Friday, October 09, 2026

Sperm whale study highlights need for ‘extensive & dynamic’ conservation

University of Exeter

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A sperm whale in the Indian Ocean.
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Credit: Maarten van Rouveroy / Greenpeace

A new study of sperm whales highlights the need for ocean conservation that covers large areas – with boundaries redrawn as our climate changes.

The research team, led by the University of Exeter, combined sperm whale surveys in the south-west Indian Ocean with predictions of how climate change will shift where the whales are found in future.

Suitable whale habitat is expected to shrink as temperatures rise – although the stronger currents predicted by more extreme warming may benefit whales.

The study also found “long-term core habitat” – places that remain key for the whales despite warming – particularly off the Seychelles and Mauritius, and the steeply shelving ridges in between.

“Sperm whales travel great distances, so protection must cover extensive areas to allow them to feed, breed and migrate,” said Alexander Lomas, from the University of Exeter.

“By identifying core habitats, our study provides a baseline to begin building this protection.

“But we also find a changing patchwork of suitable areas as the climate changes – highlighting a need for dynamic protection.”

Initiatives including the recently agreed High Seas Treaty aim to bring about global-scale conservation – addressing threats including overfishing, noise, pollution and climate change.

Dr Kirsten Young, who leads the Exeter Cetacean Research Group, said: “Extensive, dynamic protection will not only benefit iconic species like sperm whales.

“Protecting large, inter-connected swathes of the ocean would also allow the wider ecosystem – and the multitude of species with it – to recover and thrive.”

Sperm whales in the south-west Indian Ocean were targeted by the whaling industry in the past.

Evidence on their numbers and movements has been limited since then, but the new study uses data from a series of studies carried out in the last two decades.

The findings suggest underwater topography, particularly steep slopes, is key for sperm whales, as slopes promote nutrients coming from the depths into the area where their prey – deep-sea squid – can thrive.

The projected percentage of habitat lost by the year 2100 under different climate scenarios is:

40% for an “optimistic” scenario (called SSP1–2.6) where humanity’s greenhouse gas emissions decline rapidly.
37% for an “intermediate” scenario (SSP2-4.5).
20% for a “pessimistic” scenario (SSP5-8.5). The study projects that damage caused by extreme climate warming would be offset by stronger currents. However, the authors stress that they did not assess wider ecosystem impacts, which could be harmful to whales.

Dr Jeremy Kiszka, a Professor at Florida International University, in Miami, and involved in this study, said: “Climate change is predicted to substantially reduce suitable habitat for sperm whales in the southwest Indian Ocean, but we also identified places that could remain important refuges for these animals through the end of the century.”

Commenting on seeing the whales during a research trip to the Indian Ocean, Dr Young added: “Meeting these sperm whales hundreds of kilometres from land, around Saya de Malha bank, was incredible – we are some of the first people to study them since the days of whaling.

“But the threats they face are a reminder of how far human influence reaches into the natural world, and the urgent need to reduce our impact.”

Lomas added: “This paper highlights the benefits of international scientific collaboration.

“It depended on data from nine research groups – and work by governments and non-governmental organisations – from different countries around the Indian Ocean. For example, the Marine Megafauna Conservation Organisation, GLOBICE, African Aquatic Conservation Fund and the IndoCet Consortium.”

Violaine Dulau, chair of IndoCet, the Indian Ocean network for Cetacan research, said: “By bringing together data and expertise from across the western Indian Ocean, we can finally see the bigger picture. Thinking at the scale of the ocean is essential to understanding the habitats sperm whales depend on and what their future may look like.”

Dr Young concluded: “In a rapidly changing ocean, we need to know not only where animals are today, but where suitable habitat is most likely to persist in the future.”

The paper, published in the journal Endangered Species Research, is entitled: “Using ensemble ecological niche models to predict long-term core habitat of sperm whales (Physeter macrocephalus) in the southwest Indian Ocean under future climate scenarios.”

Journal

Endangered Species Research

DOI

10.3354/esr01538

Article Title

Using ensemble ecological niche models to predict long-term core habitat of sperm whales (Physeter macrocephalus) in the southwest Indian Ocean under future climate scenarios

Article Publication Date

8-Oct-2026

U$A

Hospital closures on the rise in both rural and urban areas—particularly among safety-net hospitals

Harvard T.H. Chan School of Public Health

Key points:

Although U.S. policy has focused on preventing the closure of rural hospitals, researchers found no significant difference between rural and urban hospital closure rates. Over a 15-year period, these rates increased for both types of hospitals and were higher than the rate at which new hospitals opened.
For-profit, small, and safety-net hospitals, and those in the most socially vulnerable communities, closed most often.
According to the researchers, the findings show that hospital closures aren’t just a rural problem and provide evidence that policymakers should invest in supporting vulnerable hospitals no matter where they’re located.

Boston, MA—More hospitals across the U.S. are closing than opening, and urban hospitals are closing at the same rate as rural ones, according to a new study led by Harvard T.H. Chan School of Public Health. Further, the hospitals that close are more likely to be those serving socially vulnerable communities.

The findings will be published in a research letter in JAMA on Oct. 8.

Since the passage of the “One Big Beautiful Bill Act” that included changes to Medicaid policy, hospitals have been bracing to lose billions in funding, and concern has been growing over potential hospital closures. Most of this concern has been centered on rural hospitals, such that Congress created the Rural Health Transformation Program, providing billions in state grants for these hospitals. But whether hospital closures are actually concentrated in rural areas has been little studied and remains largely unknown.

The researchers sought to fill this gap and provide a current, comprehensive picture of U.S. hospital closures and openings. To do so, they analyzed data from the American Hospital Association annual survey, characterizing hospital closures and openings occurring from 2010 to 2025.

They found that hospital closures increased by 4% year over year, and openings decreased 3% year over year, with 432 hospitals closing and only 216 opening. The result was a net loss of 216 hospitals and more than 24,000 beds. There was no significant difference between rural and urban hospital closure rates.

The researchers also observed that the hospitals that more often closed were for-profit, small, and safety-net, and those in the most socially vulnerable counties—in both rural and urban areas. Safety-net hospitals and those serving a high number of Medicaid patients rarely opened.

“Many policymakers have been treating hospital closures as a rural problem, but our data show it’s a national problem,” said corresponding author Thomas Tsai, associate professor of health policy and management and co-director of the Healthcare Quality and Outcomes Lab. “We must shift away from only asking ourselves how we can save rural hospitals, and start asking: How do we protect access to hospital care for vulnerable communities, wherever they are?”

Article information

“Longitudinal Trends and Characteristics of Hospital Closures and Openings,” Joshua E. Calianos, Julia H. Song, E. John Orav, Jose F. Figueroa, Thomas T. Tsai, JAMA, October 8, 2026, doi: 10.1001/jama.2026.18260

The research was supported by the Commonwealth Fund.

Orav reported receiving grants from the Office of the Assistant Secretary for Planning and Evaluation. Figueroa reported receiving grants from the National Institute on Aging, the National Institute of Nursing Research, the Department of Veterans Affairs, the National Institutes of Health, the Agency for Healthcare Research and Quality, the SCAN Foundation, the Robert Wood Johnson Foundation, and Arnold Ventures, and receiving personal fees from Project Hope (for editorial services for Health Affairs Scholar). Tsai reported receiving grants from the Department of Veterans Affairs and Arnold Ventures and receiving personal fees from Johnson & Johnson. No other disclosures were reported.

Visit the Harvard Chan School website for the latest news and events from our Studio.

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Harvard T.H. Chan School of Public Health is a community of innovative scientists, practitioners, educators, and students dedicated to improving health and advancing equity so all people can thrive. We research the many factors influencing health and collaborate widely to translate those insights into policies, programs, and practices that prevent disease and promote well-being for people around the world. We also educate thousands of public health leaders a year through our degree programs, postdoctoral training, fellowships, and continuing education courses. Founded in 1913 as America’s first professional training program in public health, the School continues to have an extraordinary impact in fields ranging from infectious disease to environmental justice to health systems and beyond.

Journal

JAMA

DOI

10.1001/jama.2026.18260

Method of Research

Observational study

Subject of Research

Not applicable

Article Title

Longitudinal Trends and Characteristics of Hospital Closures and Openings

Article Publication Date

8-Oct-2026

Elderly could live independently for longer thanks to new home sensor system which detects emergencies

Nottingham Trent University

Older people could be monitored safely in their own homes without the need for intrusive cameras or wearable devices thanks to new research by Nottingham Trent University (NTU).

A study, in collaboration with Integrated System Technologies Ltd, has led to the development of a low-cost monitoring system that combines radar, heat sensors and smart plugs to track daily routines while protecting privacy.

The system incorporates artificial intelligence (AI) to combine data from the three monitoring technologies to identify possible health events, such as a falls, heart attacks, strokes or other critical illness.

Dr Yangang Xing, leader researcher from NTU’s School of Architecture, Design and the Built Environment, said: “This technology aims to support the growing number of older adults who wish to remain in their own homes for longer, rather than moving into residential care.

“By combining these three technologies, we can establish a complete picture of how someone is coping at home. As well as detecting emergencies, it could provide an early warning if a person's mobility or daily routine begins to deteriorate.”

The system uses millimetre-wave radar as a low-cost way to detect movement in a property, with multiple sensors placed discreetly about the home at chosen locations.

Smart plugs – that connect to ordinary house appliances and Wi-Fi - are used to monitor behavioural patterns linked to everyday tasks such as making a cup of tea, preparing food or spending time at a desk.

Thermal sensors - that identify body posture without revealing facial features or personal identity - are used to recognise sitting, standing, walking and lying down, but are highly pixelated and kept low-resolution to prevent more intricate movements or images being displayed to protect privacy.

The AI learns an individual’s behaviour patterns over time in order to spot anything out the ordinary, such as an emergency health event, or a gradual deterioration in a person’s health.

Should an emergency be detected, care professionals and loved ones are notified to allow checks to be made on the wellbeing of the inhabitant, either remotely or in person.

For the study, the team tested the sensors in a mock domestic environment featuring six different room layouts, including bedrooms and living areas with varying furniture arrangements.

A series of activities was carried out and recorded to assess how accurately the system could identify movement and posture.

Researchers found that combining information from all sensors improved performance, suggesting the technologies worked best when used together rather than as standalone monitoring tools.

The research team included Dr Geoff Archenhold, Bilal Mohammed and Martin Harris of Integrated System Technologies Ltd; and Dr Jordan J. Bird and Dr Isibor Kennedy Ihianle of NTU’s School of Science and Technology.

The study, titled Privacy-Preserving Ambient Sensing for Activities of Daily Living: Multimodal Radar-Thermal Human Activity Recognition and Smart Plug Appliance Recognition, has been published in the journal Sensors.

Dr Archenhold, chief executive officer of Integrated System Technologies Ltd, said: “We believe that this system could form part of an ambient assisted living environment, where homes quietly monitor residents' wellbeing in the background and alert carers when unusual behaviour occurs. Changes in mobility, prolonged inactivity, altered sleep patterns or the absence of normal household routines could all potentially indicate emerging health concerns.

“The technology could ultimately allow older people to stay in their own homes for longer, giving them confidence to go about their daily business while feeling secure in the knowledge that their health and wellbeing is monitored without infringing on their privacy.”

Notes to editors:

• Press enquiries please contact Chris Birkle, Nottingham Trent University PR Manager, on telephone +44 (0)115 848 2310, or via email

Journal

Sensors

DOI

10.3390/s26165066

Method of Research

Imaging analysis

Subject of Research

People

Article Title

Privacy-Preserving Ambient Sensing for Activities of Daily Living: Multimodal Radar–Thermal Human Activity Recognition and Smart Plug Appliance Recognition

African gemsbok spreading in New Mexico: How far could they go under climate change?

College of ACES at the University of Illinois Urbana-Champaign

URBANA, Ill. — Majestic African antelopes known as gemsbok have been roaming the U.S. southwest since their introduction in the 1960s and 1970s. Brought to New Mexico as game species for hunting, gemsbok quickly settled in, expanding more than 100 kilometers from their introduction point. University of Illinois Urbana-Champaign researchers say that’s due to their exceptional adaptations to arid conditions, which they predict will dramatically expand under climate change.

In a new study, the researchers reveal the potential extent of the exotic species’ spread by the year 2100, with suitable habitat spilling well beyond New Mexico into Texas, Arizona, Utah, California, and even as far north as southern Washington and Montana. Should gemsbok disperse and proliferate into all of these spaces, the impacts to cattle, native wildlife, and plant communities could be significant.

The team mapped where gemsbok could survive under future climate scenarios based on their current habitat preferences.

“We turned towards participant science to do this work. When people contribute photos to apps like iNaturalist, the occurrence records get scraped into something called the Global Biodiversity Information Facility. From that, we were able to use a statistical method called Maxent to find habitat associations for gemsbok,” said the study’s lead author, Nathan Alexander, who began the research as a doctoral student in the Department of Natural Resources and Environmental Sciences, part of the College of Agricultural, Consumer and Environmental Sciences at U. of I. He’s now a postdoctoral scholar at Southern Illinois University.

For every gemsbok occurrence, the researchers looked at factors like temperature seasonality and precipitation, vegetation cover, terrain ruggedness, and human population density to paint a picture of where the animals spend time. Then they looked for similar habitat patterns across space and time to predict where gemsbok might go in the future. They found that many suitable habitats that now exist as isolated pockets will likely coalesce into larger, more contiguous habitats under future climate scenarios.

“When there are these isolated patches, there might be dispersal barriers that they can't cross to get to the next patch. But when these patches coalesce and connect, there might be increased opportunities for gemsbok to invade and expand into these novel habitats. We see this particularly in western Texas, but also into western New Mexico and up into Arizona, and even some regions of California, like Death Valley,” said Kieran Andreoni, who began the research as a master’s student in NRES. He’s now conservation director at the Southern Plains Land Trust in Colorado.

Native to the Kalahari Desert in southern Africa, gemsbok are particularly well suited for arid conditions and may have an advantage over southwestern native species under climate change.

“Gemsbok are famous for being really well adapted to heat and drought. In addition to other heat adaptations, they can get all of their water from plants, so they don't really need to drink. That’s really unusual for animals that big — they can weigh 450 pounds. They're the poster species for dealing with the kind of changes we're going to see in the southwest,” said study co-author Bob Schooley, professor and head of NRES.

Schooley adds that gemsbok left their natural predators — lions and hyenas — back in Africa, and southwestern predators like coyotes and mountain lions don’t kill nearly as many gemsbok. Considering their superior adaptation to arid climates and relative freedom from predators, the spread of gemsbok could threaten both domestic and native species.

The primary concern is diet overlap — with larger gemsbok herds eating the same forage as cattle and natives like pronghorn and bison, gemsbok could diminish food reserves for those species.

“Along with that diet overlap, gemsbok are able to forage on lower quality plant materials than some of our native species,” Alexander said. “So in drought years, we could imagine our native species might be a little bit more stressed and nutrient deficient, whereas the gemsbok are going to be able to move to less nutrient-rich plant material and still be able to persist in the environment.”

Schooley added, “These desert rangelands are often used for cattle grazing. When there’s a severe drought, they pull the cattle off the landscape because there's no food for them. Well, no one pulls the gemsbok off. Considering their ability to survive on low-quality forage, they could severely damage remaining grasslands. So I think that's the kind of thing we worry about — what are the implications when they get to even larger numbers?”

Alexander says there is also potential for gemsbok to carry and spread diseases to native and domestic ungulates. Gemsbok in the southwest have tested positive for malignant catarrhal fever, bovine respiratory syncytial virus, and bovine para-influenza-3, which are of concern to the cattle industry.

With competing interests between conservationists, ranchers, and hunting operations, the researchers say it will be tricky but critical to manage the population into the future to avoid potential consequences across the southwest.

The study, “Predicted range expansion of exotic Gemsbok (Oryx gazella) under climate change in the United States,” is published in the Journal of Mammalogy [DOI: 10.1093/jmammal/gyag083].

Research in the College of ACES is made possible in part by Hatch funding from USDA’s National Institute of Food and Agriculture. This study was also supported by a competitive NIFA grant (no. 7006200) and the National Science Foundation (Jornada Basin Long Term Ecological Research Program, DEB 2025166 and DEB 2425143).

Alexander and Schooley are also affiliated with the Illinois Natural History Survey, part of the Prairie Research Institute at U. of I.

Book counters AI hype by examining how researchers talk about their work

A new book by University of Illinois Urbana-Champaign English professor John Gallagher aims to counter the hype surrounding artificial intelligence by focusing on AI researchers and their work

University of Illinois at Urbana-Champaign, News Bureau
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A new book by University of Illinois Urbana-Champaign English professor John Gallagher aims to counter the hype surrounding artificial intelligence by focusing on AI researchers and their work.
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Credit: Courtesy John Gallagher

CHAMPAIGN, Ill. —The news about artificial intelligence contains a lot of hype about whether it will take our jobs or possibly kill us all, or, on the other hand, discover new medicines to cure disease and solve scientific puzzles.
A new book by University of Illinois Urbana-Champaign English professor John Gallagher aims to counter the hype by focusing on the people who work on AI and machine learning. His book “AI Through the Experts’ Eyes: Communicating Complex Ideas” examines what AI researchers do and how they communicate about their work. His goal is to help those experts communicate without hype and help others better understand and think critically about AI, particularly writing teachers or those wrestling with the role of AI technology in their classrooms.
Gallagher — who is affiliated with the School of Information Sciences and is teaching two classes this semester on AI — said he wanted to learn more about machine learning and natural language processing techniques for his research. When the COVID-19 pandemic derailed his plans to visit AI research centers, he switched to interviewing machine learning researchers about their work and their communication techniques. He interviewed more than 100 AI and machine learning experts, most of whom were in academia and in the computer science and physics disciplines.
The public may envision killer robots when they think about AI, but in reality, it is mostly mundane tools, such as the GPS software for vehicle navigation or the spam filter on your email account, Gallagher said. And creating them is the methodical work of designing a model, obtaining feedback and revising it over and over again.
“It’s boring. It’s math, a lot of math, and meetings and day-to-day normalcy,” Gallagher said. The leaders of AI companies talk about “fanciful answers and magic in the sky, not linear algebra.”
“I’m less concerned with Terminator and HAL 9000 and more concerned with the systematic error that didn’t get picked up as a bug in the code, called the alignment problem. The program still works but it’s not exactly what you wanted it to do, and it’s now doing something kind of bad,” he said.
An example he wrote about in his book is a garbage-detection program called TrashCan, designed to clean up ocean garbage patches, and the problem of training a machine to recognize what is trash.
“If it is trained on objects not meant to be in the water, you can train a machine to pick up trash. But maybe you have buoy that’s supposed to be there and is not trash, until it sinks onto the ocean bottom and it is trash. That’s an alignment problem if it collects buoys that are supposed to be there,” Gallagher said. “Or you train it on sea life. What if you get land animals swimming? It might see them as trash and collect them.”
The problem is not an evil robot, he said; it’s bad programming leading to an unintended result.
Much of the reason for the hype that either scares us or overpromises what AI can do is the hypercompetitive atmosphere in a field that is changing rapidly, he said. Researchers in academia and industry are expected to publish frequently at conferences, rather than in peer-reviewed journals that take much longer to release a paper. That pressure may lead researchers to overstate their findings or understate their limitations, Gallagher argued in the book.
Additionally, it’s no longer enough just to publish. Almost everyone Gallagher talked to mentioned the pressure of building a public relations campaign around a paper, he said.
“Now you must advertise the paper on social media. It also needs a blog post, a GitHub repository of the code, shared results on LinkedIn, Bluesky, even YouTube videos,” he said. “You can be a researcher and you also have to be a content creator and influencer, producing a conference paper and also six other content genres.”
Gallagher wrote that “the current AI publication landscape may lower publication quality while possibly sensationalizing scientific results.”
He made several suggestions for countering the hype surrounding AI. He said researchers should stress that AI is a type of automation designed to serve a specific need, such as detecting trash in the ocean or making sense of vast amounts of scientific data.
AI and machine learning researchers should be trained and encouraged to translate their research for many different audiences, including nonexperts, and they should discuss their work in the media, including explaining the technical, granular aspects of their work on long-form platforms such as YouTube, he said.
Incentives are needed to reduce the pressure on academic publishers — particularly those for conference proceedings — that encourage them to produce a high quantity of articles in a short time frame, Gallagher said.
Finally, he said that nonexperts interested in learning more should seek out technical AI researchers rather than business leaders promoting their products or podcasters seeking an audience. Many researchers have YouTube channels devoted to explaining the technical details and concepts of the field that will demystify AI technology, he said.

When AI chatbots give bad advice, no one can see the damage

New paper explores how chatbot health guidance leaves no trace for clinicians or regulators, and calls for transparency safeguards

Binghamton University

As more and more people turn to AI chatbots for quick, 24/7 medical advice, a new perspective paper co-authored by faculty at Binghamton University, State University of New York explores the risks this practice carries that are largely invisible to users – and healthcare systems.

The paper, written by researchers at Binghamton University, Stanford University, Texas A&M University, and Indiana University, and published in Nature Health, examines what happens when a chatbot gives someone bad health advice. The authors argue that the harm is hard to catch because the conversation stays on the AI company's platform, the person has no place to report the problem, and outside researchers cannot measure the damage.

“We’re getting medical advice from these chatbots, but nobody—literally no one—is looking at this. If there’s an error or an issue, there’s just no way for people to know,” said Kaicheng Yang, an assistant professor in the School of Computing at Binghamton University’s Thomas J. Watson College of Engineering and Applied Science and one of the paper’s authors.

The researchers gave the example of a 60-year-old man who asked ChatGPT how to cut chloride from his diet and swapped table salt with sodium bromide. The man ended up being hospitalized with bromide toxicity after experiencing hallucinations and paranoia. The issue this paper highlights is that because the man received this advice from a chatbot and was unable to retrieve the conversation, his doctors had no way of knowing exactly what the man was told, making it nearly impossible to piece together exactly what happened.

Because there is no system of transparency in place for AI companies as it relates to the visibility of health advice it generates for patients, this paper asserts that this built-in, systemic lack of visibility is a key aspect of AI-generated health information because it actively prevents oversight. “Harms are not only possible, but structurally hidden from the clinicians, researchers, and regulators who could otherwise detect and correct them,” the authors note.

This paper also emphasizes a key facet of chatbots generating answers for people with health questions – they can be wrong. Chatbots can generate erroneous answers confidently, oversimplify information, or draw from outdated information/false claims. However, the authors also note that those risks can trickle down to those who are not actively seeking answers. With the prevalence of AI summaries in search engines and the integration of AI in social media platforms like X and Meta, you do not have to be actively searching for an answer to be given an incorrect bit of information.

“Sometimes I’m not even looking for health information, but just by browsing my social media feeds, it’s there. It just shows up, and we believe that could have undesirable outcomes, especially if there’s medical misinformation or state actors trying to manipulate the online discussion,” Yang said.

Regardless of whether a person is actively looking for answers or comes across them incidentally, the authors of this paper argue that the harm rarely leaves traces that clinicians, regulators, or researchers can verify.

To combat this, the authors propose several methods to increase transparency and responsibility for AI companies. They note that AI companies should give users access to their own health conversations to provide them the opportunity to share this information with clinicians so they can better investigate the pathway that led to a harmful event. They also recommend that those companies develop a disclosure system to allow health guidance to be flagged, reported, and investigated.

They further recommend that social media companies take more responsibility by enhancing clear labeling of AI-generated health content, withholding that content until it is vetted by medical governing bodies, and similarly, that search engines should only utilize vetted information in summaries. Policymakers, the authors suggest, should also extend physician malpractice liability to AI chatbot companies.

“We do not think this is something we should rely on the companies to do, because their incentive is always to make more money,” Yang said. “Building such a system goes against that incentive. So we have to have some kind of third-party monitoring system, an independent evaluation.”

Journal

Nature Health

DOI

10.1038/s44360-026-00206-x

Method of Research

Commentary/editorial

Subject of Research

Not applicable

Article Title

The Invisible Risks of AI-Generated Health Information

Article Publication Date

9-Oct-2026

Introducing AlphaProof Nexus: An AI tool for formal mathematical proof discovery

Summary author: Walter Beckwith

American Association for the Advancement of Science (AAAS)

A new large language model (LLM)-based artificial intelligence framework called AlphaProof Nexus can autonomously tackle select math problems, seeking proofs and using verification to ensure the resulting solutions are logically sound, researchers report. The system solved dozens of previously open problems across several mathematical fields, suggesting that artificial intelligence (AI) could become a useful tool for automated mathematical discovery and research. “[The authors report] that even unsuccessful proof attempts by AI could help them understand the problems better and make progress on solving them,” write Jeremy Avigad and Matthew Ballard in a related Perspective. “This underscores that an essential goal of developing AI for mathematics is to support mathematicians in the search for knowledge and understanding that lead to further advances.” Large language models (LLMs) have demonstrated growing ability to solve difficult mathematical problems, but their tendency to produce subtle logical errors or “hallucinations” makes them unreliable for research without extensive human expert review. One promising way to mitigate these issues is to have AI agents generate mathematical proofs in formal programming languages such as Lean, which automatically verifies each logical step and prevents errors from going unnoticed. While this approach has been successfully applied to competition mathematics and in the human-aided formalization of natural language arguments, its potential in solving open research-level mathematical problems remains unknown.

To address this gap, George Tsoukalas and colleagues developed AlphaProof Nexus, a framework that uses multiple AI agents to search for mathematical proofs with feedback from the Lean compiler. Tsoukalas et al. also developed a more advanced, full-featured agent that coordinated subagents through an evolutionary algorithm to use AlphaProof as a specialized proof tool. In tests, the system was able to solve nine of the 353 attempted Erdős problems, including two that had remained unsolved for more than 50 years. It was also able to solve 44 of 492 open On-Line Encyclopedia of Integer Sequences (OEIS) conjectures as well as several other research-level problems in fields such as algebraic geometry, optimization, quantum optics, and graph theory.

Journal

Science

DOI

10.1126/science.aej2213

Article Title

Advancing mathematics research with AI-driven formal proof search

Article Publication Date

8-Oct-2026