The twin prime conjecture suggests that there are infinitely many pairs of prime numbers that are exactly two numbers apart. Examples include (3, 5), (5, 7), and (17, 19). Although mathematicians have studied the problem for many years, proving that there are infinitely many such pairs remains an unsolved challenge.

Stadlmann’s work was considered an important achievement after more than a decade without major progress in this particular line of research. Mathematician Kannan Soundararajan praised the difficulty of the work and highlighted Stadlmann’s persistence in continuing to study the problem.

However, the situation changed very quickly. Within just three days, AI startup Axiom Math announced results that improved on Stadlmann’s findings. The pace became even faster when OpenAI reportedly produced a result that went beyond both earlier records only two hours after Axiom’s announcement.

The speed of these developments has raised concerns among some mathematicians. They argue that mathematics is not simply about setting new records or producing better numerical results. For many researchers, understanding why a result works and developing new ideas are just as important as reaching a stronger result.

Some mathematicians feel that AI companies may be approaching mathematical research differently from traditional academic researchers. Instead of spending years developing an idea and building a deep understanding of a problem, AI systems can rapidly search through large numbers of possibilities and produce results.

Renowned mathematician Terence Tao has also expressed concerns about this approach. He criticized the focus on quickly surpassing human achievements, arguing that mathematical research is also about understanding, curiosity and expanding human knowledge.

The episode has highlighted the changing relationship between humans and AI in mathematics. Human mathematicians often spend years working on difficult problems, developing techniques and learning from failed attempts. AI systems, meanwhile, can examine mathematical possibilities at extremely high speed.

Supporters of AI in mathematics believe these tools could help researchers solve problems that have remained unanswered for decades. They argue that AI can act as a powerful assistant, helping mathematicians discover patterns, test ideas and explore difficult calculations.

The debate is therefore not simply about whether AI is better or faster than humans. It also raises a deeper question about what should count as progress in mathematics. As AI becomes more capable, mathematicians will have to find ways to combine the speed of machines with the creativity, reasoning and understanding of human researchers.

The recent developments surrounding the twin prime conjecture show how quickly this field is changing. What once took mathematicians years of work may now be challenged by AI systems within hours, creating both exciting opportunities and difficult questions for the future of mathematical research.

The September 11 attacks left a lasting impact on thousands of people. Rescue workers, firefighters, police officers, medical workers, cleanup crews, local residents, and others who worked near Ground Zero were exposed to dust, smoke, and dangerous materials released after the towers collapsed.

Over the years, many people who were exposed to the disaster have developed serious health problems. Some have suffered from respiratory diseases and cancers, while others have experienced mental health conditions such as anxiety, depression, and post-traumatic stress.

Twenty-five years after the attacks, these health problems continue to affect survivors and responders. As many of those who worked at Ground Zero grow older, some are now developing new medical conditions or seeing existing problems become more serious.

Retirement can also create additional emotional challenges. People who spent years working and staying active may find that retirement gives them more time to think about their experiences. Important anniversaries, including September 11, can bring back painful memories and emotions connected to the attacks.

Jodi Streich, a mental health director at the World Trade Center Health Program in New Jersey, has pointed out that these emotional effects do not simply disappear after the anniversary. Memories and feelings connected to the tragedy can return even many years later.

The World Trade Center Health Program was created to provide medical monitoring and treatment to people affected by the September 11 disasters. The program supports rescue and recovery workers, cleanup crews, and people who lived or worked near the World Trade Center and other attack locations.

As of 2026, more than 154,000 people are enrolled in the program. Its funding is expected to continue through 2090, allowing affected people to receive medical care for many years.

The continuing work of the program shows that the effects of September 11 did not end when the attacks were over. For many survivors and responders, the physical and emotional consequences have lasted for decades.

Twenty-five years later, healthcare providers continue to support those affected by the tragedy. Their work remains important as an aging generation of responders and survivors faces new health challenges connected to one of the darkest moments in modern American history.

The Round 2 allotment is an important step for students seeking admission to medical and dental courses through the NEET UG counselling process. Candidates will be given seats based on several factors, including their NEET rank, choices filled during counselling, category, and availability of seats.

Once the results are released, candidates should carefully check the details shown in their allotment result. Those who have been allotted a seat will need to complete the admission process within the given deadline.

Reporting Dates for Candidates

Candidates who receive a seat in Round 2 must report to their allotted colleges between September 12 and September 18, 2026. They will have to complete the required admission formalities and provide the necessary documents to the college.

Medical colleges will then verify the admission details of the candidates on September 19, 2026. Students are advised not to wait until the final date to report, as completing the process early can help avoid last-minute problems.

How to Check the NEET UG Round 2 Result

Candidates can check their allotment status online by visiting the MCC website. They will need to log in using the registration details used during the counselling process.

After logging in, candidates should look for the Round 2 seat allotment result and check whether a medical or dental seat has been allotted to them. They should also download or save a copy of the result for future admission requirements.

30 Additional Seats Added

The MCC has also added 30 new seats during Round 2 of counselling. These additional seats provide more opportunities for candidates who are participating in the admission process.

Bagalkote Medical College and Research Institute received 15 of the newly added seats. Candidates were allowed to consider these seats while making their choices during the counselling process.

The addition of new seats could benefit students who are waiting for better admission opportunities. Candidates should carefully review their allotment and follow all instructions provided by the MCC and their respective colleges.

With the Round 2 results being released, candidates who receive seats must pay close attention to the reporting and verification deadlines. Missing the required deadlines could affect the admission process.

Students are therefore advised to regularly check the official MCC website for updates and follow the instructions given in their allotment result. Completing each step on time will help candidates secure their admission without unnecessary delays.

Malaria is caused by a parasite that is spread to people through the bites of infected mosquitoes. For many years, West and Central Africa have recorded some of the highest levels of malaria because the region has generally provided suitable temperatures and rainfall for both mosquitoes and the parasite.

However, scientists say climate change is beginning to change these conditions. As temperatures rise, some areas that were previously suitable for malaria transmission may become less favourable for mosquitoes. At the same time, warmer conditions could make some areas farther east and south more suitable.

Researchers studied data covering more than a century to understand how climate conditions may have affected malaria cases across Africa. Climate scientists used information from blood samples and developed models that connected malaria levels with factors such as temperature and rainfall.

The researchers then compared the results with a model showing what malaria patterns might have looked like in a world without human-caused climate change. This comparison helped them estimate the possible influence of global warming on the spread of the disease.

The study found that between 1901 and 2014, climate change likely caused a small overall increase in malaria cases across Africa. However, the impact was not the same everywhere. Some parts of East and southern Africa experienced greater increases, while some areas in West Africa saw malaria risk decline.

Ethiopia, for example, was among the areas where malaria cases increased as conditions became more suitable for transmission. In contrast, some parts of West Africa may have become less suitable for the mosquitoes and parasites because of changing temperatures.

The researchers also looked ahead to the end of this century. Under a moderate level of global warming, their models suggest that malaria rates across sub-Saharan Africa could fall by around 2% by 2100. However, this overall decline does not mean that every country or region will experience less malaria.

The findings show that climate change can produce very different health effects in different parts of the same continent. Some communities could face a lower risk of malaria, while others may experience an increase as mosquitoes and malaria parasites move into new areas.

The changing pattern could create new challenges for health authorities. Areas that have historically experienced lower levels of malaria may need to prepare for a greater risk if environmental conditions become more suitable for transmission.

At the same time, malaria control programs will continue to be important in regions where the disease remains common. Measures such as mosquito control, bed nets, early diagnosis and effective treatment can help reduce the impact of malaria.

The study highlights that climate change is not simply making the planet warmer. It is also changing environmental conditions that affect diseases and the people who are exposed to them.

Overall, the research suggests that global warming is reshaping the distribution of malaria across Africa. While the total number of cases may change only slightly under some future climate scenarios, the movement of malaria risk between regions could have major consequences for millions of people and public health systems across the continent.

It’s possible, but unlikely. According to Joy Reidenberg, an expert on whale anatomy, a very large adult sperm whale could accidentally swallow a person. These whales can grow over 18 meters long, much bigger than most we see today. However, other large whales like fin whales wouldn’t be able to swallow someone because their throats are too narrow. Reidenberg knows this from studying whale carcasses—she barely fits her arm down their throats.

Baleen whales, including fin whales, feed on tiny creatures like krill and plankton by filtering water through baleen plates. This creates a slurry they “drink,” unlike the way toothed whales like sperm whales hunt large prey.

In rare cases, people have been caught by baleen whales while they were hunting. For example, in 2019, a Bryde’s whale briefly grabbed a photographer off South Africa before letting go. These incidents are accidental and not intentional hunting.

Sperm whales, on the other hand, hunt giant and colossal squid, which can be up to 14 meters long. While they could theoretically swallow a person, such events are extremely rare.

The Round 2 allotment is an important step for students seeking admission to medical and dental courses through the NEET UG counselling process. Candidates will be given seats based on several factors, including their NEET rank, choices filled during counselling, category, and availability of seats.

Once the results are released, candidates should carefully check the details shown in their allotment result. Those who have been allotted a seat will need to complete the admission process within the given deadline.

Reporting Dates for Candidates

Candidates who receive a seat in Round 2 must report to their allotted colleges between September 12 and September 18, 2026. They will have to complete the required admission formalities and provide the necessary documents to the college.

Medical colleges will then verify the admission details of the candidates on September 19, 2026. Students are advised not to wait until the final date to report, as completing the process early can help avoid last-minute problems.

How to Check the NEET UG Round 2 Result

Candidates can check their allotment status online by visiting the MCC website. They will need to log in using the registration details used during the counselling process.

After logging in, candidates should look for the Round 2 seat allotment result and check whether a medical or dental seat has been allotted to them. They should also download or save a copy of the result for future admission requirements.

30 Additional Seats Added

The MCC has also added 30 new seats during Round 2 of counselling. These additional seats provide more opportunities for candidates who are participating in the admission process.

Bagalkote Medical College and Research Institute received 15 of the newly added seats. Candidates were allowed to consider these seats while making their choices during the counselling process.

The addition of new seats could benefit students who are waiting for better admission opportunities. Candidates should carefully review their allotment and follow all instructions provided by the MCC and their respective colleges.

With the Round 2 results being released, candidates who receive seats must pay close attention to the reporting and verification deadlines. Missing the required deadlines could affect the admission process.

Students are therefore advised to regularly check the official MCC website for updates and follow the instructions given in their allotment result. Completing each step on time will help candidates secure their admission without unnecessary delays.

When a fresh garlic clove is crushed or chopped, it releases a powerful chemical compound called allicin. Allicin is responsible for much of garlic’s strong smell and is produced through a chemical reaction that begins when the garlic cells are damaged.

Inside an intact garlic clove, two important substances, alliin and the enzyme alliinase, are kept separate. When the garlic is crushed, the cells break apart and these substances come into contact with each other. The enzyme then helps convert alliin into allicin.

Allicin is a highly reactive sulfur-containing compound. After garlic is applied to the skin, some of its chemical compounds can interact with the skin and potentially be absorbed. The skin is not a completely sealed barrier, although how much of a substance enters the body depends on several factors, including the chemical itself, its concentration and the condition of the skin.

If garlic compounds enter the bloodstream, they can travel throughout the body. Some sulfur-containing compounds produced when garlic breaks down can eventually reach the lungs and other tissues. This is one reason garlic’s smell can remain on a person’s breath long after eating it.

One compound associated with persistent garlic odor is allyl methyl sulfide. Unlike many food compounds that are quickly broken down and removed from the body, this compound can remain in the bloodstream for some time. It can eventually reach the lungs and be released through breathing, producing the familiar smell known as garlic breath.

This helps explain why garlic-related smells can sometimes seem to come from different parts of the body. However, it is important to understand that tasting garlic after rubbing it on your feet does not mean that the feet have taste receptors connected directly to the mouth.

The sensation is better explained by the movement of volatile sulfur compounds and the way our sense of smell contributes to what we experience as taste. Much of what people describe as “taste” is actually influenced by the sense of smell.

The idea that rubbing garlic on the feet reliably causes a person to taste garlic in their mouth is often presented online as a surprising health fact. However, the exact amount of garlic compounds that can pass through intact skin and produce a noticeable taste sensation is not well established.

There is also an important safety point. Fresh garlic can irritate the skin, especially when it is crushed and left against the skin for an extended period. In some people, direct contact with raw garlic can cause redness, burning, irritation or even a chemical-like skin injury.

Therefore, the garlic-on-the-feet experiment should not be treated as a proven health treatment or a reliable way to deliver garlic compounds into the body. The interesting part of the story is the chemistry of garlic and the way sulfur compounds can produce strong smells throughout the body.

In short, you do not have hidden taste buds in your feet. If garlic-related sensations occur after skin contact, they are linked to chemical compounds in garlic and the body’s ability to absorb and process certain substances. The famous garlic smell is largely connected to sulfur-containing compounds produced when garlic is crushed, eaten or metabolized.

The problem is considered one of the biggest unanswered questions in modern mathematics. Because of its importance, the Clay Mathematics Institute placed it among the seven Millennium Prize Problems and offered a $1 million prize for a correct solution.

The Navier-Stokes equations are used to describe how fluids such as water and air move. They take into account factors including pressure, density and speed. Scientists use these equations in many areas, including weather forecasting, ocean studies, engineering and aircraft design.

The main question is whether solutions to the Navier-Stokes equations always remain smooth and well-behaved. In simple terms, mathematicians want to know whether the equations can always produce reasonable results or whether they can suddenly develop a mathematical singularity, where quantities become infinitely large.

On September 8, OpenAI announced that its researchers had obtained a solution to the Navier-Stokes problem. The announcement attracted considerable attention because solving the problem would represent a major achievement in mathematics.

The announcement came shortly after mathematicians Tristan Buckmaster and Levent Alpöge reported important progress on a related problem involving the Euler equations. The Euler equations are closely connected to the Navier-Stokes equations but are somewhat simpler because they do not include the effects of viscosity.

Buckmaster and Alpöge used AI-based methods, including models developed by OpenAI, in their work. Their research examined whether solutions to the Euler equations could “blow up.” In mathematics, this means that certain values could become infinitely large in a finite amount of time instead of remaining under control.

Their findings attracted attention because they showed how AI could potentially help mathematicians investigate extremely complicated mathematical questions. The work also led to speculation about whether the research had influenced OpenAI’s subsequent work on the Navier-Stokes problem.

OpenAI reportedly used thousands of AI agents to investigate the Navier-Stokes equations. The systems were able to explore large numbers of possible mathematical approaches much faster than a human researcher could do alone.

However, the announcement has also created debate within the mathematical community. Experts are discussing the exact nature of OpenAI’s result and whether it meets the very strict standards required for a formal mathematical proof. A mathematical solution to such a famous problem must be carefully checked by independent experts before it can be widely accepted.

There are also questions about timing. Some researchers have wondered whether OpenAI had access to or was influenced by the findings of Buckmaster and Alpöge before announcing its own work. These questions have added another layer of controversy to the story.

Despite the debate, the development shows the growing role of artificial intelligence in advanced mathematical research. AI can examine large numbers of possibilities, identify patterns and suggest approaches that researchers may not immediately consider.

The Navier-Stokes problem has challenged mathematicians for generations because of its connection to the basic laws governing fluid movement. A fully verified solution would be a landmark achievement not only for mathematics but also for the growing field of AI-assisted scientific research.

For now, experts will continue to examine the claims carefully. If the result is independently verified as a complete solution, it could mark an important moment in the history of mathematics and demonstrate how AI can contribute to solving some of science’s most difficult problems.

The findings were published in Nature Medicine. Scientists say the results are interesting because the shingles vaccine was developed to protect people from shingles, not heart disease. The possible heart-related benefit was an unexpected finding that could lead to more research.

Shingles is a painful illness that causes a rash and blisters. It is caused by the same virus that causes chickenpox. After a person recovers from chickenpox, the virus can remain inactive in the body and become active again years later, causing shingles.

Around one million people in the United States develop shingles each year. The illness can cause severe pain, and some people can continue to experience nerve pain even after the rash disappears.

The first shingles vaccine used a weakened form of the virus to help the immune system fight the infection. However, that vaccine was discontinued in 2017. Shingrix, the newer vaccine, works differently. It uses a small piece of a protein from the virus rather than using the whole virus.

Researchers wanted to understand whether the difference between the two vaccines could have other effects on people’s health. They compared health records from people who received the older vaccine in 2017 with records of people who received Shingrix in 2018.

The researchers followed the health information of these groups for about seven years. Their findings showed that people who received Shingrix had a lower rate of major heart-related problems.

According to the study, the Shingrix group had about 1.3% fewer cases of serious heart problems. These included heart failure, heart attacks and strokes.

When the results were compared for every 1,000 people, there were about 96 cases of heart problems among those who received Shingrix. In comparison, the older vaccine group had around 109 cases.

Scientists are still trying to understand why a vaccine designed to prevent shingles might also be linked to better heart health. One possibility is that preventing or reducing the effects of the shingles virus could have an impact on inflammation and blood vessels. However, researchers say this explanation has not yet been confirmed.

The findings have raised another important question: Could the shingles vaccine have benefits for blood vessels in other parts of the body? Scientists are interested in studying whether the vaccine could potentially reduce the risk of other conditions connected to blood vessel health.

However, experts caution that the study does not prove that Shingrix directly prevents heart disease. The research was based on health records and compared different groups of vaccinated people. Other factors could have influenced the results.

More studies will be needed to confirm the findings and understand the biological reasons behind them. Researchers may also need to conduct further investigations to determine whether the possible heart benefits are directly caused by the vaccine.

For now, the main purpose of the shingles vaccine remains preventing shingles and its complications. The possible protection against heart problems is an interesting additional finding that scientists will continue to investigate.

If future research confirms the connection, the discovery could make the shingles vaccine even more important for eligible adults. It could also provide scientists with new information about the relationship between viral infections, inflammation and heart health.

The discovery was made at Bianfu Cave, an archaeological site located in Yunnan Province. The cave was found at an abandoned quarry and has produced a large collection of ancient human fossils, animal remains and stone tools. Researchers say the findings could help them understand how Denisovans lived, what they ate and how they used their surroundings.

Denisovans were an ancient human group that lived across parts of Asia between about 400,000 and 30,000 years ago. They were closely related to modern humans and Neandertals. However, unlike Neandertals, Denisovans have left behind very few known fossils.

Researchers recently examined fossil fragments from Bianfu Cave using advanced scientific methods. Protein analysis and X-ray scans showed that the remains belonged to at least three Denisovans. The individuals are believed to have lived between about 167,000 and 134,000 years ago.

The discovery is especially important because the human remains were found together with other archaeological evidence. More than 1,300 stone tools were recovered from the site. These tools could provide information about the activities Denisovans carried out in the area and how they adapted to their environment.

Animal bones were also discovered at the cave. Some of the bones showed marks that suggest the animals had been butchered. This evidence could indicate that Denisovans hunted or processed animals for food, although researchers will need to study the remains further to understand exactly what happened at the site.

Paleoanthropologist Shara Bailey of New York University said the discovery provides valuable information about how Denisovans lived on the landscape. She noted that Denisovans are becoming less mysterious as researchers uncover more physical evidence about them.

Denisovans were first identified in 2010. Scientists studied DNA from a tooth and a finger bone discovered in Denisova Cave in Siberia. The genetic evidence showed that the remains belonged to a previously unknown group of ancient humans.

Since that discovery, scientists have found evidence that Denisovans had a much wider influence than the small number of fossils might suggest. DNA inherited from Denisovans is present in some modern human populations, including people in parts of the Philippines, Tibet, New Guinea and Australia.

Their genetic influence makes Denisovans an important part of human history. However, understanding their daily lives has been difficult because so few fossils have been discovered. Scientists have had limited opportunities to study Denisovan bones together with tools, animal remains and other evidence from the same location.

This lack of archaeological evidence has been a major problem for researchers. Bence Viola, a paleoanthropologist at the University of Toronto, described the situation as frustrating because scientists have learned much more about Denisovans through genetics than through traditional archaeological discoveries.

The Bianfu Cave findings could begin to change that situation. Because human remains were discovered alongside tools and butchered animal bones, researchers now have a better opportunity to connect Denisovans with specific activities and environments.

The discovery may also help scientists understand how Denisovans survived in southwestern China thousands of years ago. By studying the tools, animal remains and cave environment together, researchers can build a clearer picture of their behavior and lifestyle.

Scientists are expected to continue examining the fossils and archaeological materials from the site. Further research could reveal more about Denisovan diets, technology, movement and relationship with the environment.

Overall, the Bianfu Cave discovery is an important step in understanding one of the least-known groups in human evolution. Denisovans may have disappeared tens of thousands of years ago, but their genetic legacy remains in some modern populations. New archaeological discoveries such as this one could finally help scientists understand the people behind that genetic legacy.