Featured Post from University of Florida

New AI-powered tool helps students find creative solutions to complex math proofs

Dec 22, 2025

3 min

Math students may not blink at calculating probabilities, measuring the area beneath curves or evaluating matrices, yet they often find themselves at sea when first confronted with writing proofs.

But a new AI-powered tool called HaLLMos — developed by a team led by Professor Vincent Vatter, Ph.D., in the University of Florida Department of Mathematics — now offers a lifeline.

“Some students love proofs, but almost everyone struggles with them. The ones who love them just put in more work,” Vatter said. “It just kind of blows their minds that there’s no single correct answer — that there are many different ways to do this. It’s very different than just doing computational work.”

Building the tool

HaLLMos was developed by Vatter, as principal investigator, along with Sarah Sword, a mathematics education expert at the Education Development Center; Jay Pantone, an associate professor of mathematical and statistical sciences at Marquette University; and Ryota Matsuura, a professor of mathematics, statistics and computer science at St. Olaf College; with grant support from the National Science Foundation. The tool is freely available at hallmos.com.

The team’s goal was to develop an AI tool powered by a large language model that would support student learning rather than short-circuiting it. HaLLMos provides immediate personalized feedback that guides students through the creative struggle that writing proofs requires, without solving the proofs for them.

The tool’s name honors the late Paul Halmos, a renowned mathematician who argued that the mathematics field is a creative art, akin to how painters work.

Students using HaLLMos can select from classic exercises — such as proving that, for all integers, if the square of the integer is even, the integer is even — or use “sandbox mode” to enter exercises from any course. Faculty can create exercises and share them with students.

Vatter introduced HaLLMos to his students last spring in his “Reasoning and Proof in Mathematics” class, a core requirement for math majors that is often the first time students encounter proofs.

“They could use this tool to try out their proofs before they brought them to me. We try to identify the error in a student’s proof and let them go fix it,” Vatter said. “It is difficult for faculty to devote enough time to working individually with students. Our goal is that this tool will provide the feedback in real time to students in the way we would do it if we were there with them as they construct a proof.”

Helping professors and students excel

“I think every math professor would love to give more feedback to students than we are able to,” Vatter said. “That’s one of the things that inspired this.”

The next steps for Vatter and his colleagues include getting more pilot sites to use the tool and continuing to improve its responses.

“We’d like it to be good at any kind of undergraduate mathematics proofs,” he said.

Vatter also intends to explore moving HaLLMos to UF’s HiPerGator, the country's fastest university-owned supercomputer.

“It’s our goal to have it remain publicly accessible,” Vatter said.

This research was supported by a grant from the National Science Foundation Division of Undergraduate Education.

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Vincent Vatter

Professor

Vincent Vatter's research focuses on combinatorics, graph theory, and AI.

CombinatoricsGraph TheoryMathematics

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Apr 1, 2026

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UF develops breakthrough magnet that could transform metal production

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Mar 30, 2026

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UF researchers aim to improve nutrition for cancer patients

A new study and first-of-its-kind food pharmacy at UF aim to help patients with cancer access and eat nutritious foods, giving them the best possible shot at a healthy future. As many as a third of cancer patients face food challenges, particularly in rural areas. Good nutrition can improve outcomes during and after treatment. With a grant from the Florida Department of Health, a team of researchers at the University of Florida Health Cancer Center and Sylvester Comprehensive Cancer Center will first assess the community’s nutritional needs. Then they’ll test the usefulness of a food-focused digital tool designed to connect patients to helpful resources. An on-site food pharmacy will help patients not only get the food they need to thrive but also provide tools for lasting change. “We’re taking a community-based approach to holistic cancer care,” said Dejana Braithwaite, Ph.D., associate director for population sciences at the UF Health Cancer Center. “Patients consistently express that nutrition is an important issue for them during cancer treatment. We want to address nutritional needs from treatment through survivorship with a sustainable intervention. ASCENT brings science and community together to make that a reality in Florida.” Braithwaite, a professor and division chief in the UF Department of Surgery, is leading the multi-institution study with Tracy Crane, Ph.D., R.D.N., director of lifestyle medicine, prevention and digital health and co-lead of the Cancer Control Program at Sylvester, part of the University of Miami Health System. Researchers from the UF colleges of Journalism, Medicine, and Public Health and Health Professions and UF/IFAS Extension are participating. The Florida Partnership for Adding Social Context to Address Cancer Survivorship Outcomes study, which the researchers have nicknamed ASCENT, will focus on those affected by the most prevalent cancers in Florida, including breast, lung, colorectal, prostate and blood cancers. “Cancer survivors who follow a healthy dietary pattern have a lower risk of recurrence and death,” said Cora Best, Ph.D., R.D.N., an assistant professor of nutritional sciences in the UF College of Agricultural and Life Sciences and study team member. “Some cancer therapies have long-term or late side effects that increase the risk for chronic conditions, like osteoporosis, which can be alleviated with good nutrition. That means a healthy diet during and after oncologic treatment can enhance lifespan and quality of life.” Researchers will start by conducting interviews with patients, providers and community-based organizations. They want to understand how to best use resources to meet the nutritional needs of those with cancer, such as food security and diet quality. “Community outreach and engagement with various groups is a cornerstone of the study,” said Francis Dalisay, Ph.D., an associate professor in the UF College of Journalism and Communications who helped develop the interview guides. The team will use the information to build a diet intervention with online surveys and patient navigator support, which they will test in a randomized clinical study at UF Health and Sylvester. Patient navigators will connect patients with resources like community programs or specialist referrals. The food pharmacy, located at the UF Clinical and Translational Sciences Metabolic Kitchen, will help cancer patients get healthy, whole nutrient-dense foods like high-protein items, fruits, vegetables and pantry staples. It will also provide workshops, personalized recipes and meal plans. Although the United States is a wealthy nation, food insecurity remains common, including in Florida, Best said. “The ASCENT study pairs evidence-based dietary guidance for cancer survivors with innovative strategies to overcome barriers like food insecurity,” she said. Ultimately, the study aims to empower patients so they can address lifestyle factors in their control, boosting their well-being. “I am hopeful this study will provide patients with appropriate resources to improve their overall nutrition, especially those who are malnourished,” said Paul Crispen, M.D., the Cancer Center’s associate director for clinical research and a study adviser.

Mar 27, 2026

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New light-based chip boosts power efficiency of AI tasks 100 fold

A team of engineers has developed a new kind of computer chip that uses light instead of electricity to perform one of the most power-intensive parts of artificial intelligence — image recognition and similar pattern-finding tasks. Using light dramatically cuts the power needed to perform these tasks, with efficiency 10 or even 100 times that of current chips performing the same calculations. Using this approach could help rein in the enormous demand for electricity that is straining power grids and enable higher performance AI models and systems. This machine learning task, called “convolution,” is at the heart of how AI systems process pictures, videos and even language. Convolution operations currently require large amounts of computing resources and time. These new chips, though, use lasers and microscopic lenses fabricated onto circuit boards to perform convolutions with far less power and at faster speeds. In tests, the new chip successfully classified handwritten digits with about 98% accuracy, on par with traditional chips “Performing a key machine learning computation at near zero energy is a leap forward for future AI systems,” said study leader Volker J. Sorger, Ph.D., the Rhines Endowed Professor in Semiconductor Photonics at the University of Florida. “This is critical to keep scaling up AI capabilities in years to come.” “This is the first time anyone has put this type of optical computation on a chip and applied it to an AI neural network,” said Hangbo Yang, Ph.D., a research associate professor in Sorger’s group at UF and co-author of the study. Sorger’s team collaborated with researchers at UF’s Florida Semiconductor Institute, the University of California, Los Angeles and George Washington University on study. The team published their findings, which were supported by the Office of Naval Research, Sept. 8 in the journal Advanced Photonics The prototype chip uses two sets of miniature Fresnel lenses using standard manufacturing processes. These two-dimensional versions of the same lenses found in lighthouses are just a fraction of the width of a human hair. Machine learning data, such as from an image or other pattern-recognition tasks, are converted into laser light on-chip and passed through the lenses. The results are then converted back into a digital signal to complete the AI task. This lens-based convolution system is not only more computationally efficient, but it also reduces the computing time. Using light instead of electricity has other benefits, too. Sorger’s group designed a chip that could use different colored lasers to process multiple data streams in parallel. “We can have multiple wavelengths, or colors, of light passing through the lens at the same time,” Yang said. “That’s a key advantage of photonics.” Chip manufacturers, such as industry leader NVIDIA, already incorporate optical elements into other parts of their AI systems, which could make the addition of convolution lenses more seamless. “In the near future, chip-based optics will become a key part of every AI chip we use daily,” said Sorger, who is also deputy director for strategic initiatives at the Florida Semiconductor Institute. “And optical AI computing is next.”