres to measure-theoretic constraints still requires expert oversight. Benchmarks such as QED-focused suites reveal that the generation stage is increasingly saturated, whereas automated verification of proofs lags behind, creating an alignment gap between what models can propose and what can be certified 4,14. For high school students, this means that AI can help them move into spaces that resemble research proof exploration, but their learning and any claimed advances must be grounded in collaborative checking with teachers or more formal tools that enforce correctness.
Ethical and epistemic objections
Not all educators or mathematicians view AI-mediated frontier experiences for teenagers positively. Surveys of university students show substantial minorities who worry that reliance on generative systems may erode critical thinking or diminish the perceived value of their education 7. In mathematics specifically, several reviews report that while AI encourages motivation and gives personalised support, its reasoning accuracy remains uneven, with roughly one tenth of studies identifying predominantly limited effects on conceptual understanding 5,13. There is also the epistemic concern that students might attribute understanding to themselves when they are in fact reproducing or slightly modifying AI outputs. Within formal research cultures, this maps onto longstanding debates about the status of computer-assisted proofs and automated theorem checking: to what extent does delegation to a machine undermine claims of human insight, and how should credit be apportioned when computational tools are indispensable to the reasoning process 4,15. When these questions are pushed down into the secondary school context, they become more acute, because adolescents are still forming their intellectual identities and ethical sensibilities around authorship, collaboration and honesty.
AI, socio-emotional learning and mathematical identity
One of the less discussed dimensions of AI in mathematics is its impact on socio-emotional learning and mathematical identity. Research on pragmatic AI in education points out that properly designed AI supports can reduce mathematics anxiety, help regulate emotional responses to failure and provide transparent dashboards of progress that allow learners to see both cognitive gains and affective patterns over time 15. From a systems perspective, models that analyse performance data and adjust task difficulty can maintain learners in an optimal challenge zone, preventing the discouragement that arises when problems are consistently too hard or too easy. In symbolic terms, an adaptive tutor might treat a students evolving mastery as a time series and use parameters such as \mu and \sigma to estimate typical performance and variability, then set subsequent problems at difficulty levels that keep expected error rates within constructive bounds. When such mechanisms are integrated into mathematics education, secondary students who venture into research-like tasks with AI support can experience frontier exploration not as a demoralising encounter with unsolved problems, but as a guided process in which their efforts, missteps and partial insights are recognised as meaningful contributions to their development.
Policy, curriculum and teacher preparation
Systematic reviews of AI in mathematics education and broader empirical syntheses stress that responsible integration requires careful policy design, curriculum adjustments and substantial teacher preparation 5,8,13. Teachers must be trained not only in the technical operation of AI systems but also in the pedagogical strategies that preserve conceptual rigour, ethical integrity and inclusive participation. Practical guidance includes allocating AI to procedural tasks while reserving higher-order reasoning for human-led instruction, establishing verification routines for AI-generated solutions, and introducing frontier-style tasks progressively rather than as high-stakes assessments 5,9. At the curriculum level, there is an emerging argument for explicitly designing modules in which students engage with open problems, model exploration and research methodologies, using AI as a collaborative partner rather than a hidden assistant. Such modules can help pupils understand the difference between generating plausible conjectures and proving them, and can frame AI tools as instruments whose limitations must be known and managed rather than omniscient oracles.
Why early frontier participation matters
The strategic significance of enabling high school students to engage with mathematical research frontiers goes beyond individual motivation. When adolescents are invited into genuine problem spaces, supported by AI scaffolds and human mentors, they begin to see themselves as potential contributors to long-running intellectual projects rather than mere consumers of established results. Systematic analyses of global trends in AI-supported mathematics learning emphasise that, under thoughtful design, these tools can foster structured reasoning, exploratory problem solving, learner agency and inclusive practices 13,14. For under-represented groups, AI-mediated access to research-style tasks may counter structural barriers by providing low-cost exploration environments and instant feedback that was previously unavailable. At the same time, community norms around credit, authenticity and rigor must evolve so that contributions originating in AI-assisted school projects are neither dismissed outright nor accepted uncritically. Wrestling with this balance is likely to shape how the next generation of mathematicians, educators and AI researchers understand the boundary between human creativity and machine-augmented discovery, and it will influence whether the promise of widened participation translates into durable, equitable intellectual progress.
References
1. Quanquan Gu – Computer Science – UCLA – https://web.cs.ucla.edu/~qgu/
2. Quanquan Gu (@QuanquanGu) / … – 2017-08-26 – https://x.com/QuanquanGu
3. Artificial Intelligence and the Future of Teaching and Learning Mathematics in a Global Context: An Overview of Contemporary Research – 2025-02-03 – https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5126695
4. QEDBench: Quantifying the Alignment Gap – WildAlg Lab – https://quanquancliu.com/wildalg-lab/post-qedbench.html
5. Applications, multidimensional challenges, and … – Frontiers – 2026-08-26 – https://www.frontiersin.org/journals/education/articles/10.3389/feduc.2026.1931535/full
6. The Impact of AI-Supported Think-Pair-Share Instruction on … – 2026-08-01 – https://onlinelibrary.wiley.com/doi/10.1002/jcal.70271
7. Generative AI Use & Perspectives from the Class of 2025 – 2026-04-22 – https://teaching.ucla.edu/news/ucla-student-ai-use-perspectives/
8. Harnessing AI-Powered Learning Media in Mathematics Education: A … – 2025-11-13 – https://ejournal.yasin-alsys.org/IJEMT/article/view/7922
9. Inaugural Teaching Symposium Explores Adapting Instruction in the … – 2026-06-24 – https://teaching.ucla.edu/news/teaching-symposium-explores-ai/
10. High School (9-12) – Stanford SCALE Initiative – https://scale.stanford.edu/ai/repository/high-school-9-12?page=14
11. Research Article – https://pdf.eu-jer.com/EU-JER_14_1_323.pdf
12. Quanquan Gu – 2022-01-01 – https://web.cs.ucla.edu/~qgu/service.html
13. A systematic review of artificial intelligence in mathematics … – 2024-07-01 – https://www.ejmste.com/article/a-systematic-review-of-artificial-intelligence-in-mathematics-education-the-emergence-of-4ir-14762
14. A Systematic Review of Global Trends and Emerging … – https://www.jmste.com/artificial-intelligence-in-mathematics-education-a-systematic-review-of-global-trends-and-emerging-themes
15. Pragmatic AI in education and its role in mathematics learning and teaching – 2025-05-11 – https://www.nature.com/articles/s41539-025-00315-4
