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Masaki Kashiwara, Japanese Mathematician, Wins 2025 Abel Prize

Published

1 year ago

March 26, 2025

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.”

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Science

Video: NASA’s Artemis II Crew Returns to Houston After Lunar Mission

Published

7 hours ago

April 12, 2026

Press Room

Video: NASA’s Artemis II Crew Returns to Houston After Lunar Mission

new video loaded: NASA’s Artemis II Crew Returns to Houston After Lunar Mission

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NASA’s Artemis II Crew Returns to Houston After Lunar Mission

After splashing down in the Pacific Ocean, the Artemis II crew members reunited with their friends, families and fellow NASA astronauts in Houston on Saturday. Their voyage was the first trip by humans into deep space in more than half a century.

: “Your Artemis II crew.” “I have not processed what we just did, and I’m afraid to start even trying. The gratitude of seeing what we saw, doing what we did and being with who I was with, it’s too big to just be in one body.” “Before you launch, it feels like it’s the greatest dream on Earth. And when you’re out there, you just want to get back to your families and your friends. It’s a special thing to be a human, and it’s a special thing to be on planet Earth.” “When we saw tiny Earth, people asked our crew what impressions we had. Earth was just this lifeboat hanging undisturbingly in the universe.” “Splashdown! Sending post landing command now.” “Splashdown confirmed.” “When you look up here, you’re not looking at us. We are a mirror reflecting you. And if you like what you see, then just look a little deeper. This is you.”
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After splashing down in the Pacific Ocean, the Artemis II crew members reunited with their friends, families and fellow NASA astronauts in Houston on Saturday. Their voyage was the first trip by humans into deep space in more than half a century.

By Jorge Mitssunaga

April 12, 2026

Science

How to watch NASA’s moon mission splash down off San Diego today

Published

8 hours ago

April 12, 2026

Press Room

How to watch NASA’s moon mission splash down off San Diego today

Four days after astronauts flew around the moon for the first time in a half-century, ground crews across Southern California are making final preparations for their high-energy reentry and splashdown off the coast of San Diego, expected around 5 p.m. Pacific time Friday.

Southern Californians likely won’t be able to see reentry or splashdown in person, NASA officials said. However, NASA will livestream the event. Here’s what you should know:

The four members of the Artemis II crew will rip through the atmosphere at roughly 24,000 mph — over 30 times the speed of sound — agitating the air around the capsule into a fireball roughly half as hot as the surface of the sun.

NASA will use a new, more direct reentry technique, after the heat shield for the 2022 Artemis I test mission, which had no one aboard, unexpectedly chipped in more than 100 spots.

Artemis II pilot and SoCal native Victor Glover has been thinking about reentry since he was assigned the mission in 2023. When Glover, still in space, was asked Wednesday evening about the moments from this mission he’ll carry with him for the rest of his life, he joked: “We’ve still got two more days, and riding a fireball through the atmosphere is profound as well.”

How to watch

“The path we’re coming in, I don’t expect it to be visible for folks in California,” Artemis II Lead Flight Director Jeff Radigan said at a news conference Thursday.

Nonetheless, San Diegans hoping to catch a glimpse can look west over the Pacific around 5 p.m. for the best chance to see the Orion capsule, which would appear as a fast and bright streak low in the sky.

For anyone hoping to get a closer view via boat, “I would caution folks, please avoid the area,” Radigan said. “There’s a lot of debris that comes down, and we work with our recovery forces in order to ensure that it doesn’t hit them. But of course we don’t want it to hit anyone else.”

The last time NASA astronauts splashed down in a brand-new vehicle, lookie-loos caused some serious safety concerns, including potentially exposing boaters to toxic chemicals and delaying the recovery of astronauts if there was an emergency.

For the best, up-close views, NASA is livestreaming reentry and splashdown on YouTube, Netflix and HBO Max. The Times will also carry live views of the dynamic return to Earth on latimes.com.

The San Diego Air & Space Museum will also host a family-friendly viewing party.

The plan for reentry

NASA expects reentry to begin at approximately 4:53 p.m. Pacific time. (Yes, NASA “approximations” are that precise.)

When it does, the agency expects to lose communication for about six minutes as the Orion capsule holding the astronauts is enveloped in a fireball.

During all this, a team of NASA and Department of Defense test pilots will chase the capsule in airplanes as researchers in the back point telescopes and sensors at its heat shield. NASA hopes to use this data to better understand how that protection holds up under the agency’s new reentry technique.

Around 5:03 p.m., two small parachutes will deploy, slowing the craft down to about 300 mph. A minute later, much larger chutes will deploy, slowing the capsule to about 17 mph. Three minutes later, around 5:07 p.m., the capsule will splash down in the Pacific Ocean.

A team of Navy divers will then help the astronauts out of the capsule, and Navy helicopters will swoop in to recover them.

The helicopters will take the astronauts to the U.S.S. John P. Murtha, a 680-foot-long, 25,000-ton Navy transport dock warship, for an immediate medical evaluation. Navy divers will then secure the capsule and guide it to the Murtha’s deck.

Then they’ll bring the astronauts back ashore as the Murtha slowly returns to San Diego. The astronauts will fly to Houston to NASA’s Johnson Space Center to reunite with their families.

Boots on the moon and someday Mars

The Artemis program ultimately aims to land humans back on the moon. NASA eventually hopes to establish a lunar base that will serve as the testing grounds for future missions to Mars.

This mission primarily aimed to test the capsule’s life support systems to help create a smoother ride for future crews that will have to deal with the headaches of actually landing on the moon. This included troubleshooting the capsule’s space toilet (multiple times), piloting the spacecraft by hand, and testing procedures such as sheltering from solar radiation in the cargo locker.

NASA plans to launch Artemis III, a mission in Earth’s orbit to test docking the Orion spacecraft with SpaceX’s and Blue Origin’s lunar landers, in 2027. It aspires to launch Artemis IV, which would put humans on the surface of the moon, in 2028.

Science

Rain — and maybe thunderstorms — are expected in Los Angeles this weekend

Published

21 hours ago

April 12, 2026

Press Room

Rain — and maybe thunderstorms — are expected in Los Angeles this weekend

Heavier rain is expected to fall across Los Angeles this weekend, bringing wetter weather and a chance for thunderstorms after spring kicked into full bloom.

“This is when the weather gets a little more wild, technically, because we’re starting to see some more differential heating on the Earth,” said Todd Hall, a meteorologist at the National Weather Service.

Parts of Los Angeles will probably see rain after 11 p.m. Saturday, according to a forecast from the National Weather Service. Scattered showers are anticipated on Sunday afternoon before 2, and there is a potential for thunderstorms in some parts of the city.

There’s a 15% to 25% chance of thunderstorms, according to the forecast discussion from the NWS Los Angeles on Saturday. “Any thunderstorms that develop will likely produce brief heavy rain, gusty outflow winds, small hail and potentially waterspouts or weak, short-lived, tornadoes,” the NWS said.

A ridge of high pressure has already moved east, and now a storm system is arriving in the area.

There’s a chance that the storm system will linger across parts of Los Angeles through Monday, Hall said. Snow levels are expected to drop at high elevations, but some places, such as the northern Ventura County mountains, could have wet snow, so drivers should be cautious.

Gusty winds are expected in portions of the Mojave Desert as well.

“Just like in the ocean, we have waves. The atmosphere behaves the same way,” Hall said.

The total rainfall through Sunday night is anticipated to be between 0.50 and 1.50 inches. On average across L.A., temperatures on Sunday are expected to reach a high of 65 degrees — a full 26 degrees lower than the high recorded a week ago.

Dry and warm weather is expected to return after Monday. Temperatures are forecast to climb to more than 75 degrees later in the week and reach nearly 80 degrees next Saturday.

Heavier rain — including some thunderstorms — is expected in other parts of California such as the counties of San Luis Obispo, Santa Barbara and Ventura, the National Weather Service Los Angeles said Saturday afternoon on X.

Wind gusts north of Point Conception in Santa Barbara County could come with risks such as downed trees or powerlines. Major flooding and debris flows are unlikely, the social media post said.

Up north, the San Francisco Bay Area has already been experiencing the severe weather. Heavy rain hammered the region Saturday, and wind gusts were expected to reach up to 28 mph. The National Weather Service was advising people to allow extra time for travel because of the slippery roads.

In Southern California, the National Weather Service suggested that people be ready to adjust plans and monitor the situation.