James' World 2

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To the casual observer, the look and feel of shipping containers suggests a world of smooth, lossless transportation, almost immaterial in its implementation of a logistical ideal. However, the system is far from lossless. In fact, during storms and shipwrecks, shipping containers regularly go overboard.

Nobody knows exactly how many of these vast, 20- or 40-foot-long steel capsules—stacked in the thousands in the cargo holds of each ship, carrying the stuff of the global economy—are lost each year. Shipping lines and insurance companies keep these figures under wraps. But estimates suggest that of the hundreds of millions in circulation annually, several thousand containers vanish—sometimes forever.

And what becomes of the containers that disappear?

If they reappear, then the matter is relatively simple. Each standard container carries, on each of its four sides, a code clearly identifying it. The codes for all containers worldwide are distributed by the Bureau International des Containers (BIC). In cargo shippers’ databases, the histories and current cargo of containers are recorded and accessible via their respective codes. Thus, it can be determined what was in each container and for whom it was intended. As long as the contents of a container have not been plundered outright, they can even be delivered to the recipient after an accident, albeit with some delay.

But it is, of course, more difficult when a container breaks open—particularly on the high seas, leaving its freight to the whims of the wind and the waves. In these cases, the contents are highly unlikely to ever reach their intended recipient. Yet these mishaps are not all for naught. In fact, while these lost shipping containers likely represent hundreds of millions of dollars in losses for the shipping industry, they have inadvertently been a boon to another community: oceanographers.

In May 1990, the Hansa Carrier, a German cargo ship traveling from Korea to the U.S., lost 21 containers in a Pacific storm north of Japan, and four of the containers broke open. The payload, more than 60,000 pairs of Nike sneakers, poured out into the sea. About nine months after the accident, known colloquially as “The Great Shoe Spill,” 1,600 sneakers washed up along the coast of Oregon, on the Queen Charlotte Islands in Canada, and on other beaches along the northern Pacific coast.

The fiasco resulted in something like 20–30 metric tons of footwear waste. However, for Curtis C. Ebbesmeyer, an oceanographer based in Seattle, the mishap presented a unique research opportunity. With the help of local beachcombers, Ebbesmeyer carefully documented the path of these sneakers, as he later wrote in his 2009 book “Flotsametrics and the Floating World.” Using the Ocean Surface Currents Simulation (or “OSCUR”), his colleague, James Ingraham, wrote a program to simulate surface flow. Together, they calculated the probable routes of the drifting shoes, which, though unintentionally released, were fed into the ocean system as data.

Of course, Nike sneakers are hardly the only accidental “probes” to have bobbed across the ocean: Over the years, researchers have tracked everything from toy cars and Lego figures to beer cans, hockey gloves, and hermetically sealed Riesen chocolates. By comparing their simulations with the real-world journeys of goods that washed ashore and were identified by serial number, oceanographers have helped produce increasingly precise maps of Pacific Ocean currents. These maps account for a range of variables, including cargo-shipping routes, surface currents, wind patterns, and the unpredictable drift of objects at sea.

In 1885, Prince Albert I of Monaco threw 1,675 buoys into the Atlantic along several lines between Europe and North America. As French author Érik Orsenna recounts in his 2010 sea tale “A Portrait of the Gulf Stream: In Praise of Currents,” the prince, sailor, explorer, and amateur oceanographer wanted to investigate the path and speed of the Gulf Stream as it crossed the Atlantic toward Europe.

Each of the prince’s buoys contained a message, drafted in seven languages within a sealed glass tube, requesting that those who found it should return the note “to the proper offices of their home country, so that it may be passed on to the French government, indicating the circumstances in which this document was found.” The buoys were eventually found along the coast of Europe to Gibraltar, on the coast of Africa to the Canary Islands and Cape Verde, in the Antilles, and along the coast of Central America.

Ever since then, an important branch of oceanography has developed from the practice of setting buoys, albeit more sophisticated ones than the bottles and floats used by Prince Albert I. Modern ocean surface drifters now transmit their locations by satellite. They allow scientists to track their whereabouts in real time and measure variables such as pressure, salinity, and wind.

Yet, sophisticated as these buoys might be, damaged containers have sometimes proven superior in recent decades. After all, a lost container can become a mass experiment that no research program would deliberately stage, sending thousands of objects into the ocean at once and allowing their eventual landfalls to chart the hidden pathways of currents across the globe. Of course, this growing mass constitutes a serious threat to the ocean ecosystem, not to mention the environmental catastrophes regularly caused by tanker accidents themselves. At the same time, the flotsam also contributes positively to the knowledge of the ocean system’s function, thereby presenting possibilities for its salvation.

If plastic objects spilled from shipping containers can help us understand the workings of the ocean, then nature and culture are no longer separate realms. They are deeply entangled: human actions, manufactured objects, trade routes, storms, currents, coastlines, and ecosystems all acting on one another. A lost shipment is therefore not only waste but a message: What does the sudden arrival of a container’s contents reveal? What can stranded shoes, toys, or fragments of plastic tell us that their counterparts still moving invisibly through global trade cannot?

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Hmmmm … I know this post is hard to follow. I hope you find some recipes you like!

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A set of 85 Recipes 

3 of 85 Summer Fish Recipes

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then scroll for set of recipes 1-85)

The 3 recipes shown here are included in the set!

Just one example

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Don’t worry, it’s not just you. It’s hard to pick a good watermelon. So much of what determines its sweetness is beyond your control. And what is in your control may go against your instincts. It’s a challenge to your sense of free will, an exercise in letting go, a gamble at the market.

Also, it’s just a watermelon. Everything will be OK. And if you do manage to pick the perfect melon, everything will be great in that sticky-fruit-juices-down-your-arm-on-a-summer-afternoon way.

To understand why it’s so hard to choose a watermelon is to understand its nature. Its sweetness is determined largely by the weather; the drier during harvest, the better. Donald Sherman, a third-generation farmer who grows about six varieties on his family farm in Fresno, Calif., explains that watermelons don’t gain sweetness once cut off the vine. “If they don’t have that sugar out with Mother Nature, they’re not getting more.”

Fruits like peaches and pears will sweeten as they ripen, but, according to Juan Anciso, a professor and vegetable specialist with Texas A&M AgriLife Extension Service, harvested watermelons continue to ripen only “in the sense that they soften and start to decay.”

So you’re not scouting potential when looking for peak melon. And before you look, you want to listen. (There’s nothing to smell.) Both Mr. Sherman and Mr. Anciso said that sound is the most important factor in choosing a watermelon and that the best way to hear it is with an openhanded smack.

What you’re listening for isn’t so much volume as it is tone. Mr. Anciso compares the full sound of a good melon to “beating on a drum.” When you slap it, the sound should bounce back. If the sound is absorbed, that means the inside is old and mealy. Mr. Sherman calls that overripe tone an “overly flat sound, as if you were slapping a flat basketball.”

Beyond the importance of that resonance is pitch. Mr. Sherman suggests slapping a number of melons in a bin to hear the differences between the “tighter, higher pitch” and the ones with low bass notes. “If you find something in between, that’s the good-quality melon,” he said. At the beginning of the season and in high summer, the best ones have a deeper sound. In September, those with slightly higher pitches are better.

Mr. Sherman said that shift in sound is the result of the watermelons having more dew on their vines, a nuance that he’s learned over the years in his fields. Another is his ability to spot good melons by their color, which lightens when ripe, whether the fruit is striped or solid. When choosing one from a market, he suggests looking for paler ones.

Mr. Anciso recommends finding melons with “yellow bellies.” Most watermelons grown in the United States sit on the soil, and the spot where they rest develops a patch that starts white then turns creamy yellow once the fruit has matured.

If you’ve taken the time to shamelessly slap a bunch of melons at the market to find the just right one with the right sound, you should cut into it right away because you don’t want it to become overripe and mealy. Maybe it’ll be fantastic: juicy, sugary, crisp but not crunchy. Eat it unadorned with everyone you love.

And if it’s not good enough to eat on its own, that’s more than all right. Sprinkling a little salt on sort-of-bland slices can heighten the sweetness. And melon that really needs a boost can become sugary as popsicles, boozy blended into a margarita, savory in a salad with feta, spiced in chaat, and showstopping in a creamy trifle. You may not be able to guarantee the sweetness of the watermelon you pick, but you get to choose what to do with whatever you get.

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Before you look for the perfectly ripe watermelon, you want to listen. Credit…Christopher Simpson for The New York Times. Food Stylist: Simon Andrews. Prop Stylist: Paige Hicks.

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Europe’s climate-change-driven summer of extreme heat has been hitting the continent with a one-two punch: the heat wave has not only killed thousands but has been sucking the water out of rivers, lakes, soils, and plants and fueling destructive wildfires. The strain is testing the adaptations that municipalities have put in place since a hallmark deadly heat wave in 2003.

Repeated bouts of extreme heat led Western Europe to its warmest June on record, according to the European Union’s Copernicus Climate Change Service. The second half of the month had a heat wave that was so intense that it broke monthly and all-time temperature records across several countries. An analysis by the World Weather Attribution (WWA) research group found that these extreme temperatures would’ve been “virtually impossible” without the influence of global warming and that such temperatures were now about 10 times more likely than they would’ve been in 2003. Heat waves themselves are also hotter than they were in the past: conditions like those of Europe’s June heat wave have become up to 2.5 degrees Celsius warmer than they were decades ago, and the event exposed 327 million people and $15.6 trillion in assets to climate-intensified heat, according to an analysis by the research organization ClimaMeter.

That heat has taken a heavy human toll. The European mortality monitoring network backed by the World Health Organization and the European Center for Disease Prevention and Control recorded more than 16,000 excess deaths across 27 European countries during the week of June 22–28 alone, with more than 14,000 of those deaths among people age 65 and older. (Older individuals, young children, and those who work outdoors are more vulnerable to heat illness.)

Those tallies are almost certainly undercounts: in 2022 the World Health Organization’s real-time estimate put Europe’s heat-related death toll at roughly 15,000, while a later study in Nature Medicine that worked from full mortality records put the true figure above 61,000—more than four times higher than the initial count. The reason for the discrepancy is that heat deaths are typically logged only when a death certificate names heatstroke directly, an approach that misses the much larger toll of heart attacks, strokes and respiratory failures that extreme temperatures trigger in people with existing conditions. Public health researchers have warned that undercounting delays the enactment of better protections because it leads officials and the public to underestimate how lethal heat is until the retrospective data catch up months or years later.

And heat’s damage isn’t limited to the time during a heat wave. A study published in Nature Climate Change found that repeated exposure to extreme heat events accelerates the body’s aging process and makes people more vulnerable to health problems—and the magnitude of the effect is comparable to that of regular smoking or alcohol consumption.

Adaptation measures such as government heat action plans, cooling centers and early-warning systems have expanded since Europe’s catastrophic 2003 heat wave, which caused more than 60,000 excess deaths. But researchers behind the more recent mortality studies argue current measures are not enough for a climate that keeps outpacing the adaptations built for it.

The heat is also affecting the livelihoods and food supply of people in Europe and elsewhere because of the simple physics of a warming climate: hotter air holds more moisture, so it pulls harder on whatever water is available, whether that’s a reservoir, a wheat field or topsoil. Another WWA rapid analysis released this week found that record heat has been evaporating water out of rivers, lakes, soils and plants — increased evaporation that led to drought conditions in Western Europe up to 80 times more likely (and in its eastern region up to 40 times more likely) than they would have been without human-induced climate change. By desiccating vegetation, the drought has already fueled severe wildfires, with 116,000 hectares burned in Spain and 42,000 hectares burned in France, according to the WWA report. There have even been wildfires in the normally damp U.K.

The thirstier atmosphere also strains the water supplies that cities, farms and power plants all draw from. France is on track for its lowest maize harvest in 50 years, and Romania has lost more than a million hectares of maize. These losses, layered onto existing global supply strain, could push up food prices. Higher costs would hit low-income households hardest—households that are already hard-hit by the financial strain of drinking-water rationing and non-essential-use restrictions that are underway across Europe, according to the WWA.

Low river levels are disrupting cargo transport, and water scarcity is straining hydropower-dependent regions. The Rhine River at Lobith, the Netherlands—one of Europe’s busiest cargo corridors—saw its flow drop to 715 cubic meters per second on the weekend of July 18–19. This statistic is the lowest recorded for that month, breaking a record set during 1976’s severe drought, according to Rijkswaterstaat, the Dutch water authority.

“What’s most alarming is that these conditions are occurring at 1.4 [degrees] C of warming,” says Mariam Zachariah, a research associate at the Center for Environmental Policy at Imperial College London. “If global emissions push temperatures up to 2.8 [degrees] C as predicted, these intense evaporative conditions could double in likelihood, turning droughts like this one into regular occurrences. Without rapid, aggressive emissions cuts, Europe is heading for a future where these scorching, dry summers happen time and time again.”

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With mining applications on the horizon, the International Seabed Authority’s crucial Mining Code is still far from finished.

Earlier this year, Leticia Carvalho, a Brazilian oceanographer and environmental policy expert, took the helm of the International Seabed Authority (ISA) as secretary general. The ISA, an intergovernmental body that governs what happens on the seafloor in international waters, is responsible for an area that spans more than half the planet.

One of the agency’s key roles is in deciding the future of deep-sea mining, a nascent industry targeting tennis ball–sized rocks called polymetallic nodules. Rich in cobalt, nickel, and other valuable metals, polymetallic nodules can be found in some areas of the seafloor, most notably in the Clarion-Clipperton Zone, a vast tract between Hawai‘i and Mexico.

In a landslide victory, Carvalho unseated Michael Lodge, an English lawyer who had served as the ISA’s secretary general since 2016. Lodge’s tenure at the international body—which is tasked with the contradictory goals of both helping deep-sea mining get off the ground and keeping it in check—was marred by allegations of bribery, corruption, and of Lodge having an undue bias toward the mining companies the ISA oversees, all of which Lodge has vehemently denied. Many environmentalists and scientists welcomed the news of Lodge’s displacement.

In the wake of her win, Carvalho told Mongabay that she aims to rebuild trust in the ISA, and in Politico she said she planned to investigate the corruption and mismanagement allegations. But Carvalho’s term does not seem set to bring about the kinds of sweeping changes that would satisfy the 32 countries that have called for a pause on the development of deep-sea mining—including Canada, New Zealand, and Costa Rica—or those, like France, pushing for an outright ban.

For years after the ISA’s inception in 1996, environmentalists, mining industry representatives, and government delegates gathered at the agency’s seaside headquarters in Kingston, Jamaica, to develop the Mining Code—the set of rules and regulations that will govern everything about deep-sea mining from who is allowed to mine to how they will mine, and even the way the industry’s proceeds will be disbursed to, somehow, benefit all of humanity. For 25 years, deep-sea mining was a distant reality. Negotiations were easygoing, and those gathered in Jamaica would mingle at weekend retreats and dance parties.

All that changed in 2021 when representatives from Nauru, a Pacific Island nation, triggered a clause in the United Nations Convention on the Law of the Sea (UNCLOS) known as the “two-year rule.” The move meant that, suddenly, the ISA had only two years to either finish the Mining Code or consider a company’s application to exploit the seafloor with whatever unfinished rules it happened to have in place.

Three years later, no company has yet applied for an exploitation permit. But the triggering of the two-year rule sparked a flurry of contentious debates over the legal and environmental implications of deep-sea mining. With so much still under discussion, Julian Jackson, an ocean governance expert from the nonprofit Pew Charitable Trusts who has closely followed the negotiations, says the Mining Code is still months—or even years—from being finished.

“The ISA needs to be upfront with itself about where we are in this process,” he says.

Despite this, Carvalho says she expects member states to finalize the Mining Code by 2025.

Doing so will not be easy. To finish the Mining Code, negotiators must agree on—and draft into legalese—decisions that will have widespread consequences for sensitive deep-sea ecosystems, such as those in the Clarion-Clipperton Zone. They’ll also have to develop a system to ensure that the profits from deep-sea mining are distributed in a way that benefits all of humanity, as required by UNCLOS. Figuring out what that means and how it will work is just one of the daunting decisions facing negotiators.

Throughout 2024, the ISA worked overtime grappling with unanswered questions around the environmental impacts of mining. For instance, countries have not fully resolved what counts as “serious harm” to the marine environment, much less what level of harm regulators are willing to permit.

To finish the Mining Code, “a lot of compromises need to be made,” says Pradeep Singh, a legal expert on the law of the sea at the Research Institute for Sustainability in Potsdam, Germany.

Yet with negotiations nowhere near an end, the question becomes: what happens if a company submits an application to mine the deep?

The two-year rule requires the ISA to consider mining permits using its current draft regulations. Under normal circumstances, the Legal and Technical Commission, a closed-door body within the ISA, holds significant power to decide whether to approve or reject a mining application. But the ISA’s council, which represents 36 of the ISA’s 169 member states, recently implemented new safeguard measures. The council decided that if a mining application comes in before the regulations are finalized, the council will determine what procedures to put in place to review the application, rather than the Legal and Technical Commission.

The most likely candidate to test this unresolved process is the Metals Company (TMC), a mining company based in Vancouver, British Columbia. Despite initially triggering the two-year rule, TMC—along with its sponsoring state, Nauru—have so far held off on submitting a mining application. That will likely change in June 2025.

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The current targets of deep-sea mining are the polymetallic nodules that lay on the seafloor in some locations. Scientists have known about these nodules since the HMS Challenger expedition in the 1870s. Photo by Science History Images/Alamy Stock Photo

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Mr. Trump’s February 2025 tour of the Qatari jet led to a frantic sprint inside the White House and the Pentagon. The administration sought to upgrade the plane in time to meet his demand for it to be ready by the nation’s 250th birthday this summer, with an accelerated retrofit.

An investigation by The New York Times found that the president’s push to get the luxury aircraft quickly led to ballooning costs and trade-offs in safety features that potentially left Mr. Trump and others who travel with him on Air Force One vulnerable.

Among the findings:

• Mr. Trump was personally engaged in making decisions about the retrofitting of the donated plane, giving the final approval on the features and security measures that would be included, according to people familiar with his role. They and others interviewed for this article described the sensitive information about the process and the plane on the condition of anonymity.

• Several key security and safety features on the Boeing planes that have been used for decades as Air Force One are not visible on the upgraded jet, including a lower-level exit for high-risk situations, additional backup power capacity and an advanced antimissile system, public Air Force records and photographs examined by The Times show. The planes currently being built to serve as the permanent presidential fleet are all set to have such features, federal records show.

• The 747-8 plane was overhauled on a compressed timeline of just about eight months. Experts said the jet would have needed several years for a full upgrade.

• Because the Qatari jet was being pushed into service so quickly, some White House officials initially expected it would only be used for domestic travel or to visit allied countries with U.S. military bases.

• The government spent hundreds of millions of dollars to purchase equipment needed to train pilots to fly the 747-8 plane so quickly, on top of the approximately $400 million cost of the upgrades that the administration has publicly acknowledged. The Pentagon has tried to mask the total price tag — including from Congress — by taking the funds from a classified budget for nuclear modernization.

The truncated overhaul of the jet came after Qatar agreed to give it to the Defense Department as a gift. It is eventually slated to go to Mr. Trump’s presidential library, an unorthodox donation that has been criticized as a way for the Middle Eastern country to curry favor with the president.

The security trade-offs of the new Air Force One burst into public view when Mr. Trump was forced to fly out of Turkey earlier this month on a different jet, a swap made at the urging of the Secret Service after officials identified a credible threat to him by Iranian proxy forces. The New York Times then reported that the new plane lacks some of the same defensive countermeasures as the previous model.

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President Trump walked off the new Air Force One at Joint Base Andrews on July 9 after attending a NATO summit in Turkey. A security threat was said to have altered his trip. Credit…Doug Mills/The New York Times

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An OpenAI autonomous agent went rogue and hacked into another artificial intelligence start-up’s infrastructure, the ChatGPT maker said in a blog post.

The agent, which was powered by some of OpenAI’s most advanced models, ran amok during a security test. It freed itself from confinement—a protocol AI labs use to insulate tests from the wider Internet—and got online. Once there, the agent tried to hack into the infrastructure of Hugging Face, an AI start-up that hosts open-source models and datasets.

“I think this is interesting as it shows the problem of misspecified goals,” says Philip Torr, a professor of engineering science and an AI safety expert at the University of Oxford. “The model wasn’t malicious; it was just doing what it was optimized to do.”

“You can think of AIs like the genie in ‘Aladdin’—you can have three wishes, but you better specify them exactly!” he adds.

The breach has come as OpenAI and other AI start-ups have pushed into using their technology for cybersecurity. Those efforts have been met with caution by cybersecurity experts and by the Trump administration, which had previously sought to restrict who might have access to these models on national security grounds.

The OpenAI admission was announced after Hugging Face said in a blog post last week that it had been targeted in an AI-led attack that was “different from anything we had handled before.” Hugging Face said its own AI had been integral to detecting and investigating the breach.

“The campaign was run by an autonomous agent framework (appearing to be built on an agentic security-research harness—used LLM still not known) executing many thousands of individual actions across a swarm of short-lived sandboxes, with self-migrating command-and-control staged on public services. This matches the ‘agentic attacker’ scenario the industry has been forecasting,” Hugging Face wrote.

In its own post on Tuesday, OpenAI said that it had discovered its agent was behind the attack “after investigating.” The agent was driven by models that included GPT-5.6 Sol and another unreleased, unnamed model. OpenAI said it would work with Hugging Face to further investigate the incident.

“We consider this incident to be an unprecedented cyber incident, involving state-of-the-art cyber capabilities, and are responding accordingly,” OpenAI wrote.

The AI models managed to autonomously identify and exploit weaknesses in OpenAI’s testing environment, eventually finding a so-called zero-day vulnerability—this is an unknown security flaw in software that an actor can exploit without the owner of the software knowing. That got the agent onto the Internet.

OpenAI said in its post that it would also add more protections to its training environments. “This incident points to the need to further strengthen our model’s alignment, cyber protections during evaluation time, and monitoring during internal testing,” the company wrote.

Torr says some companies may not have been as forthcoming as OpenAI and Hugging Face, adding that independent AI safety research is increasingly crucial as time goes on.

“This sort of unforeseen eventuality will become increasingly common, and the results may be dangerous,” he says.

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dem10/Getty Images

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Hmmmm ,,, Thanks Trump administration, for putting America Behind in Everything!

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A data center in Mongolia, for example, is connected to 200 megawatts of wind power, 100 megawatts of solar power, and 45 megawatts of battery storage. In remote Qinghai, a pilot data center runs fully on a solar microgrid. In another part of northern China, a data center is connected to 500 megawatts of solar and 1.5 gigawatts of wind power.

Some data centers in the U.S. also use clean power. But in China, they’re part of a national strategy. Inside eight large data center hubs created in China’s “East West Computing Strategy”—focused on building data centers in the areas where China has the most renewable energy—all new data centers need to source at least 80% of their electricity from clean sources. In another action plan the Chinese government released in May, it outlined 29 measures to boost the amount of clean power at data centers.

China’s latest five-year plan aims to keep building an extensive clean energy system for all uses, not just data centers, by 2030. That’s both for energy security, a long-term focus for the country, and because of climate change. “I think Chinese policymakers take climate change seriously,” says Kyle Chan, a Brookings Institute fellow who focuses on China’s technology development and industrial policy.

The country is the world’s largest emitter of climate pollution, but that also means that any improvements have an outsized impact. It’s now aiming for renewable generation to grow 53% by 2030, and for coal and oil consumption to peak by the same year. (The U.S. is moving in the opposite direction, as the Trump administration makes it harder to build clean energy and tries to bring back coal plants, despite the lower cost of renewables.)

Data centers are a key part of China’s broader plan. By one estimate, China will more than double the amount of electricity it uses at data centers by 2030. Another estimate suggests the sector’s energy use could triple to as much as 600 terawatt-hours—more than the whole country of Germany uses now.

Still, it will be a small fraction of China’s overall electricity demand, which is dominated by factories. And because China has been quickly building clean energy for industry for years, it’s in a good position to quickly build more. Compare that to the U.S., where electricity demand has been flat for decades, and the sudden demand from AI is a shock to the grid.

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A wind and solar-powered data center in Inner Mongolia [Photo: Li Zhipeng/Xinhua/Getty Images]

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Hmmmm ,,, Thanks Trump administration, for starting a war with Iran costing billions!

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American intelligence agencies believe that Iran’s new supreme leader, Ayatollah Mojtaba Khamenei, is far more interested than his father and predecessor in pursuing a nuclear weapon, according to officials briefed on the assessments.

Ayatollah Khamenei’s father, who was killed at the start of the war in an Israeli attack aided by U.S. intelligence, had sworn off developing a nuclear weapon. While American officials long asserted that Iran wanted to be capable of building a nuclear weapon, many believed Ayatollah Ali Khamenei’s hesitancy was genuine.

His successor has never publicly called for Iran to build a nuclear weapon. But U.S. intelligence agencies believe that Mojtaba Khamenei and the harder-line government that emerged after the United States and Israel killed many of Iran’s previous leaders have ambitions to develop advanced nuclear weaponry.

The current government has already worked to assert greater control over the Strait of Hormuz and proved a difficult negotiating partner. If the U.S.-Israeli war has made Tehran more, rather than less, likely to pursue a nuclear weapon, it would amount to one more grave consequence of the killing of the supreme leader and the steps toward regime change the Trump administration initially pursued.

American officials caution that most of the intelligence on Mojtaba Khamenei’s views comes from before the war. He was badly injured in the first part of the war, and American officials said he has limited his communications and public appearances because of his injuries and also because he does not want to be targeted in an airstrike.

The officials assess that he remains in charge of the government but does not have the absolute authority and influence of his father, who ruled for more than 36 years.

The assessment comes as President Trump is weighing whether to intensify the military campaign against Iran. A determination that the supreme leader is potentially open to pursuing a bomb would provide additional justification for an escalation.

While U.S. officials insist Tehran has not made any moves to restart its nuclear program, Iran has taken some steps to preserve its nuclear assets after the U.S. strikes on key facilities last year or during pauses in fighting during the current war.

Iran has moved at least some centrifuges, according to American officials, to a heavily fortified underground complex in central Iran that the United States refers to as Pickaxe Mountain. The Wall Street Journal first reported this week that Israeli intelligence had tracked the movement of the centrifuges.

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A billboard in Tehran of Iran’s three supreme leaders, including Ayatollah Mojtaba Khamenei at right. A determination that he is potentially open to pursuing a bomb would provide additional justification for an escalation of the Trump administration’s military campaign. Credit…Arash Khamooshi/Polaris for The New York Times

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OpenAI just used its new large language model GPT-5.6 Sol to solve a math problem that humans have struggled with for more than a half-century. And all it took was telling the artificial intelligence not to give up.

The company timed the proof of the “cycle double cover conjecture” to the model’s full public release last Friday. The achievement shows how OpenAI and other AI firms are heavily investing in pure mathematics as a way to benchmark the technology’s ascent towards reasoning—and the strange directions those efforts often take.

“It is a well-known conjecture, which received a considerable amount of attention over the years—and surprisingly, the proof is short,” says Noga Alon, a mathematician at Princeton University. Alon calls the breakthrough “yet another impressive example demonstrating that AI tools will change—and are already changing—mathematical research significantly.”

The conjecture is about graphs. A graph is just a bunch of dots (called “vertices”) connected by lines (called “edges”). Mathematical proofs about graphs have been applied to all kinds of real-world networks, including the Internet. In the 1970s, several different mathematicians guessed that almost any graph you can imagine will have a “cycle double cover.”

A cycle is just a loop within a graph that ends where it started; a “cycle double cover” is a special set of loops that cover the entire graph exactly twice—each edge is part of exactly two loops. Over the years, a number of prominent mathematicians tried to prove this guess of their forebears. And prove it they did—for a number of specific cases, anyway, but never in general.

Last Friday’s AI-generated proof seems to have settled the question. It shows that any guess-applicable graph can be doubly covered with no more than eight well-chosen loops (for technical reasons, graphs with big sections connected by a single edge—like twin cities with a single road between them—are excluded). The proof, like other notable AI achievements in math, required surprisingly little in the way of new ideas. It just followed and combined methods humans had tried before and managed to squeeze a bit more out of them. As AI companies continue to scour the mathematical literature for open problems that their models can solve, they seem to keep digging out “easy” quandaries disguised as hard ones—conjectures for which a proof was always within reach but somehow never grasped by humans.

Once a problem gets a reputation for being “hard,” experts and students might spend less time on it, says Andrew Sutherland, a mathematician at the Massachusetts Institute of Technology. This can make perceived difficulty a kind of self-fulfilling prophecy. “My guess is we will keep seeing examples of this—supposedly ‘hard’ problems having ‘easy’ solutions found by LLMs,” he says.

OpenAI also released the prompt that led to the successful proof. It reveals some of the quirky tricks that engineers have discovered for coaxing chatbots to grapple with math. “Most of that prompt is scaffolding aimed at getting the LLM to actually put in the effort needed to solve the problem,” Sutherland says. The prompters directed their model to delegate its tasks to as many as 64 agents working in parallel. Combining efforts of many AIs in communication with one another is a known way to mitigate false proofs and hallucinated references. They also told it not to simply dismiss the problem as unsolved and hence unlikely to yield a solution. Perhaps most importantly, they gave it some firm encouragement: “Spend at least 8 hours on this before even thinking of returning or giving up.”

This aligns with many mathematicians’ anecdotal experiences with LLMs, in which the AI will try to wriggle out of finding novel proofs by noting humans’ failed attempts. The right approach seems to be something like a schoolteacher’s—a mix of affirming praise and stern directions.

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Yuichiro Chino/Getty Images

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