Science
Masaki Kashiwara, Japanese Mathematician, Wins 2025 Abel Prize
Masaki Kashiwara, a Japanese mathematician, received this year’s Abel Prize, which aspires to be the equivalent of the Nobel Prize in math. Dr. Kashiwara’s highly abstract work combined algebra, geometry and differential equations in surprising ways.
The Norwegian Academy of Science and Letters, which manages the Abel Prize, announced the honor on Wednesday morning.
“First of all, he has solved some open conjectures — hard problems that have been around,” said Helge Holden, chairman of the prize committee. “And second, he has opened new avenues, connecting areas that were not known to be connected before. This is something that always surprises mathematicians.”
Mathematicians use connections between different areas of math to tackle recalcitrant problems, allowing them to recast those problems into concepts they better understand.
That has made Dr. Kashiwara, 78, of Kyoto University, “very important in many different areas of mathematics,” Dr. Holden said.
But have uses been found for Dr. Kashiwara’s work in solving concrete, real-world problems?
“No, nothing,” Dr. Kashiwara said in an interview.
The honor is accompanied by 7.5 million Norwegian kroner, or about $700,000.
Unlike Nobel Prize laureates, who are frequently surprised with middle-of-the-night phone calls just before the honors are publicly announced, Dr. Kashiwara has known of his honor for a week.
The Norwegian academy informs Abel Prize recipients with ruses similar to those used to spring a surprise birthday party on an unsuspecting person. “The director of my institute told me that there is a Zoom meeting at 4 o’clock in the afternoon, and please attend,” Dr. Kashiwara recalled in an interview.
On the video teleconference call, he did not recognize many of the faces. “There were many non-Japanese people in the Zoom meeting, and I’m wondering what’s going on,” Dr. Kashiwara said.
Marit Westergaard, secretary general of the Norwegian academy, introduced herself and told Dr. Kashiwara that he had been chosen for the year’s Abel.
“Congratulations,” she said.
Dr. Kashiwara, who was having trouble with his internet connection, was initially confused. “I don’t completely understand what you said,” he said.
When his Japanese colleagues repeated the news in Japanese, Dr. Kashiwara said: “That is not what I expected at all. I’m very surprised and honored.”
Growing up in Japan in the postwar years, Dr. Kashiwara was drawn to math. He recalled a common Japanese math problem known as tsurukamezan, which translates as the “crane and turtle calculation.”
The problem states: “There are cranes and turtles. The count of heads is X and the count of legs is Y. How many cranes and turtles are there?” (For example, for 21 heads and 54 legs, the answer is 15 cranes and six turtles.)
This is a simple algebra word problem similar to what students solve in middle school. But Dr. Kashiwara was much younger when he encountered the problem and read an encyclopedia to learn how to come up with the answer. “I was a kid, so I can’t remember, but I think I was 6 years old,” he said.
In college, he attended a seminar by Mikio Sato, a Japanese mathematician, and was fascinated by Sato’s groundbreaking work in what is now known as algebraic analysis.
“Analysis, that is described by the inequality,” Dr. Kashiwara said. “Something is bigger or something is smaller than the other.” Algebra deals with equalities, solving equations for some unknown quantity. “Sato wanted to bring the equality world into analysis.”
Phenomena in the real world are described by real numbers like 1, –4/3 and pi. There are also what are known as imaginary numbers like i, which is the square root of –1, and complex numbers, which are sums of real and imaginary numbers.
Real numbers are a subset of complex numbers. The real world, described by the mathematical functions of real numbers, “is surrounded by a complex world” involving functions of complex numbers, Dr. Kashiwara said.
For some equations with singularities — points where the answers turn into infinity — looking at the nearby behavior with complex numbers can sometimes provide insight. “So the inference from the complex world is reflected to the singularities in the real world,” Dr. Kashiwara said.
He wrote — by hand, in Japanese — a master’s thesis using algebra to study partial differential equations, developing techniques that he would employ throughout his career.
Dr. Kashiwara’s work also pulled in what is known as representation theory, which uses knowledge of symmetries to help solve a problem. “Imagine you have a figure drawn on the floor,” said Olivier Schiffmann, a mathematician at the University of Paris-Saclay and the French National Center for Scientific Research. “Unfortunately, it is all covered in mud and all you can see is, say, a 15-degree sector of it.”
But if one knows that the figure remains unchanged when rotated by 15 degrees, one can reconstruct it through successive rotations. Because of the symmetry, “I only need to know a small part in order to understand the whole,” Dr. Schiffman said. “Representation theory allows you to do that in much more complex situations.”
Another invention of Dr. Kashiwara’s was called crystal bases. He drew inspiration from statistical physics, which analyzes critical temperatures when materials change phases, like when ice melts to water. The crystal bases allowed complex, seemingly impossible calculations to be replaced with much simpler graphs of vertices connected by lines.
“This purely combinatorial object in fact encodes a lot of information,” Dr. Schiffmann said. “It opened up a whole new area of research.”
Confusingly, however, the crystals of crystal bases are completely different from the sparkly faceted gemstones that most people think of as crystals.
“Perhaps crystal is not a good word,” Dr. Kashiwara admitted.
Dr. Holden said Dr. Kashiwara’s work was difficult to explain to non-mathematicians, because it was much more abstract than that of some earlier Abel prize laureates.
For example, the research of Michel Talagrand, last year’s laureate, studied randomness in the universe like the heights of ocean waves, and the work of Luis Caffarelli, who was honored two years ago, can be applied to phenomena like the melting of a piece of ice.
Dr. Kashiwara’s work is more like tying together several abstract ideas of mathematics into more abstract combinations that are insightful to mathematicians tackling a variety of problems.
“I think it’s not easy,” Dr. Kashiwara said. “I’m sorry.”
Dr. Holden pointed to one particular work, in which Dr. Kashiwara deduced the existence of crystal bases, as a “masterpiece of a theorem,” with 14 steps of induction, using inference to recursively prove a series of assertions.
“He has to solve one by solving the others, and they’re all connected,” Dr. Holden said. “And if one falls, the whole thing falls. So he is able to combine them in a very deep and very clever way.”
But Dr. Holden said he could not provide a simple explanation of the proof. “That’s hard,” he said. “I can see the 14 steps.”
Days before the 2024 presidential election, future Health and Human Services Secretary Robert F. Kennedy Jr. posted a statement on X promising to end the U.S. Food and Drug Administration’s “aggressive suppression” of such alternative therapies as raw milk, ivermectin, psychedelics and, somewhat perplexingly, “sunshine.”
While the post did not explain how the FDA was limiting Americans’ access to the sun, many dermatologists were dismayed when Kennedy abruptly withdrew a proposed FDA rule that would have banned minors from using devices that mimic sunlight — indoor tanning lamps.
The rule, which was withdrawn March 16, would have also required indoor tanning facility users to sign a form acknowledging the risk of cancer, early skin aging and other health effects.
Kennedy’s action comes at a time when many adherents of his Make America Healthy Again movement have adopted regular sun exposure as a core principle of wellness, with social media influencers encouraging followers to abandon sunscreen and build up their “solar callus,” or sun tolerance, instead.
The trend has frustrated many dermatologists, who warn that the damage of frequent sunburns and tans accumulates over a lifetime, and those acquired early in life appear to play a disproportionate role in later risk of skin cancer. The Skin Cancer Foundation notes also that you cannot build up a tolerance to sun exposure and “there is no such thing as a ‘solar callus.’”
Dermatologists have long cautioned that indoor tanning lamps are no less dangerous, since they expose users to ultraviolet light at concentrations far above natural sunlight. Like sunlight, the lamps emit two different types of ultraviolet wavelengths: UVA, which are longer and penetrate more deeply into the skin, and UVB, which are shorter and more easily burn the outer layers.
Both light sources darken skin through the same biological process: UV rays change the structure and chemical profile of DNA in the skin, which then produces more melanin in order to prevent further damage.
A tanning bed session exposes users to UVB rays akin to those at noon at the equator — an intense experience, but at least one with a terrestrial equivalent, said Hunter Shain, an associate professor of dermatology at UC San Francisco. The UVA radiation in a tanning bed is roughly 15 times that found anywhere on the surface of the planet.
“They’re really blasting you with these super physiological doses of UV radiation that you couldn’t even find in a natural environment,” he said.
The World Health Organization counts UV-emitting tanning beds as a Group 1 carcinogen, alongside other known human carcinogens like tobacco cigarettes and asbestos. One study Shain co-authored found that tanning beds accelerate DNA mutations in parts of the body not typically exposed to the sun, leading to a nearly threefold increase in indoor tanners’ lifetime melanoma risk. Rates of melanoma diagnoses have increased by 46% in the last decade.
The tanning lamp rule, which was first proposed in 2015, focused on age as a specific risk factor. Tanning bed usage before the age of 35 is associated with a 75% increase in the risk of melanoma, the most serious and frequently fatal form of skin cancer.
The rule drew more than 9,000 public comments from both physicians and cancer research organizations supporting its implementation and from tanning bed industry representatives and business owners opposed.
Kennedy, who was photographed leaving a Washington tanning salon last year, was ultimately unconvinced of the need to ban minors from such establishments.
“In light of the scientific and technical concerns raised in the comments on the Proposed Rule, concerns regarding possible unintended consequences of certain proposals in the Proposed Rule, and potential alternatives proposed in comments received on the Proposed Rule, FDA is withdrawing the Proposed Rule in order to reconsider the best means for addressing the issues,” Kennedy wrote in the withdrawal letter.
Health and Human Services did not respond to questions about what scientific concerns and unintended consequences Kennedy was referring to.
Nineteen states (including California) and the District of Columbia have already banned people under 18 from indoor tanning salons. Roughly two dozen more have some kind of regulations regarding minors and indoor tanning, such as requiring parental permission or barring only younger children.
The collapse of the proposed federal ban has left many dermatologists disappointed.
“As you can see, when it’s left to the states, the implementation and the guardrails to minimize the exposure to carcinogens are not consistent. … Why are you going to default to a system that we know isn’t working correctly?” said Dr. Clara Curiel-Lewandrowski, chair of dermatology and co-director of the Skin Cancer Institute at the University of Arizona.
Minors in sun-baked Arizona are free to patronize indoor tanning establishments as long as they have a note from their parents. Curiel-Lewandrowski has treated many former sunbed enthusiasts for advanced melanoma in their 20s and 30s, she said.
“There’s a lot of regret. Regret for not knowing more, for not getting more help to understand the threat,” she said. “This is an age group that has a very hard time assessing risk. At that age, they don’t view carcinogens as a real threat.”
The U.S. is a bit of an outlier in its permissive approach to youth indoor tanning. Australia and Brazil have banned cosmetic indoor tanning entirely for people of all ages. Most western European countries ban minors from indoor tanning, as do most Canadian provinces.
“After the proposal lay dormant for more than a decade, I can’t say I was surprised to hear that the FDA withdrew it,” said Dr. Deborah S. Sarnoff, president of the Skin Cancer Foundation. “On the positive side, we made the public very aware of this issue, and this fight is far from over. We won’t be satisfied until tanning beds are banned in this country.”
Over the next month, if you take a ferry from the center of Venice to the island of Giudecca and walk into a former 15th-century convent, you will find yourself figuratively plunging underwater.
The haunting songs of humpback whales will flow around you. A fish will sing its evensong from the sea grass meadows of the Mediterranean. Boats recorded from beneath the surface of the Venetian lagoon will buzz like insects. A galaxy of bioluminescent plankton will glimmer in the sloshing waves.
This audiovisual symphony is part of “As Above, So Below,” a collateral exhibit running during the first month of the Venice Biennale, from Saturday through June 8. The exhibition brings together works by seven artists and art collectives who combine cutting-edge science and technology with traditional methods. Their installations surround visitors with natural sounds, merge their perspectives with those of other species and take them on an immersive journey into the sea, the soil and even a tree to highlight humans’ interdependence with the natural world.
As Elizabeth Zhivkova, a co-curator of the exhibition, put it: “‘As Above, So Below’ emerged from a shared urgency to rethink our relationship with nature, not as something separate from us, but as an interconnected system in which human, ecological and cosmic rhythms reflect one another.”
In addition to the exhibition, “As Above, So Below” is an ongoing research project that includes artist residencies and a podcast featuring conversations with artists and ocean advocates.
The project was born out of a partnership between Zeitgeist19, an environmental curatorial collective founded by Zhivkova and the show’s other co-curator, Farah Piriye Coene, and One Ocean Foundation, a scientific conservation organization based in Milan.
The name, “As Above, So Below,” comes from the Principle of Correspondence in Hermeticism, a spiritual tradition that blends Greek and Egyptian philosophies. It serves as a reminder that everything is connected. “The sea, the soil, the atmosphere, the human body are not separate realms; they are part of one relational field,” Coene said. “The exhibition asks whether art can help us feel that relation again.”
The exhibition’s setting in the former convent and church of Santi Cosma e Damiano — now a science and art innovation hub — fosters a contemplative atmosphere. In lieu of a central altarpiece, visitors encounter an immersive installation from the London-based artist collective Marshmallow Laser Feast, titled “Seeing Echoes in the Mind of the Whale.” In the work, a large-screen video immerses viewers in the sensory perspectives of a bottlenose dolphin, a humpback whale and a sperm whale as they dive and resurface to breathe.
The video plays recordings of dolphins’ trilling whistles, humpbacks’ meditative melodies and sperm whales’ Morse code-like clicks, which resonate throughout the space. To illustrate the use of echolocation to “see” through sound, these vocalizations are coordinated with visual effects. Shimmering swirls and pulsating pixels surround you, giving a sense of what bottlenose dolphins might “see” as they sweep sonar beams across colorful coral reefs, or what sperm whales might sense by blasting clicks to spy giant squid in the dark depths.
Ersin Han Ersin, one of the Marshmallow Laser Feast artists, explained in a video interview that the aim was for audiences to “disembody their own body, and momentarily embody what it is like to be a bottlenose dolphin or a whale.”
While visually speculative, the video is rooted in research. The members of the collective pored over scientific papers, compiled extensive hydrophone recordings and underwater videography, and collaborated with marine biologists and bioacousticians to dive into the sensory experiences of whales and dolphins, Ersin said.
In the process, he said, the artists became more sensitive to the ways noise pollution — the squeals of military sonar, the drumming of shipping traffic and the boom of seismic blasting to find fossil fuels — may be turning the ocean into an acoustic dystopia for animals and plants that live underwater.
“One part of me wants to scream that we are ruining these oceans, but the other part of me knows the best action is always cultivated from a place of love,” Ersin said. That is one goal of the installation, he added: To “make people fall in love with species that they never thought they can relate to.”
In another installation, “Fish String Theory,” Antoine Bertin, an artist who splits his time between Paris and Alicudi island, Italy, amplifies the surprisingly talkative world of fish. Bertin was inspired by reports of a “kwa” sound emanating from Mediterranean seagrass meadows. Scientists found that the kwa chorus most likely comes from scorpionfish. These venomous creatures have a muscular apparatus that functions like an internal violin.
Bertin made underwater recordings of scorpionfish and created fish-shaped sculptures with strings. When his recordings of scorpionfish play, the frequencies from the recordings activate electromagnets that vibrate the strings on the fish sculptures, creating a sound similar to a guitar or harp. The installation also includes Bertin’s underwater recordings of the Venetian lagoon, forming a dialogue between the scorpionfish song and the city’s aquatic soundscape.
Bertin is fascinated by the fact that life emerged in primordial seas, and said in an interview that he hoped that his installation would help people “return to the ocean as listeners.” His aim, he added, was to “create an experience that connects humans and fish in a sort of co-presence, to find out if we can resonate together.”
In “Water Older Than the Sun (Caspian),” the Kazakhstan-born artist Almagul Menlibayeva connects viewers to the Caspian Sea, which is shrinking because of climate change and water diversion — and being contaminated by drilling for oil and gas.
Menlibayeva pointed out that modern societies often see water as a resource to be used. She said in an interview that her installation positions water as an archive of deep time and as a “cosmic, alive entity.” As the title suggests, water is older than the sun because this cosmic compound formed as a result of supernovae explosions, then eventually came to Earth and condensed into oceans that gave rise to life. As such, “water has a memory,” Menlibayeva said, adding: “Water witnessed us as we appeared.”
At the center of Menlibayeva’s installation is a textile made from hand-sewn fabrics and A.I.-generated images of her artwork printed on synthetic silk that depict water, animals and robot-like humans. Fishing nets collected from the Caspian Sea dangle around the textile. Screens placed on the floor like a shoreline show surreal images, such as hands sewing water. Projected behind these pieces is “Requiem for the Caspian” by the London-based filmmaker Suad Gara, a short documentary that reveals the impact of the sea’s collapse on local people.
Just inside the entrance of the church, the Azerbaijan-born artist Elnara Nasirli has turned a reclaimed Italian olive tree into an instrument in “Whispering Forest.” Nasirli translated trees’ bioelectric rhythms into music and vibrations that softly play from contact points triggered by motion detection. Only by touching or hugging the tree, or leaning in very close and listening carefully, can visitors fully hear its whispered song.
Also in the exhibition, artworks bring viewers up close to underground mycelial networks, a holographic jellyfish and bioluminescent plankton that spell out “No blue, no green,” a quote from the marine biologist Sylvia Earle about the vital importance of marine ecosystems.
Altogether, the exhibition invites people to attune to the intelligence and voices of other species and, as Bertin said, to “stretch their sense of self to include the vastness of the ocean.”
A suspected outbreak of hantavirus, a rare but deadly disease that attacks the lungs, has left three people dead and several others severely ill aboard a luxury cruise ship.
Here’s what we know about the voyage and the virus that also made headlines last year after it killed Gene Hackman’s 65-year-old wife, Betsy Arakawa.
What’s going on?
Global health officials and the cruise operator, Oceanwide Expeditions, are investigating and working to contain the illnesses suspected to have been brought on by the rodent-borne illness aboard the MV Hondius — a Dutch-flagged ship, according to the World Health Organization.
On Monday, the WHO announced that the luxury ship carrying 147 passengers and crew had two laboratory-confirmed cases and five suspected cases of hantavirus. The three deaths are included in that total.
The cruise ship, which was on a 46-day journey that traveled from Antarctica with stops in Argentina, has remained off the coast of Cape Verde in the Atlantic Ocean. During a news conference, WHO officials said they’re planning to medically evacuate two individuals with suspected infections.
The vessel departed Ushuaia, Argentina, on April 1 and traveled across the Atlantic with multiple stops in remote and ecological diverse regions, according to the WHO.
“The extent of passenger contact with local wildlife during the voyage, or prior to boarding in Ushuaia, remains undetermined,” the organization said in a statement.
What we know about hantavirus
Typically, hantavirus spreads by inhaling particles contaminated with the urine, feces or saliva of wild rodents.
“What we don’t know about this current outbreak is whether someone got onto the ship and was already sick or there were rodents on the cruise,” said Dr. Gaby Frank, director of the Johns Hopkins Special Pathogens Center.
There is, however, a strain of hantavirus that can be spread from human to human, known as the Andes virus, Frank said.
In such a case, a person would first be infected by a wild rodent’s contaminated particles and then, after becoming infected themselves, pass the infection to another person.
There are 50 species of hantavirus. The virus that’s found in the Americas tends to cause a cardiopulmonary syndrome, a condition that affects the heart and the lungs, according to Frank.
There have been 890 laboratory-confirmed cases of hantavirus disease reported in the United States since surveillance began in 1993, according to the most recent data from the U.S. Centers for Disease Control and Prevention.
The data suggest that contracting hantavirus is rare, said Dr. Afif El-Hasan, member of the American Lung Assn.’s national board of directors.
“That being said, it’s probably underdiagnosed because the symptoms are a lot like the flu or other illness,” El-Hasan said. “And a lot of people may have passed away or had hantavirus, but it was never diagnosed.”
There is no vaccine or specific antiviral medicine for hantavirius.
The ICU treatment may include intubation and oxygen therapy, fluid replacement and use of medications to lower blood pressure, according to the American Lung Assn.
Know the signs of hantavirus and next steps
Early symptoms of hantavirus are similar to the flu and include fatigue, fever and muscle aches, according to the CDC. Signs of these symptoms start to show within one to eight weeks after contact with an infected rodent.
Half of those who contract the virus also experience headaches, dizziness, chills, nausea, vomiting, diarrhea and abdominal pain.
Four to 10 days after the initial phase of the illness, another round of symptoms can develop, which include coughing, shortness of breath and possible tightness in the chest as the lungs fill with fluid.
Even though contracting hantavirus in the United States continues to be a rare event, El-Hasan said, people should take these initial symptoms seriously and promptly seek medical care.
Hantavirus can be deadly. CDC officials said 38% of people who develop respiratory symptoms may die from the disease.
How to protect yourself
Hantavirus cases can occur year-round, but the peak seasons in the United States are in the spring and summer, which coincide with the reproductive seasons for deer mice.
To lessen your risk of infection, keep wild rodents out of your home, workplace, shed, cabin, car or other enclosed spaces.
Los Angeles County public health officials offer suggestions on how you can keep rodents at bay, which include:
- Sealing up holes, the width of a pencil or larger, that mice can squeeze into.
- Place snap traps to catch any rodents. The CDC cautions against using glue or live traps because they can scare the rodents, causing them to urinate, which increases your chances of exposure to any virus they may be carrying.
- Store all food items in rodent-proof containers.
If you find evidence of mice in a space that you frequent, local and state officials advise:
- Before you clean, air out the space for 30 minutes. Equip yourself with rubber or plastic gloves, an N-95 mask and a disinfectant or mixture of bleach and water.
- While cleaning, spray the contaminated areas with your disinfectant and let it soak for at least five minutes. Do not sweep or vacuum the area, the movement could stir up the infectious materials in the air. Instead, use paper towels, a sponge or a mop to clean. When you’re done, put everything, including cleaning materials, in a bag and toss it in your trash bin.
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