When Ilya Rusinov returned to the Russian work force after rehabilitating a vertebra damaged in the Ukraine war, his first job was teaching in a school.

But he had also launched a side project, a patriotic club he called Zveno, or “Squad,” that provides military training for different age groups, including teenagers. After struggling at first, it found growing demand for its training sessions, including from instructors at similar patriotic organizations. Mr. Rusinov eventually left his teaching job to help run Zveno full time.

Almost three years after a mortar shell blew a hole in his back, Mr. Rusinov, who fought as part of the Wagner mercenary group, is one of a growing group of veterans whom Russian officials claim are being rewarded with an enhanced standing in society — speaking at public events, school lectures and with local news outlets.

It is part of the Kremlin’s very public effort to elevate veterans to leadership positions, offering business opportunities and some forgiveness on loans, all while priming society to accept and appreciate them.

Today, veterans address school groups as young as kindergarten age and give basic weapons training to students, which since September is a mandatory part of every curriculum starting in eighth grade. Billboards proclaiming the heroism of soldiers line major roads, and the Kremlin has made a show of appointing veterans to top jobs.

An hourlong daytime TV show on state-owned Rossiya 1 called “Ours” features breathless coverage of veterans. Some give live performances of frontline ballads, others tell of their “heroism” on the front.

To be sure, veterans’ re-entry into society can be rocky. A lingering stigma endures. Badly injured or visibly traumatized soldiers are a rarity in public. Psychological struggles are left undiscussed, and there is a lack of mental health support. Some of the programs created for veterans are charades and do not lift up rank-and-file veterans, critics say, while Ukrainians have alleged that some of those being lauded were involved in war crimes.

Analysts say Moscow is attempting to learn from the experiences of the Afghan and Chechen wars, when traumatized veterans with access to weapons returned to a society that questioned why they had been fighting and looked down on them as killers.

Mr. Rusinov heard about those days from his father, who fought in Afghanistan for the Soviet Army. At the time, the Kremlin was trying to minimize society’s awareness of how many soldiers the country had deployed, and just how many of them died — sending the dead home in zinc coffins.

“My father told me that they came back, nobody really needed them and, in general, they were pushed aside and viewed with skepticism,” he said of the soldiers returning from Afghanistan. “You went and fought, you know a lot of things, but nobody needs you.”

“Now the situation is completely different,” said Mr. Rusinov.

The withdrawal from Afghanistan is still seen as an embarrassment to Moscow. But this time, the Kremlin has sought to burnish the image of veterans in public life.

One of the most trumpeted components of its plan is a postgraduate program, “Time of Heroes,” that aims to foster a generation of warrior leaders.

The Kremlin has billed Time of Heroes as a pathway to remake the country’s elites — reducing the presence of oligarchic businessmen and elevating patriotic veterans. The program, which mixes management and leadership courses for veterans with the opportunity to intern in administrative positions, attracted more than 44,000 applicants for its first 83 spots. It is accepting a second round of applicants.

“The elite are those who serve Russia, not those who lined their pockets in the 1990s,” President Vladimir V. Putin said when he announced the creation of the program last February. “In the future, Russia can be handed over and entrusted to people like the current heroes” of the war in Ukraine.

Mr. Putin announced his candidacy for a fifth term as president in a carefully choreographed public appearance in which a veteran asked him to “finish what he had started.” The veteran, Artem Zhoga, originally from Ukraine’s Donbas region, later joined Time of Heroes in its inaugural class.

Members of Time of Heroes soon found themselves on an upward career track. Mr. Zhoga became the presidential envoy to the Urals district, and in October was invited to join the Security Council.

Another participant in Time of Heroes, Yevgeny Pervyshov, a former mayor of the southern city of Krasnodar who signed up to fight in Ukraine in 2022, was named interim governor of the Tambov region. In December, one former member was given a role advising the leadership of Rosatom, the state nuclear corporation. Another became the deputy chairman of a St. Petersburg committee on law and order.

“As Vladimir Vladimirovich Putin said, we are forming a new elite of people who have shown that they can give everything for their homeland and for the state, including their lives,” said Oleg V. Panchurin, a career officer who leads the Association of Veterans of the Special Military Operation (the Kremlin’s euphemism for the war).

After being injured in the leg by a Ukrainian drone, Mr. Panchurin returned to Moscow and was among hundreds of veterans encouraged to run in the primaries of the ruling party, United Russia. The party allocated Ukraine veterans 25 extra percentage points on top of the votes they received, to give them a leg up.

Mr. Panchurin returned to the front and didn’t advance in the elections. But he has returned to Moscow, recently took the admission exam for the second class of Time of Heroes and aims to join Russia’s lower house of Parliament.

But independent observers say Time of Heroes is largely recycling people of means and not benefiting the lower rung of society, including many veterans, by giving them access to good administrative jobs.

“We still do not yet see any appointments to really high positions,” besides Mr. Zhoga, said Andrey Pertsev, a journalist with the exiled media outlet Meduza who covers the Russian presidential administration. “It is a P.R. tool.”

Mr. Pertsev noted that the region where Mr. Pervyshov was interim governor had a population and a budget smaller than the city where he was mayor. And a Time of Heroes alumnus appointed to Russia’s upper house of Parliament in September, Aleksey Kondratyev, had already served in the body on behalf of a different region from 2015 to 2020.

On top of that, Mr. Pertsev said, applicants for Time of Heroes are required with rare exceptions to already have a university degree.

Novaya Gazeta Europe, another independent outlet operating in exile, studied the biographies of 80 of the 83 participants in the first Time of Heroes cohort, and found that almost 80 percent were career military personnel, with only three mobilized soldiers. At least three of the participants have also been named by Ukrainian security services in war crimes accusations.

That hasn’t stopped the program from featuring heavily in the Kremlin’s messaging celebrating the war effort. Overseen by Mr. Putin’s powerful deputy chief of staff Sergei V. Kiriyenko, Time of Heroes has been heavily supported by Kremlin funding and is regularly featured in the media. Mr. Putin spoke about it repeatedly last month, including during a visit to a rehabilitation center, when he pledged to replicate Time of Heroes on a regional level.

Each appointment for a Time of Heroes graduate receives broad coverage in state and local media. Some of the men will play a role shaping Russia’s youngest generation, just as Mr. Rusinov hopes to.

Late last month, for instance, one Time of Heroes alumnus was appointed head of the Yunarmia, or Youth Army, a militarized throwback to the Young Pioneers of the Soviet era; it has more than one million participants, according to the state news agency TASS.

Mr. Rusinov hopes to follow suit. Since his return from the war he has lectured at schools and universities in the Samara region, and is training instructors in military-patriotic education.

In November, he sat the entrance exam for Time of Heroes and said he dreams of one day becoming the director of what he called a “military version of Hogwarts.”

Over the past year, Muanema Fakira noticed something odd about the eyes of her 1-year-old daughter Sumaya. Her left eye was cloudy. It did not gleam with curiosity or glint in the sun. When the problem persisted, Ms. Fakira made the rounds to health clinics in their town in central Mozambique. Doctors said they could not help.

But they knew of someone who could, if Ms. Fakira could take Sumaya, now 2, on a 100-mile journey to the coast.

The family made the trip to the city of Quelimane, where Dr. Isaac Vasco da Gama examined Sumaya’s eyes and quickly diagnosed a congenital cataract.

Ms. Fakira was skeptical — cataracts are for old people, she said. But Dr. da Gama explained that an infection at birth, or shortly after, can cause cataracts in children. The condition is particularly worrying because vision problems affect the development of a child’s physical function. But the good news, he said, was that the problem can be solved with a simple surgery, one he does a dozen times a week at Quelimane Central Hospital.

This was particularly lucky for Sumaya because Dr. da Gama is one of just three pediatric ophthalmologists in Mozambique, a country of 30 million people.

Sumaya had her surgery in November, and a day later headed home, already recovering. Dr. da Gama was pleased to have seen her while she was still young, before permanent damage was done.

It was a sign that a system he and colleagues have been trying to put in place for the last few years might be taking hold: Sumaya’s parents sought help from the medical system for an eye problem — rather than a traditional healer, or a sorcerer to remove a curse.

When Sumaya was referred for care, it was a long and expensive trip, but she got help relatively quickly for a problem that might otherwise have blighted her life. Ideally her cataract would have been spotted at birth by a midwife.

“I do believe that by pushing forward, we can slowly overcome this challenge,” Dr. da Gama said.

In Mozambique, as in much of sub-Saharan Africa, awareness of vision problems is so low, and access to help so limited, that few children get the care they need, even though many suffer from easily treatable problems.

In 2021, a global commission on eye health reported that 510 million people around the world, 90 percent of them in low- and middle-income countries, had uncorrected vision impairment. That is, they could not see properly because they did not have glasses.

The consequences are enormous: Children with vision loss in these countries are significantly less likely to be in school. One study found that for those who do attend school, those with uncorrected vision problems learn half as much as their peers with normal vision.

Access to treatment is so limited because of a scarcity of trained staff and a failure to integrate vision care into health systems. Children are not screened for vision loss, and parents and teachers don’t understand the simple causes of eye trouble that can manifest in distraction, lack of physical coordination and behavior issues.

Mozambique has just 20 ophthalmologists, up from six two decades ago. Almost all of them are based in the capital, Maputo, in the south.

Dr. da Gama completed his studies in India in 2017 and set up a clinic in Quelimane, a seaport town halfway up Mozambique’s long Indian Ocean coastline. But to his surprise, he saw very few patients in the first year. He discovered that no one was being referred to him because health workers did not recognize treatable eye diseases. He started traveling to local clinics to tell medical workers about screening and solutions.

Then he teamed up with the charity Light for the World, which had sponsored him to complete specialized training in pediatric eye care in Tanzania. They designed an outreach program to show teachers, community health workers, traditional healers and local leaders how to spot vision problems and to refer children to the new ophthalmology ward at the Quelimane hospital.

Now, a couple of times a year, for up to a month at a time, he takes a mobile clinic to small communities to do surgeries on children with cataracts, glaucoma or strabismus (misaligned eyes).

Cataracts cause nearly half the preventable blindness in Mozambique’s children; they can be genetic, or the result of trauma (like a stick or a stone in the eye), or of an untreated eye infection.

On his outreach journeys, Dr. da Gama teaches other health care workers how to perform the simple surgeries, and how to spot the conditions. “Operating per se is not a problem: We can train in a week, two weeks, how to operate on a cataract,” he said. “But it is how to identify the children who need the operations.”

Mozambique’s Ministry of Health is trying to build awareness of vision problems and refractive errors, for which a pair of glasses is a life-altering intervention.

Glasses or simple surgeries that keep children in school can change the future for their families, and for the country as a whole. “If you have children less educated or with fewer skills,” he said, “the future of the economy is affected.”

In Quelimane, Dr. da Gama also sees cases of retinoblastoma, a cancer of the retina. When patients come early enough, he can save their lives, if not their eyes.

Camilo Rosario brought his daughter Grace, 3, to his clinic in November, from their home in a village 300 kilometers (about 185 miles) away. She had a tumor protruding from her eye that caused her excruciating pain. Mr. Rosario said she had begun to complain about her eye just weeks before. He shifted anxiously from foot to foot while Dr. da Gama explained that he would operate quickly to remove the tumor, but that he feared the disease was already in her brain.

Grace soon recovered from the first surgery, clinging to her father with a bulky bandage around her head. But as Dr. da Gama had feared, she had come to him too late; she died in early January.

Aminata Kaba was screened alongside her classmates in high school last year — and was surprised to learn that she was myopic. After she got glasses, school became significantly easier, she said, and her grades soon improved. Now, she said, she will continue on in school, and she hopes to be a lawyer.

Screening older children is easy; coaxing cooperation out of the small ones is a much greater challenge, Dr. da Gama said. They rarely look where he needs them to for eye exams. The eyedrops, the equipment, even his white coat, all can be frightening. He said he smiles and sings to distract, removing the coat when required.

“I like difficult things,” he said.

The world’s largest gathering of mathematicians convened in Seattle from Jan. 8 to Jan. 11 — 5,444 mathematicians, 3,272 talks. This year the program diverged somewhat from the its traditional kaleidoscopic panorama. An official theme, “Mathematics in the Age of A.I.,” was set by Bryna Kra, the president of the American Mathematical Society, which hosts the event in collaboration with 16 partner organizations. In one configuration or another, the meeting, called the Joint Mathematics Meetings, or the J.M.M., has been held more or less annually for over a century.

Dr. Kra intended the A.I. theme as a “wake-up call.” “A.I. is something that is in our lives, and it’s time to start thinking about how it impacts your teaching, your students, your research,” she said in an interview with The New York Times. “What does it mean to have A.I. as a co-author? These are the kinds of questions that we have to grapple with.”

On the second evening, Yann LeCun, the chief A.I. scientist at Meta, gave a keynote lecture titled “Mathematical Obstacles on the Way to Human-Level A.I.” Dr. LeCun got a bit into the technical weeds, but there were digestible tidbits.

“The current state of machine learning is that it sucks,” he said during the lecture, to much chortling. “Never mind humans, never mind trying to reproduce mathematicians or scientists; we can’t even reproduce what a cat can do.”

Instead of the generative large language models powering chatbots, he argued, a “large-scale world model” would be the better bet for advancing and improving the technology. Such a system, he said in an interview after the lecture, “can reason and plan because it has a mental model of the world that predicts consequences of its action.” But there are obstacles, he admitted — some mathematically intractable problems, their solutions nowhere in sight.

Deirdre Haskell, the director of the Fields Institute for Research in Mathematical Sciences in Toronto and a mathematician at McMaster University, said she appreciated Dr. LeCun’s reminder that, as she recalled, “the way we use the term A.I. today is only one way of possibly having an ‘artificial intelligence.’”

Dr. LeCun had noted in his lecture that the term artificial general intelligence, or A.G.I. — a machine with human-level intelligence — was a misnomer. Humans “do not have general intelligence at all,” he said. “We’re extremely specialized.” The preferred term at Meta, he said, is “advanced machine intelligence,” or AMI — “we pronounce it ‘ami,’ which means friend in French.”

Dr. Haskell was already sold on the importance of “using A.I. to do math, and the huge problem of understanding the math of A.I.” An expert in mathematical logic, she is working on the equivalent of a textbook: a collection of results that can be used by A.I. systems to generate and verify more complex mathematical research and proofs.

For Kenny Banks, an undergraduate at the University of North Carolina at Greensboro who attended the J.M.M., artificial intelligence does not appeal as a tool for guiding exploration. “I think the mathematics that people currently love is driven by human curiosity, and what computers find interesting cannot be the same as what humans find interesting,” he said in an email. Nevertheless, he regretted not squeezing any A.I.-related talks into his itinerary. “The math + A.I. theme was definitely of interest, it just ended up not working with all the things I had planned!”

Here are some other highlights from the mathapalooza in Seattle:

Day 1

At 6 p.m. on Wednesday, Jan. 8, after a ribbon-cutting and awards ceremony, attendees stampeded to the grand-opening reception in an exhibit hall. The draw was a) free food, and b) exhibitor booths occupied by publishers and purveyors of various mathy wares. At Booth 337, Robert Fathauer was selling an impressive inventory of dice — including the new “5-Player Go First Dice,” a colorful set of five 60-sided dice that share no number in common, allowing five game players an equal shot when they roll to determine who starts first. Dr. Fathauer, who is based in Arizona, was also co-organizer of the meeting’s art exhibit and contributed two ceramic sculptures of his own, “Hyperbolic Helicoid” and “Cubic Squeeze.”

The exhibit’s award-winning art submissions were “Saddle Monster,” crocheted in wool, copper and nylon, by Shiying Dong of Greenwich, Conn., a mathematical artist with a Ph.D. in physics …

… and “Twisted” and “Untwisted,” created using a vector graphics app on an iPad, by Rashmi Sunder-Raj, a mathematical artist in Waterloo, Ontario.

Rebecca Lin, a Ph.D. student in computer science at M.I.T., received an honorable mention for a laser-cut engraving on paper titled “Disintegrating (State of Mind).”

Day 2

On Thursday, Jon Wild, a music theorist at McGill University in Montreal who does math on the side, was invited to a session on applied mathematics to discuss his investigations into “counting arrangements of circles” in the plane. Given certain constraints, there is one way to draw one circle, three ways to draw two circles, 14 ways to draw three, 173 ways for four, and 16,951 ways to draw five. (The enumeration of six circles is yet to be computed.) Dr. Wild was surprised to learn that this research was relevant to 3-D printing: that is, to how multiple printer heads could each trace circular arcs while avoiding collisions. “I was tickled,” Dr. Wild said.

During a session on mathematics and the arts, Susan Goldstine, a mathematician at St. Mary’s College of Maryland, lectured about her “Poincaré Blues” craft project. Named for the French mathematician Henri Poincaré, the project involved making a patchwork denim skirt from old jeans. As she described in a write-up: “After noodling around with different patterns, I settled on the tiling of the Poincaré disk model of the hyperbolic plane by 30º-45º-90º triangles,” which was familiar to her from an illustration by the classical geometer H.S.M. Coxeter (and which also inspired the Dutch artist M.C. Escher).

Day 3

At midday, the undergraduate poster session buzzed with expositions on topics including lunar time synchronization; the math of piano tuning; loops in four-dimensional space; and a model for wildfire containment, smoke spread and their public health consequences.

During another session on mathematics and the arts, Barry Cipra, a mathematician from Minnesota, gave a talk about “gelbes feld” (“yellow field”), a painting by the Bauhaus-trained Swiss artist Max Bill.

It may appear to be a solid canvas of color, Dr. Cipra said, but there is a faint pattern of contrasting dots, or, more precisely, squares. “Let’s look at an abstract version of Bill’s abstract,” he said. “Can you spot what Bill is up to?”

By Dr. Cipra’s analysis, the artist encoded in the painting a classic 3-by-3 magic square — a square array of numbers that form a logic puzzle wherein the sum of each row, column and diagonal equals 15.

Another peculiarity was that each row, column and diagonal had five pips (as on dice or dominoes):

Dr. Cipra noted, “It looks like Bill posed and solved an original mathematics problem and hid it in a painting: Can you place the pips within each square of the 3-by-3 magic square so that there are exactly five pips along each row, column and main diagonal of the 9-by-9 subgrid?” The same question could be asked for 5-by-5 and larger magic squares of odd sizes, he said. “But it’s far from clear what the answer is going to be.”

Dr. Goldstine found Dr. Cipra’s discovery compelling. “I am always excited when math turns up in a place where you wouldn’t expect it,” she said in an email. “I often use these surprising connections to get students who might be afraid of or bored by math to see some of its beauty.”

Day 4

The final day offered a number of public events, including a mini math festival with hands-on puzzles and games.

“Why is it math?” asked Aleksandra Upton, 7, of a geometric puzzle.

“Because we can count all the different ways that we put the shapes together,” said her mother, Karolina Sarnowska-Upton, a software engineering manager at Microsoft in Redmond, Wash.

In one public lecture, Ravi Vakil, a mathematician at Stanford and the incoming president of the American Mathematical Society, explored the simultaneously playful and profound “mathematics of doodling.”

In another, Eugenia Cheng, a mathematician and pianist at the School of the Art Institute of Chicago, addressed “Math, Art, Social Justice.” One of her salient messages: “Pure mathematics is a framework for agreeing on things.” She sang some of the lecture alongside a recorded video of herself playing the piano.

And there was a world premiere of a documentary film, “Creating Pathways,” the second in the “Journeys of Black Mathematicians” series by the director George Csicsery. (It airs on public television stations in February.) The film’s senior consultant was Johnny Houston, an emeritus professor at Elizabeth City State University in North Carolina. After the screening, Dr. Houston remarked on the timeliness of the 2025 premiere: In 1925, Elbert Frank Cox became the first African American — and first Black person in the world — to receive a Ph.D. in mathematics. Of his own journey, and that of many Black mathematicians, Dr. Houston said that with exposure, experience and opportunity, “we can do as well as any mathematician in earning a Ph.D. and beyond.”

The last of the talks wound down that evening. By 3 a.m. the next morning, as some attendees headed to the airport, two mathematicians were just heading to bed, but not before riding the elevator down to the hotel lobby to ask reception for a late checkout.

India and China have agreed to resume direct flights between the two countries after nearly five years, the latest thaw between the two Asian giants that until recently were on war-footing over a deadly border dispute.

The rapprochement also included agreements on improving access to journalists from both sides and facilitating pilgrimages to a Hindu shrine in Tibet. They were announced by both sides on Monday, after India’s foreign secretary, Vikram Misri, visited Beijing.

The two nations have made substantial progress in recent months to restore some normalcy in ties. Their relationship had plunged to its worst in decades following an incursion by Chinese soldiers into the Indian side of a disputed border in 2020. The skirmishes left soldiers dead on both sides.

In October, Prime Minister Narendra Modi of India met with China’s leader, Xi Jinping, on the sidelines of a summit in Russia. It was the first time the two leaders had sat down for proper talks in five years. That conversation was made possible by more than two dozen rounds of negotiations between military leaders and diplomats over disengaging their forces along the border high in the Himalayas.

Mr. Misri’s trip to Beijing was to follow up over a series of “people-centric steps to stabilize and rebuild ties,” India’s foreign ministry said in a statement after the visit.

The ministry added that officials from the two sides would meet to discuss the technical details of resuming flights, which have remained suspended since the Covid-19 outbreak in 2020. Flights to Hong Kong resumed after the pandemic lockdowns eased, but those to mainland China did not because of the tension between the two countries.

In his meeting with Mr. Misri, Wang Yi, China’s foreign minister, called on both sides to “seize the opportunity, meet each other halfway” in the hopes of ending “mutual suspicion, mutual alienation and mutual attrition,” according to a statement from the Chinese foreign ministry.

Berry Wang contributed reporting from Hong Kong.