A team led by the University of Florida has unveiled an artificial intelligence system intended to give targeted feedback on students' written mathematical proofs while deliberately avoiding providing full solutions, a development designed to preserve what educators call productive struggle.
Preserving the learning process
The project, led by Professor Vincent Vatter of UF's Department of Mathematics, produces a tool called HaLLMos, which the researchers say is freely available and intended for use in advanced undergraduate courses. The initial rollout will focus on classes such as linear algebra, real analysis and topology.
“How can artificial intelligence support student learning without replacing the thinking that makes it possible?”
The question framed by the team encapsulates a widespread concern among educators: while powerful AI systems can now solve many mathematical problems that once marked the frontier of research, their ease of use risks short‑circuiting the reflective, effortful work that builds deep understanding and transferable problem‑solving skills.
How HaLLMos is positioned
According to the team, HaLLMos is designed to provide feedback on students' written proofs rather than offering complete answers. The stated aim is to encourage learners to engage with difficult but achievable problems and to develop independence in reasoning—core elements of the pedagogical idea of productive struggle.
- Target courses: linear algebra, real analysis, topology
- Primary function: give feedback on written proofs without supplying full solutions
- Access: described by the developers as freely available
By focusing on written proofs, the system addresses an area of mathematical learning that is both foundational for higher mathematics and challenging to assess at scale. Proof writing demands not only correct results but clear logical structure and justification—qualities that conventional automated marking systems struggle to evaluate reliably.
Implications for teaching and assessment
HaLLMos represents a pragmatic response to two simultaneous forces reshaping higher education: the rapid advance of AI capability and the longstanding pedagogical consensus that struggling productively with problems promotes durable learning. If the tool performs as intended, it could allow educators to integrate AI assistance into courses while reducing the risk that students rely on the technology to do their reasoning for them.
The developers emphasise that the tool is designed to 'support student learning' rather than replace human instruction. That positioning aligns with growing calls across the sector for carefully designed AI tools that augment, rather than supplant, teachers and tutors.
Adoption of such systems raises practical questions for departments and institutions: how to align AI feedback with course learning outcomes, how to train staff to interpret and act upon automated comments, and how to ensure academic integrity while encouraging legitimate use of supportive technology.
| Feature | Detail |
|---|---|
| Tool name | HaLLMos |
| Lead institution | University of Florida |
| Target courses | Linear algebra, Real analysis, Topology |
| Availability | Freely available (developers' description) |
For UK universities and further education providers, the project will be watched closely. Departments offering rigorous proof‑based modules face the same tension between harnessing technological efficiency and safeguarding the pedagogical value of challenge. Tools that can provide scaffolded, non‑solution feedback may help instructors scale personalised guidance without eroding the cognitive work that underpins expertise.
Ultimately, the effectiveness of HaLLMos will depend on transparent evaluation in classroom settings: whether its feedback leads students to revise and deepen their reasoning, whether it reduces common errors, and how it interacts with human feedback from tutors and peers.
As AI becomes more capable in specialist domains, the central educational question will remain how to use those capabilities to strengthen, rather than shortcut, the processes that produce independent thinkers and skilled practitioners.
