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.”
A steadfast figure in the anti-vaccine movement who has helped shape Health Secretary Robert F. Kennedy Jr.’s thinking on a possible link to autism has joined his department to work on a study examining the long-debunked theory, according to people familiar with the matter.
The new analyst, David Geier, has published numerous articles in the medical literature attempting to tie mercury in vaccines to autism. In 2012, state authorities in Maryland found that he had been practicing medicine without a license alongside his father, Mark Geier, who was a doctor at the time.
Maryland authorities also suspended Mark Geier’s medical license following claims that he endangered children with autism and exploited their parents, according to state records.
Federal judges have rejected their research on autism and vaccines as too unreliable to stand up in court.
David Geier’s new government role has stunned public health experts, who had already expressed concerns about Mr. Kennedy’s decisions to cancel a long-held vaccine meeting and to cut grants focused on understanding vaccine hesitancy.
In addition, David Geier’s involvement in government research heightens their fears that vaccine confidence could be further eroded, especially after Mr. Kennedy’s recent embrace of questionable alternative treatments for measles during the sprawling outbreak in Texas.
“If we increase vaccine hesitancy and immunization rates go down further, we will see more vaccine-preventable disease outbreaks,” said Dr. Christopher Beyrer, director of the Duke Global Health Institute. “That’s how it works.”
Several experts said that appointing David Geier to work on a study of vaccine safety preordains the outcome — like having a basketball referee show up in one team’s jersey.
“You’d think you’d want a fresh eye,” said Edward L. Hunter, a former head of the Washington office of the Centers for Disease Control and Prevention.
“This isn’t a fresh eye. They have already published their results, and spending all this time and money is not going to help anyone. I am quite certain they’ll come to the same conclusion.”
An official with Mr. Kennedy’s Department of Health and Human Services declined to comment. Two White House spokesmen did not respond to a request for comment. David Geier did not reply to emails or calls requesting comment.
Mary Holland, chief executive of Children’s Health Defense, the anti-vaccine nonprofit Mr. Kennedy ran until his presidential bid, praised David Geier on its website on Wednesday, describing him as “a brilliant, extremely knowledgeable researcher with deep expertise on mercury.”
(Over the weekend, federal officials ordered the nonprofit to remove a mock C.D.C. web page suggesting a link between vaccines and autism.)
David Geier is listed in the Department of Health and Human Services directory as a “senior data analyst.” News of his role in the agency was initially reported by The Washington Post.
Earlier this month, federal officials announced plans for a large study to re-examine whether there was a connection between vaccines and autism. Mr. Trump has voiced support for H.H.S. officials who wanted to revisit the issue, citing increases in autism diagnoses in children over the decades.
About 1 in 36 children have an autism diagnosis, according to C.D.C. data collected in 11 states, compared with 1 in 150 children in 2000.
Many scientists believe the rise is due in part to increased awareness of the disorder and changes in how it is diagnosed by medical professionals, though genetic and environmental factors could be playing a role as well.
The Senate confirmed Mr. Kennedy largely because he won over the chairman of the Senate health committee, Bill Cassidy, Republican of Louisiana, who is a medical doctor and strong proponent of childhood vaccines.
Mr. Cassidy has said that further research into any supposed link between vaccines and autism would be a waste of money and a distraction from studies that might shed light on the “true reason” for the rise in autism rates.
On Thursday, Mr. Cassidy said he wanted confirmation of David Geier’s role, aside from news reports. He mentioned that he had breakfast with Mr. Kennedy on Thursday but said the topic did not come up.
At one of his confirmation hearings, Mr. Kennedy shot back at Mr. Cassidy, citing a study from an ecosystem of vaccine critics that he said proved a connection between vaccines and autism.
David Geier comes from a similar circle of researchers. Along with his father, he played a formative role in Mr. Kennedy’s thinking.
Mr. Kennedy interviewed David Geier for an essay in 2005, “Tobacco Science and the Thimerosal Scandal,” in which he accused the C.D.C. of deliberately hiding vaccine data, under chapter headings like “Conspiracy” and “The Cover-Up.”
Mr. Kennedy described the Geiers’ belief that thimerosal, a mercury-containing preservative used in some vaccines, was linked to childhood autism. The preservative has since been removed from most childhood vaccines but is still used in some flu shots.
In a Rolling Stone article called “Deadly Immunity,” Mr. Kennedy credited the Geiers with being among the few who had gained access to C.D.C. vaccine data, which he said they used to “demonstrate a powerful correlation between thimerosal and neurological damage in children.” (The magazine later withdrew the article, but did not elaborate.)
Almost a decade later, in Mr. Kennedy’s book, “Thimerosal: Let The Science Speak,” he paid homage to the Geiers, mentioning them nearly 250 times. He called them a “father-and-son team of independent medical researchers” who had “published extensively on the topic of thimerosal and its potential link to neurodevelopmental disorders, particularly autism.”
Mr. Kennedy acknowledged that the two had become “lightning rods of controversy in the vaccine safety debate.”
“The Geiers have published no fewer than thirteen epidemiological studies of the associations between Thimerosal and health effects in U.S. populations, employing accepted statistical practices,” Mr. Kennedy wrote in the book.
On a podcast in 2022, Mr. Kennedy credited the Geiers’ research for showing that vaccines “had nothing to do with” a decline in infectious diseases over decades. “It was all an illusion,” Mr. Kennedy said, attributing the decrease to improving sanitation and nutrition.
The Geiers’ work has been repeatedly discredited by other scientists and federal court decisions.
An extensive review of the purported link between vaccines and autism in 2004 by the Institute of Medicine, an elite group of doctors and researchers, panned the Geiers’ studies. The review found their work to be marred by flaws “making their results uninterpretable.”
The institute’s report on a connection with the measles shots said: “The committee concludes that the evidence favor rejection of a causal relationship between M.M.R. vaccine and autism.”
In 2011, the Maryland Medical Board accused David Geier of practicing medicine without a license alongside his father at a Rockville, Md., clinic for children with autism.
One mother of a 10-year-old boy with autism balked when David Geier reportedly ordered 24 different blood tests for her son.
His father, Mark Geier, lost his medical license in 2012. Records in that case indicate that both father and son promoted a theory that thimerosal caused autism.
State authorities found that the Geiers had offered treatment with puberty-blocking drugs. To some patients, they offered chelation, a procedure to remove heavy metals from the blood, records show. David Geier was assessed a $10,000 fine.
Judges have rejected the Geiers’ efforts to serve as experts on vaccine safety in court. Records show that judges challenged the father-son team’s billings for hundreds of thousands of dollars related to services they provided as experts for a specialized vaccine injury court.
The judges cited David Geier’s lack of qualifications, which include a bachelor’s degree in biology, and raised concerns about his father’s credibility.
Judge George L. Hastings Jr. said in 2016 that David Geier was not qualified to render an expert opinion in a National Vaccine Injury Compensation court case.
Judge Hastings said his report “is neither useful nor relevant, because he is not qualified as an expert concerning the matters he discusses.”
In a review of two Geier studies this week, Jeffrey S. Morris, director of the division of biostatistics at the University of Pennsylvania, said he found what appeared to be a numerical sleight of hand that made it appear that vaccines caused a spike in autism.
“When I look at these two studies, they are so fatally flawed that I have serious concerns that any study that they’re going to design is going” to be rigorous enough, he said, “to yield valid results.”
To Mr. Hunter, formerly of the C.D.C., the decision to spend federal funds on a new study of a debunked theory would come at the cost of a meaningful discovery.
Since he became health secretary, Mr. Kennedy has presided over cutbacks involving research into nearly every aspect of health care and diseases. On Thursday, he announced a massive reorganization and reduction in the work force from 82,000 to 62,000.
“To me, the big shame is that with budget cuts, we are not ramping up research into what is actually causing autism,” Mr. Hunter said. “And if you are worried about vaccine-preventable disease, this is such a clear setback.”
Michael Gold contributed reporting from Washington. Alain Delaquérière contributed research. Jeremy Singer-Vine provided data analysis.
Statements from the Trump administration that officials are considering cuts to key programs for the prevention of HIV and AIDS are generating outrage among two of the largest LGBTQ+ service organizations in Southern California.
Leaders of the LGBT Center in Los Angeles and DAP Health in the Coachella Valley said that a sharp cut in the Centers for Disease Control and Prevention’s Division of HIV Prevention could endanger many lives and potentially drive up the long-term cost to taxpayers, if incidence of the virus that causes AIDS increases.
When the Wall Street Journal first broke news of the potential cut in mid-March, a spokesman said no “final decision” had been made “on streamlining CDC’s HIV Prevention Division.”
Asked this week for an update, CDC spokesman Nicholas Spinelli referred questions to the agency’s parent organization, the Department of Health and Human Services, which did not respond. The White House also did not respond to a request for comment Friday.
Health agencies across the nation have helped drive down the incidence of HIV, largely through testing, counseling and the distribution of medications that prevent the spread of the disease. Much of the funding for that work came from the Centers for Disease Control and Prevention. The rate of decline was 12% nationally between 2018 and 2022, with an even sharper 21% in the 50 local areas where the CDC focused its prevention efforts.
The LGBT Center in Los Angeles, which provides outreach, testing and HIV-preventative medications, said it has been left in limbo about what will become of its $450,000 CDC grant to support that work.
“We have seen tremendous gains in the fight to end HIV because of the real investments that have been made in prevention and care,” said Joe Hollendoner, CEO of the LGBT Center. “We’ve even been talking about how, in our lifetime, we could end the HIV epidemic and get to zero new cases.”
“But if we are terminating HIV prevention contracts in the way that we anticipate … it is not hyperbole to say it’s going to cost human lives.”
That echoed concerns voiced by DAP Health, which operates 25 clinics in Riverside and San Diego counties, including many in the Coachella Valley, which has a large gay population and where the HIV rate is four times the national average.
“This ‘cost-saving’ strategy of decimating the CDC’s HIV prevention program will only increase costs, both human and financial,” David Brinkman, the CEO of DAP Health, said in a statement.
Brinkman pointed to research that showed the average cost of lifetime treatment for a patient who contracts HIV to be about $500,000 a year. The estimated potential “savings” of $1.8 billion if the federal disease agency eliminates the HIV program would quickly disappear if more than 3,600 Americans were newly infected, Brinkman said, adding: “And we know the toll of lives impacted by HIV with this slashing will be in the tens of thousands.”
An outspoken voice against a possible reduction or elimination of the anti-HIV program is Rep. Raul Ruiz (D-Palm Desert), a former emergency room doctor who represents the Coachella Valley.
“The CDC’s Division of HIV Prevention plays a vital role in reducing new infections, saving billions in preventable health care costs, and ensuring that individuals can access life-saving medication,” Ruiz said in a statement.
Ruiz noted that the CDC program also plays a central role in responding to viral hepatitis and TB. The congressman joined 100 other Democrats in the House and Senate in sending a letter to President Trump, urging him to reconsider any plan to reduce or eliminate the disease prevention program.
The lawmakers reminded Trump that during his first term, in 2019, he declared the goal of ending the HIV epidemic. “One of the pillars of your initiative, as shown on CDC’s website, is prevention,” the letter said. “It is imperative that you uphold this commitment.”
C.J. Tobe, chief transformation officer for DAP Health, said the Trump administration’s potential change of course seemed inexplicable.
“It’s a 180-degree turn, to threaten to take this away,” Tobe said. “It feels personal and it makes zero sense.”
Confusion and turmoil have also enveloped U.S. government-supported research around HIV.
CNN reported this week that the National Institutes of Health had eliminated funding for dozens of HIV-related research grants. The news outlet cited a Department of Health and Human Services database and quoted scientists who said the cuts would also deal a crippling blow to the goal of ending HIV.
Among those on the chopping block were grants related to PrEP, the regimen of drugs that can thwart HIV infection, scientists told the New York Times.
Funding for intervention against the disease overseas also appeared endangered when the Trump administration froze foreign aid and then all but eliminated the U.S. Agency for International Development, the main American agency for delivering assistance to other countries.
A study published in the Lancet said that a reduction in support from the U.S. and other major funding countries could lead to 4.4 million to 10.7 million new HIV infections worldwide by 2030, killing 770,000 to nearly 3 million more people.
“Unmitigated funding reductions could significantly reverse progress in the HIV response by 2030, disproportionately affecting sub-Saharan African countries and key and vulnerable populations,” the study said.
Many people use a smartwatch to monitor their cardiovascular health, often by counting the number of steps they take over the course of their day, or recording their average daily heart rate. Now, researchers are proposing an enhanced metric, which combines the two using basic math: Divide your average daily heart rate by your daily average number of steps.
The resulting ratio — the daily heart rate per step, or DHRPS — provides insight into how efficiently the heart is working, according to a study conducted by researchers at the Feinberg School of Medicine at Northwestern University and published today in the Journal of the American Heart Association.
The study found that people whose hearts work less efficiently, by this metric, were more prone to various diseases, including Type II diabetes, hypertension, heart failure, stroke, coronary atherosclerosis and myocardial infarction.
“It’s a measure of inefficiency,” said Zhanlin Chen, a third-year medical student at the Feinberg School of Medicine at Northwestern University and lead author of the new study; his coauthors included several Feinberg faculty physicians. “It looks at how badly your heart is doing,” he added. “You’re just going to have to do a tiny bit of math.”
Some experts said they saw wisdom in DHRPS as a metric. Dr. Peter Aziz, a pediatric cardiologist at the Cleveland Clinic, said it appeared to be an advance on the information provided by daily steps or average heart rate alone.
“What is probably more important for cardio fitness is what your heart does for the amount of work it has to do,” he said. “This is a reasonable way to measure that.”
The metric does not look at heart rate during exercise. But, Dr. Aziz said, it still provided an overall sense of efficiency that, importantly, was shown by researchers to have an association with disease.
The size of the study added validity to the findings, Dr. Aziz said. The scientists mapped Fitbit data from nearly 7,000 Smartwatch users against electronic medical records.
Mr. Chen said that a simple way to grasp the value of the new metric was to compare two hypothetical individuals. Both take 10,000 steps a day, but one has an average daily resting heart rate of 80 — in the middle of the healthy range — while the other’s daily resting heart rate is 120.
The first person would have a DHRPS of 0.008, the second 0.012. The higher the ratio, the stronger the signaling of cardiac risk.
In the study, the 6,947 participants were divided into three groups based on their ratios; those with the highest showed a stronger association with disease than other participants did. The D.H.R.P.S. metric was also better at revealing disease risk than were step counts or heart rates alone, the study found.
“We designed this metric to be low-cost and to use data we’re already collecting,” Mr. Chen said. “People who want to be in charge of their own health can do a little bit of math to figure this out.”
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