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The speed of light in a vacuum has been known as both a universal constant and a hard speed limit for all matter in the universe ever since Albert Einstein published his special theory of relativity in 1905. Rules, however, are made to be broken. And an international team of physicists appears to have found just such a loophole: the only thing that goes faster than light, it turns out, is darkness.

More specifically, individual dark spots known as optical vortices, or phase singularities, do so. As a light wave travels through space, it oscillates and twists—at the center of that twist, the peaks and troughs of the light wave cancel each other out, creating dark spots that—under certain conditions—outrun the light wave itself. The research was conducted by Technion–Israel Institute of Technology physicist Ido Kaminer and his colleagues.

“Our discovery reveals universal laws of nature shared by all types of waves, from sound waves and fluid flows to complex systems such as superconductors,” Kaminer said in a statement. The discovery confirms a prediction dating to the 1970s. Importantly, these vortices don’t carry mass, energy, or information, so they don’t violate Einstein’s rules, according to the researchers. “Phase singularities do not carry energy or information and thus can ‘move’ superluminally without breaking causality,” the physicists wrote in their study, which was published last month in Nature.

To make their discovery, the researchers constructed a unique microscope system that let them observe optical vortices in hexagonal boron nitride, a two-dimensional form of ceramic that can be used to convert light into quasiparticles that are a mixture of light and matter called polaritons. Polaritons move relatively sluggishly—around 100 times slower than the speed of light. With that speed, the team was able to observe how oppositely charged singularities approached each other and accelerated each other to superluminal, or faster-than-light, speeds before they were annihilated.

The technique used to measure the singularities’ velocity could open the door to studying other tiny, fast phenomena in physics, chemistry, and biology—or perhaps to find new ways to encode quantum information in materials, according to the researchers.

“We believe these innovative microscopy techniques will enable the study of hidden processes in physics, chemistry, and biology, revealing for the first time how nature behaves in its fastest and most elusive moments,” Kaminer said.

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Diners who had been skipping sit-down meals returned first, fueling triple-digit spending gains at casual chains.

Key Points

• Tax refunds are giving Americans a short-term boost in dining out, with restaurant spending jumping 53% in the two weeks after refunds were deposited, according to Chime data.
• Full-service restaurants are seeing the biggest gains, as diners use refunds to return to sit-down meals they had been skipping due to rising costs.
• While grocery spending also increased, much of it went toward restocking essentials, highlighting how refunds briefly ease budget pressures.

The cost of eating out has climbed faster than grocery prices for three straight years, with full-service restaurant prices rising another 0.3% in March, according to the Bureau of Labor Statistics  More than 70% of consumers would dine out more often if they had more disposable income, the National Restaurant Association’s 2026 State of the Restaurant Industry report found — but for most Americans, that extra room simply hasn’t been there.

Tax refund season changed that, at least temporarily. Chime, a financial services app that tracked spending among members who filed taxes through its platform, found that overall spending jumped 85% in the two weeks after refunds were deposited, with restaurant spending rising 53% in that same window.

The analysis covered 148,000 members who deposited their refunds through the app and made 15 or more purchases per month in the four months before and after filing. The surge came after members had already set aside a portion in savings, meaning the jump reflects people choosing to eat out, not just spending because the money was there.

The refunds arriving this season are also larger than in recent years. The average refund reached $3,462 in 2026, up more than 11% from the same point last year, according to the IRS’s filing season update on April 3. For many lower- and middle-income families, that check is the largest single deposit of the year, and a significant share of it went to a restaurant table.

Janelle Sallenave, Chime’s chief operating officer, notes that members came into tax season ready to act. “More than half of those using the in-app tool filed in January and February,” Sallenave says. “Members were deliberate with their refunds, both increasing their spending and also setting aside a portion for savings. On the savings side, we see about a quarter of the refund moved to savings accounts on average, and balances remained up nearly 50% several months later.”

Diners splurge on sit-down meals after tax refunds

 

Diners who had been skipping sit-down meals returned to full-service restaurants first once refunds were in hand. Spending climbed 183% at Chili’s, 127% at Texas Roadhouse, and 80% at Buffalo Wild Wings. McDonald’s saw a 36% increase, which is meaningful but well below what the sit-down chains recorded. Diners have been heading back to chain steakhouses like Texas Roadhouse steadily since mid-2024, drawn by meals that feel worth the spend even when budgets are tight. For people who had been choosing between cooking at home and grabbing something quick, the refund was enough to bring them back to the kind of meal they’d been putting off.

More people were walking into restaurants in February than at any point in the previous nine months, according to the National Restaurant Association’s Restaurant Performance Index. The timing lines up with early refund deposits, though whether those diners keep coming back once the money works its way through is another question.

Shoppers restocked groceries, but spending stayed modest

 

Shoppers who had been paring down their grocery lists for months used the refund to add back what they’d dropped. Spending at Kroger, Safeway, Publix, and Food Lion generally rose by less than 60%, while growing by closer to 115% each at Walmart and Target. At traditional grocers, people were restocking essentials like meat, dairy, and cereals — categories where the Bureau of Labor Statistics reported falling prices in March. At Walmart and Target, they were buying across the store, picking up household items and other things that had been kept off the list because budgets were stretched.

Refund-fueled spending may already be slowing

 

Tax Day falls on April 15, and the IRS has issued 69.8 million refunds as of early April, with more still processing. Restaurant prices haven’t come down, and the pressure that kept diners away from sit-down meals for most of last year hasn’t eased. The refund gave Americans a few weeks to eat the way they wanted to, not the way they had to — and for most, that window may already be closing again.

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The Fifth Circuit court’s ruling, which is being appealed, reinstates a requirement that patients visit a health care provider in person to obtain mifepristone, upending abortion access in the United States.

More than a hundred reproductive health physicians were gathered in Washington, D.C., on Friday afternoon, listening to an update on the shifting legal landscape of reproductive health care.

The presentation was delivered by Molly Meegan, the chief legal officer of the American College of Obstetricians and Gynecologists, who had no idea that another ruling on the abortion pill mifepristone had arrived as she spoke, temporarily blocking the drug’s prescription by telemedicine and delivery by mail.

“This is not a ruling based in evidence, science, or best interests of women,” she said, after learning of the decision by a panel of the U.S. Court of Appeals for the Fifth Circuit.

The order is already being challenged, but if the Supreme Court lets it stand, it would upend access to a means of abortion that has been steadily growing in recent years. The ruling has also thrust abortion into the national spotlight in advance of the midterm elections, as organizations that provide and support abortion services and those that oppose abortions unleashed a flurry of responses.

“This decision represents the most sweeping threat to abortion since the overturning of Roe v. Wade,” said Kelly Baden, vice president for public policy at the Guttmacher Institute, a research organization that supports abortion rights. “If allowed to stand, it would severely restrict access to mifepristone in every state, including those where abortion is broadly legal and where voters have acted to protect abortion rights.”

Louisiana, which has a near-total ban on abortion, went to court to stop distribution of the drug by mail. The appeals court said that while that lawsuit proceeded, the Food and Drug Administration needed to reinstate a requirement that patients visit medical providers in person to obtain mifepristone.

A mifepristone manufacturer filed an emergency appeal to the Supreme Court on Saturday, asking it to restore full access to mifepristone. A second mifepristone maker said it would file a similar appeal. The Trump administration has so far declined to comment on the ruling or what steps it might take.

Anti-abortion groups celebrated the ruling. Marjorie Dannenfelser, president of Susan B. Anthony Pro-Life America, called the court’s decision “a huge victory for victims and survivors of Biden’s reckless mail-order abortion drug regime.”

Carol Tobias, president of National Right to Life, said in a news release that the ruling “recognizes that the FDA cannot simply sweep legitimate safety concerns aside in favor of politics.”

Abortion opponents have argued that the F.D.A.’s decision to allow abortion pills to be available by mail posed safety risks to women and violated the sovereignty of states that had banned abortion. Major medical organizations and supporters of reproductive rights have pointed out that more than 100 studies have found the pills to be safe and effective, with serious side effects being rare.

Medication is now the method used in nearly two-thirds of abortions in the United States, and is typically delivered in the form of a two-drug regimen through the first 12 weeks of pregnancy.

The first of those drugs is mifepristone, which was approved in 2000, and blocks a hormone needed for a pregnancy to develop. The second drug, misoprostol, has many other medical uses and was not affected by the Fifth Circuit ruling.

Typically, misoprostol, which causes contractions similar to a miscarriage, is taken 24 to 48 hours after mifepristone. But several providers said they were prepared to continue telemedicine services, prescribing only misoprostol, which can be used on its own for abortion, although it is considered somewhat less effective and more likely to have side effects.

Earlier on the day of the ruling, Planned Parenthood of Greater New York had announced an expansion of its telemedicine abortion service. After the Fifth Circuit decision, the organization said it would continue to provide telehealth abortion with misoprostol.

“In the wake of yesterday’s harmful decision by the Fifth Circuit, Planned Parenthood Direct is mailing misoprostol-only prescription kits,” said Jacquelyn Marrero, a spokesperson for Planned Parenthood of Greater New York.

Telemedicine abortion has steadily increased since the F.D.A. began allowing it in 2021. As of the first six months of 2025, more than one-fourth of abortions in the country were provided via telemedicine, according to a report from a reproductive rights research group.

Although abortion is currently banned or restricted in 20 states, over 100,000 patients per year in those states have been receiving pills through the mail. Those pills are prescribed and shipped by medical practitioners in states that have abortion shield laws. Officials in those shield-law states are prevented from obeying subpoenas, extradition requests and other legal actions that states with bans take against abortion providers.

The laws are being tested by several cases that are expected to lead to a constitutional showdown over whether states must honor one another’s abortion laws. Some abortion providers said they had anticipated the Fifth Circuit’s ruling, given the court’s conservative leanings, and many had already developed contingency plans.

Julie Burkhart, who runs Wyoming’s only abortion clinic, said that the Fifth Circuit’s ruling was “devastating, but it’s not surprising.” Ms. Burkhart said her clinic had temporarily suspended telehealth medication abortion appointments in response to the decision, but hoped to quickly reopen them.

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If the court’s temporary ruling stands, patients would have to make an in-person visit to obtain the abortion pill mifepristone. Credit…Hannah Yoon for The New York Times

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Ozempic, Zepbound, and other glucagonlike peptide 1 (GLP-1) drugs have shown sweeping health benefits—they can control blood sugar, manage body weight, and improve heart health. And last year, GLP-1 drugs received U.S. Food and Drug Administration approval to treat kidney and liver disease.

Some scientists think these body-wide benefits are likely tied to the drugs’ weight-loss effects, but growing research suggests another factor may be at play: taming inflammation. To tease this out, researchers are trying to chart which anti-inflammatory pathways the drugs might activate. This could help them better understand what’s been seen clinically and open the door to GLP-1 treatments for a variety of inflammatory diseases, says Daniel Drucker, an endocrinologist at the University of Toronto, who is studying GLP-1 drugs’ widespread effects.

“Yes, weight loss is important, but it’s by no means the whole story,” he says. “We have patients [taking GLP-1s] who are telling us, ‘Wow, my arthritis is better,’ ‘My Crohn’s or colitis is better,’ and that motivates us to say, ‘Well, how is that happening?’”

When a healthy immune system kicks into gear, it boosts inflammation to help fight off threats, such as bacteria or viruses. But research has shown that several metabolic and heart diseases impair the immune system’s ability to moderate inflammation, causing harmful levels of inflammation in response to high cholesterol, fat, or glucose.

“The immune system gets ramped up where it shouldn’t,” says Marc Bonaca, a cardiologist and vascular medicine specialist at the University of Colorado Anschutz. Treatments that suppress the immune system can help lower chronic inflammation. But there’s a trade-off: dampening the immune system weakens its ability to tackle real infections.

Clinical trials and real-world data suggest that GLP-1s may be able to strike this balance, Bonaca says. Studies have shown that semaglutide (the active ingredient in Ozempic) leads to about a 40 percent reduction in the inflammation blood marker C-reactive protein—independent of weight loss. Other analyses suggest that GLP-1 drugs lower the risk of infections. Combined, this evidence suggests the drugs may be “calibrating or resetting the immune system in a way, not just suppressing it,” Bonaca says.

The receptors for GLP-1—the main hormone that the drugs mimic—are found in the gut and in many other organs. This means GLP-1 drugs can bind to cells throughout the body. “The liver, the heart, the blood vessels, the kidney, and probably the brain as well—those are the major organs where we are pretty confident there’s a reduction of inflammation [from GLP-1 drugs],” Drucker says. This aligns with the list of conditions GLP-1 drugs have been approved to treat so far.

Most recently, Drucker’s team published a paper this month investigating cells of mice that were engineered to have a type of severe liver disease called metabolic dysfunction-associated steatohepatitis (MASH). Excess fat in the liver drives inflammation, which, over time, can lead to fibrosis—a severe scarring and stiffening of tissues. If the condition remains untreated, people can develop cirrhosis and require a liver transplant.

“Type 2 diabetes and obesity will [over time] contribute substantially to accumulating fat in the liver,” Drucker says. “So there’s no question that controlling blood sugar and losing weight are helpful. But very often that’s extremely difficult to do in people with metabolic liver disease, and diet and lifestyle modification alone has never been proven to substantially reverse the disease in a clinical trial.”

Semaglutide has been shown to help resolve MASH in human clinical trials, and the FDA approved the drug for that disease last year. Drucker’s team wanted to know if these clinical improvements were driven purely by weight loss or by lower inflammation as well.

GLP-1 receptors are expressed at very low levels in the liver, specifically in rare cells called liver sinusoidal endothelial cells. These specialized cells are part of the immune barrier between the gut and liver and “are intimately involved in tissue defense,” says Adnan Said, a gastroenterologist and liver transplant expert at the University of Wisconsin–Madison, who was not involved in the recent study.

By turning off genes that express GLP-1 receptors involved in weight loss outside of the liver, Drucker’s team demonstrated that activating liver sinusoidal endothelial cells with semaglutide independently improved liver disease in mice. When the drug bound to the GLP-1 receptors in this small subset of liver cells, they secreted proteins that turned on a half-dozen other cell types throughout the liver. Those proteins are linked to an array of regulatory actions, including fat synthesis, liver metabolism, immune function, and cell survival.

“All of the information that flows out of this subpopulation of liver cells ends up being very important for healing the liver—reducing the amount of fat that’s in the liver, reducing the amount of inflammation that’s in the liver, reducing the amount of fibrosis,” Drucker says. “It’s a very powerful, orchestrated system that’s directed by semaglutide.”

In the liver, the researchers also found GLP-1 receptors in immune cells called T cells, which could contribute some anti-inflammatory benefits, but their role couldn’t be confirmed in the study. While GLP-1 receptors are present in the same set of liver cells in humans, the mechanism will need to be verified through human tissue studies.

“This is preclinical work, and mice models may not replicate the GLP-1 pathways in [a] human liver,” Said says. Other weight-independent benefits of semaglutide, such as increased insulin sensitivity, may also be involved in the observed liver disease improvements, he says.

Still, the findings open compelling new avenues of investigation into how GLP-1 drugs’ anti-inflammatory effects may help with other conditions such as heart failure, sleep apnea, and chronic kidney disease, Said says.

Bonaca, who was not involved in the recent research, says the study aligns with observations he and other groups have made on GLP-1 treatments for cardiovascular conditions. He led a trial funded by Novo Nordisk (which makes and sells Ozempic) that tested semaglutide on peripheral artery disease—blockages in the large arteries of the legs that can cause severe cramping and mobility issues. Bonaca suspects that the walking improvements seen in trial participants who took semaglutide were likely from anti-inflammatory mechanisms in the vascular endothelial muscles.

“We see a unique therapeutic profile for these agents, and it’s really unrelated to weight loss,” he says. Bonaca adds that the insights from the new study on MASH reinforces the point. “These are vascular, anti-inflammatory drugs with broad benefits,” he says.

Drucker is interested in seeing similar molecular studies that could clarify anti-inflammatory pathways in other organs. Researchers are already investigating the drugs’ use for various chronic inflammatory diseases. Eli Lilly, the developer of the GLP-1 drugs Zepbound and Mounjaro, is currently running clinical trials on GLP-1 treatments for Chron’s disease, arthritis, and psoriasis.

There are limitations: how much GLP-1 drugs curb inflammation matters for different diseases. The anti-inflammatory properties might help with liver disease, for instance, but may have little or no effect in improving other conditions. “We’ll have to look at each disease one by one,” Drucker says. (Drucker has consulted and given talks for Eli Lilly and Novo Nordisk.)

As more evidence reveals the ways in which these drugs work beyond weight loss and blood sugar control, it could change how they are used and prescribed, he says.

The new evidence reflects “an evolution” in how scientists are thinking about GLP-1 drugs, Drucker says. “If your health is more complicated, then your health care provider needs to understand that achieving weight-loss thresholds is not the [clearest] way to think about the benefits of these medicines.”

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Data journalist and pollster G. Elliott Morris says that President Donald Trump’s approval rating on inflation is so low that he had to redo his graph to account for it.

Recent polling shows that the president faces historic disapproval on reducing the cost of living. A new Reuters/Ipsos poll has found that only 21 percent of Americans approve of his handling of inflation.

A poll from Fox News showed that he has only a 28 percent approval rating on inflation, while 72 percent of Americans disapprove of his handling of it. Meanwhile, the Associated Press-NORC Center for Public Affairs Research released a poll last month showing that his approval on the economy dropped from 38 percent in March to 30 percent in April.

Morris, who runs the polling aggregator 50plusOne, showed that the polling average for Trump’s approval rating on inflation and the cost of living is well below what he had set on his graph. His website shows as of the end of April, his approval rating on inflation is at negative 40.3 percent.

“Trump literally broke the scale of this graph on my data portal,” Morris tweeted.

Trump largely won the 2024 presidential election due to frustration from voters about the increased cost of living. But ever since returning to office, Trump has enacted an aggressive policy of imposing tariffs on foreign countries, causing prices to increase.

In addition, the war in Iran has caused the price of gas to skyrocket not just in the United States but around the world. Iran has largely responded to the Trump administration’s assault by closing off the Strait of Hormuz, through which 20 percent of the world’s oil supply passes.

There are few signs that inflation will abate. Last month, the Bureau of Labor Statistics released its survey showing that the Consumer Price Index rose 0.9 percent in March as the war in Iran began, and the report showed that prices rose 3.3 percent in the past year.

On Thursday, the Bureau of Economic Analysis released the latest Personal Consumption Expenditures index, a key inflation indicator used by the Federal Reserve to determine how to set interest rates.

The data showed that the number jumped to its highest level in three years, hitting 0.7 percent in March, 3.2 percent higher than it was a year ago. Bloomberg’s April survey of economists showed that economists expect the PCE index to increase 3.6 percent in the second

The price of gas also hit $4.23 a gallon, its highest since Russia invaded Ukraine.

All of this could spell dire news for Republicans ahead of the 2026 midterm election. Morris’s website shows that ahead of the midterm, Democrats a five-point lead on the generic ballot, which measures whether voters would prefer to vote for a generic Democrat versus a generic Republican to Congress.

Earlier this week, Federal Reserve Chairman Jerome Powell said in his last meeting as chairman that the central bank would keep interest rates steady amid concerns about inflation. Trump has tried to push Powell to reduce interest rates.

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Trump broke the scale!

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Millions of Americans appear to be dropping Obamacare coverage in the months since Congress failed to extend the generous subsidies that had become a defining feature of the Affordable Care Act.

Initial sign-ups had already fallen by about 1.2 million people. But insurance companies, state officials, and industry analysts are reporting that many more have lost Obamacare coverage now that people are facing long-term higher costs. The federal government has yet to report current enrollment data.

Many insurers and analysts are estimating overall declines of about 20 percent, dropping to around 19 million from the 24 million who were covered under the A.C.A. last year. Other indications suggest there could be even larger potential losses by the end of the year, a deep retrenchment for Obamacare coverage, and a reversal of significant gains in the last several years.

The rising cost of health care has shown up as a top concern among Americans in several public opinion polls. Premiums are rising for Americans who get insurance through work, too, as health care costs have been increasing nationwide. Out-of-pocket costs are growing, too, as plans with high deductibles have become popular.

Though health care has faded somewhat as a priority for the Republican-controlled Congress since lawmakers hit a stalemate over the subsidies at the end of 2025, it is likely to figure prominently in the midterm elections this year.

One analysis, by Wakely Consulting Group, a firm with access to detailed insurance industry data, estimates that coverage in the marketplaces will drop by as much as 26 percent this year compared with last year’s average enrollment.

In Georgia, where coverage had nearly tripled since Congress first authorized the extra financial help in 2021, state data show enrollment has fallen by more than a third, according to information obtained by the news organizations The Current GA and The Georgia Recorder.

The Georgia state insurance department did not respond to a request for comment.

Some Blue Cross plans lost 20 to 30 percent of customers this year. And many people are switching to plans with lower premiums but much higher out-of-pocket costs, said David Merritt, a spokesman for the Blue Cross Blue Shield Association. “We are waiting on official data like everyone else,” he said.

The insurers and state officials said early retirees with middle-class incomes, who faced the largest increases in premiums, appeared to be among the hardest hit. In some markets, the cost of insurance for this group rose by $1,000 a month or more.

In many states, around 10 percent of people who are still insured have chosen less generous coverage by picking so-called bronze plans, which carry deductibles as high as $10,600 a year.

The Trump administration has downplayed the losses. Officials at the Centers for Medicare and Medicaid Services, which oversees the marketplaces, have characterized the current enrollment as a success. “The marketplace remains strong and resilient, continuing to provide millions of Americans with access to high-quality, affordable health care coverage options,” said Chris Krepich, the agency’s director of communications.

In testimony before the House Committee on Education and the Workforce last month, Robert F. Kennedy, Jr., the nation’s health secretary, attributed the initial reductions to an administration crackdown on fraud.

Mr. Kennedy also emphasized the low cost of much of the insurance for most people who are buying it. He said 87 percent of people enrolled in Obamacare in January owed less than $96 a month, numbers contained in a federal report in March.

But a swath of Americans are paying much more. The escalating cost of insurance — and the expected coverage losses — was a major Democratic theme this winter, and Democratic lawmakers’ effort to extend the financing was a central demand during the record 43-day government shutdown.

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Older people who are medically high risk, but too young for Medicare, are facing unaffordable health insurance premiums after federal health care credits lapsed earlier this year. Now that the grace period has expired, some Americans are struggling to get the care they need. CreditCredit…Lauren-Pruitt/The New York Times

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On Sunday, three runners at the London Marathon set the sporting world on fire—not least because of their shared choice of footwear. Kenya’s Sabastian Sawe won the men’s race with a record-setting time of one hour, 59 minutes and 30 seconds (1:59:30) while Ethiopia’s Yomif Kejelcha came in second, finishing in 1:59:41, and fellow Ethiopian Tigist Assefa broke the women’s record with a time of 2:15:41. All three were wearing a pair of new Adidas shoes specifically designed for marathoning, the Adizero Adios Pro Evo 3.

The shoes’ apparent success is the latest shot fired in a long-simmering war among athletic wear companies to design footwear to help people move faster on long-distance runs. While “it’s gotta be the shoes” was once used as a tongue-in-cheek tagline for Air Jordans, there’s quite a bit of truth to that sentiment when it comes to marathoning, says Brad Wilkins, director of the University of Oregon’s Performance Research Laboratory.

“People are just getting faster and faster and faster, partially due to equipment, partially due to belief in the fact that we can run this fast, and partially due to training and adaptations because of that belief,” he says.

The Adizero Adios Pro Evo 3 is somewhat odd-looking when compared to a regular running shoe. The sole is packed with padding that surrounds a curved carbon plate, all of which gives the shoe the appearance of the bottom of a rocking chair. The design is all about economy, Wilkins explains. The padding is made of ultralightweight foam, which keeps the shoe’s mass as low as possible while still providing cushioning for the foot. The carbon plate, meanwhile, is designed to put the runner “kind of in a forward tilt,” he says. If you were just walking in the shoes, you would find it more difficult to get around than you would in an average pair of sneakers. But a long-distance runner’s stride is fundamentally different from the gait of someone going for a stroll.

“It puts you more on your forefoot,” Wilkins says, referring to the bend in such running shoes. “Some of the models of these shoes don’t even have outsoles in the heel. They’re basically expecting that you’re going to be running on your forefoot the whole time.”

The reason for that assumption is that conserving energy is one of the keys to success in marathoning. A running gait that primarily uses the front of the foot is more efficient than one that has the heel making contact with the ground. That’s because pressing down on the ground with the heel can generate backward momentum, requiring the runner to use more energy to propel themselves forward.

The materials and design of these shoes combine to “increase the springlike capability of the leg by adding, essentially, a spring on your foot,” says Daniel Lieberman, a professor of biological sciences at Harvard University and an amateur marathoner. “When a runner hits the ground with these shoes, the shoe is storing up elastic energy, and then it’s recoiling, pushing the runner back up into the air.”

He estimates that the latest generation of marathon shoes could help runners expend 4 to 6 percent less energy per stride.

“There’s no question, study after study shows these shoes are responsible for people running faster because they have more energy, and more energy means more gas on the tank,” he says.

In a statement, Adidas’ general manager of running, Patrick Nava said that the Adizero Adios Pro Evo 3 shoes are the result of “more than a dozen iterations, working closely with our athletes and testing everywhere from our labs in Herzogenaurach [in Germany] to high-altitude camps in Kenya and Ethiopia.”

“At that level, every detail really matters—we were measuring things down to the nearest nanogram,” Nava said. “It was a long process, but it’s led to something we believe genuinely changes what a race-day shoe can feel like.”

Marathon times have grown steadily shorter since the distance of 42.195 kilometers (26.2 miles) was formalized in 1921. That’s not to say that footwear technology is the sole reason for the improved performance. Initially, winning times tended to be just under three hours. By the 1950s, they were down to around two hours and 20 minutes—and athletes have been shaving minutes and seconds off ever since. Lieberman says that because training and nutrition sciences have also improved over time, it’s impossible to determine how much credit to give new shoes for the improvement.

“When you have somebody running 26.2 miles, and you try to figure out scientifically what it is that’s causing one person to run faster than another, nobody can figure that out,” he says.

He points to the late neurologist Roger Bannister, who, as a medical student, ran the first sub-four-minute mile in 1954, as a comparison point.

“Now you’ve got these fancy, big shoes and these companies, and it’s a different world,” he says. “To me, it’s not quite the same thing, and there’s no question: the shoes have had a major effect on the ability to do it. This is technology-assisted, which is not to say that these athletes aren’t exceptional. But to me, it’s not quite exactly the same thing.”

As impressive as breaking the two-hour mark is, Wilkins says he doesn’t think humans have come close to their maximum long-distance speed. Seconds and minutes will continue to be stripped away as technology and training improves, he says.

“The bar has 100 percent been changed,” he says. “I think it’ll be very soon where, if you’re not running sub-two hours, you’re no longer in the elite kind of category.”

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The lawmakers who represent Alabama’s two Black congressional districts, who are now at risk of losing their seats after the Supreme Court effectively decimated the Voting Rights Act, said the decision sends the US “backwards”.

The 6-3 ruling in Louisiana v Callais on Wednesday weakens a key provision of the Voting Rights Act, opening the door for Republicans to eliminate majority-minority congressional districts across the south, and representatives Terri Sewell and Shomari Figures stand in the crosshairs.

“People in my home town fought, braved, died, marched for the right of all Americans to vote,” Sewell, who represents Alabama’s seventh congressional district, said shortly before Wednesday’s decision. “And I know I wouldn’t be here, were it not for the Voting Rights Act. I mean, actually, all Black elected officials. It’s pretty frightening to think that on our collective watch, we’re going backwards and not forwards.”

Figures, who represents Alabama’s newly drawn second congressional district, said the ruling threatens far more than the seats currently held by Black members of Congress. “The impact will be great,” he said in an interview before the decision, anticipating that the court would weaken the landmark voting law. “At the end of the day, the Voting Rights Act is about fairness. It’s about having the opportunity to elect members of Congress of your choice, and not have the district lines drawn in a way that inhibits the ability of a significant racial group to have an impact in the outcome of an election.”

In a ruling split along ideological lines, the Supreme Court affirmed that Louisiana’s congressional maps violated the equal protection clause. Writing for the majority, Justice Samuel Alito held that section 2 of the Voting Rights Act of 1965, which for four decades had been used to challenge electoral maps producing racially discriminatory results, does not require states to draw majority-minority districts. Justice Elena Kagan, in a dissent joined by justices Sonia Sotomayor and Ketanji Brown Jackson, wrote that the decision effectively eviscerates the law. 

‘All we want is fair representation.’

The implications for Alabama are immediate and deeply personal for both Sewell and Figures. Republican lawmakers in Alabama will likely move quickly to redraw the state’s congressional maps, Sewell said, but not in time to affect the 2026 midterms. The state’s deadline to qualify as a major party candidate for the 19 May primary was in January, meaning it’s likely too late for Republicans to change maps before the upcoming elections. Sewell and Figures may be safe in November, but Republicans will likely redraw their districts and push them out of Congress in 2028.

Sewell, who represents a swath of the state’s Black Belt that includes Selma, the city where she grew up – has served in Congress since 2011. For 13 of those years, she was the only Democrat in Alabama’s congressional delegation and the only representative from a district where Black voters could elect a candidate of their own choice. Her district, which winds through some of the poorest counties in the nation, was itself a product of the Voting Rights Act, redrawn to give Black Alabamians, who make up about 28% of the state’s population, a voice in federal representation.

Figures’ district, the newly drawn second district, exists solely because of a recent legal victory. The seat was created after the Supreme Court ruled in Allen v Milligan in 2023 that Alabama’s congressional map illegally diluted Black voting power. That decision reaffirmed section 2 of the Voting Rights Act and compelled Alabama to draw a second opportunity district. Figures, a first-term congressman from Mobile, won that seat in 2024 in what Sewell called a historic moment: for the first time in modern Alabama history, two Black representatives sat together in the congressional delegation.

“It was a long time coming,” Sewell said of that day. “When you think about representation, all we want is fair representation.”

Wednesday’s ruling puts that representation directly at risk. But Sewell and Figures were both clear that the threat extends far beyond Congress. With the Voting Rights Act weakened, representation at all levels is threatened, Sewell said, including in state legislatures, county commissions, city councils, and school boards.

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The 6-3 ruling in Louisiana v Callais weakens a key provision of the Voting Rights Act. Composite: Javier Palma/The Guardian/Getty Images

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Jerome H. Powell capped off his eight-year tenure as chair of the Federal Reserve with the most divisive policy meeting in decades, as three officials suggested the central bank should more directly signal that the Fed’s next move could just as likely be a rate increase as a cut.

Adding to the drama was an announcement by Mr. Powell that he would remain as governor at the central bank after his term as chair ends May 15 and President Trump’s handpicked successor, Kevin M. Warsh, takes over. That decision will deny Mr. Trump the opportunity to appoint another governor to the Fed’s seven-member board until Mr. Powell leaves.

Mr. Powell’s decision to stay, which he can do until January 2028, breaks with tradition. But he pegged it to the numerous broadsides that Mr. Trump and his administration had launched against the Fed in the last year, which he warned put the central bank’s independence “at risk.”

Wednesday’s meeting, at which the Fed voted to keep rates unchanged at a range of 3.5 to 3.75 percent, encapsulated the acute challenges that Mr. Warsh will inherit once he steps into the role. In his confirmation hearing, Mr. Warsh said he wanted “messier” meetings and for the Fed to have a good “family fight,” which he seems likely to get.

But he is also at risk of becoming Mr. Trump’s newest target if he is unable to deliver the rate cuts that the president has long demanded. He has spent years attacking Mr. Powell for not cutting rates quickly or aggressively enough, calling him a series of names, including “too late,” “a stupid person,” and a “moron.”

Mr. Trump on Wednesday reiterated that it was a “good time” to lower rates, just as officials at the Fed were making clear that they had turned more wary about providing that relief. Inside the central bank, the debate has shifted away from when to cut again toward whether to do so at all, resulting in the most divisive meeting since 1992. The calculus has changed largely because of the war in Iran, which has sent energy prices soaring and lifted inflation.

Stephen I. Miran, who was appointed to the Fed last year by Mr. Trump, issued his sixth straight dissent and voted for a quarter-point cut. Presidents from three of the regional reserve banks supported the decision to hold rates steady. But they wanted the Fed to signal more explicitly in its policy statement that the next move from the central bank was not necessarily another rate cut.

Instead, the Fed maintained in its statement that “in considering the extent and timing of additional adjustments to the target range for the federal funds rate, the Committee will carefully assess incoming data, the evolving outlook and the balance of risks.”

The dissents came from Beth Hammack, president of the Cleveland Fed; Lorie Logan, who runs the Dallas Fed; and Neel Kashkari, who heads up the Minneapolis Fed.

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Jerome H. Powell on Wednesday said that he would remain at the central bank after his term as chair ends on May 15 and his successor, Kevin M. Warsh, takes over. Credit…Anna Rose Layden for The New York Times

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The plot of “The Wizard of Evergreen Terrace” seems like that of a typical Simpsons episode. In it, Homer struggles with a midlife crisis. Disappointed by a lack of accomplishments in his life, he decides to emulate famous inventor Thomas Edison and, in turn, tries to develop technical innovations, which, of course, all end in disaster. But if you follow the episode carefully, which was first broadcast in 1998, you’ll be in for a surprise—at least if you know anything about mathematics.

In one particular scene, Homer stands pensively at a fully scribbled blackboard. Next to the obligatory drawings of doughnuts, which are not only Homer’s favorite food but also critical to the field of topology, there is a seemingly harmless equation: 3,987¹² + 4,365¹² = 4,472¹². Type it into a calculator, and it appears correct. But amazingly, it contradicts one of the most established theorems of mathematics.

The Great Theorem of Fermat: A Centuries-Old Mathematical Riddle

This story dates back to the 17th century. It starts with the equation xⁿ + yⁿ = zⁿ. If you choose n = 1, then this equation will always be satisfied: no matter how one chooses the values for x and y, z will always be a positive integer result. For example, 3 + 6 = 9.

For n = 2, it gets a bit trickier because the equation becomes quadratic: x²+ y² = z². This formulation feels familiar, particularly if you like geometry—it’s the Pythagorean theorem. Still, there are some quirks: if x and y have integer values, z is not necessarily an integer. For example, for x = 1 and y = 2, the formula 1² + 2² = 5. But 5 is not a square number.

Look at the equation again when n = 3, and things get strange. You cannot find a solution that is an integer for x³ + y³ = z³. That means you cannot divide a cube with integer side lengths z into two smaller cubes that have integer side lengths x and y. The same is true for all other values of n.

Seventeenth-century French scholar Pierre de Fermat recognized this, too, and claimed to have discovered a proof for the statement that there are no three positive integers x, y, and z that can satisfy xⁿ + yⁿ = zⁿ when n is greater than 2. The catch: he wrote about achieving this mathematical wizardry in a note in the margins of a book by an ancient scientist, Diophantus of Alexandria, and he didn’t actually spell out the proof.

Fermat left similar scribbles behind frequently. And all of them—except this one—were successfully proved by later experts. So this mystery proof became known as Fermat’s last theorem.

Generations of scholars took a crack at it until, finally, more than 350 years later, in 1994, mathematician Andrew Wiles solved the puzzle. His impressive work made waves: he developed novel methods that led to further groundbreaking discoveries in the field. For this, among other things, he was honored in 2016 with the Abel Prize, one of the highest honors in mathematics.

For Wiles’s proof, you have to leave the algebra you know from school and enter more branched mathematical areas. In fact, you have to enter into the esoteric realms of elliptic curves and modular forms—concepts developed in the 1980s.

Nobody seriously doubts that Wiles’s approach is correct. His technical paper has been reviewed by many experts, especially because some of his techniques are repeatedly revisited to reveal other mathematical relationships. This reduces the probability that an error could have crept in somewhere.

But Fermat could not have known about elliptic curves and modular forms. So that creates new questions: Had the scholar been joking? Had he miscalculated? Or does a substantially simpler proof exist? The debate goes on.

Homer Simpson versus Pierre de Fermat

Fortunately, the Homer Simpson mystery is easier to solve. Yes, 3,987¹² + 4,365¹² = 4,472¹² represents an integer solution of the equation xⁿ + yⁿ = zⁿ for n = 12. But the problem here is in the conventional calculator.

The numbers 3,987¹² + 4,365¹² are enormously large values consisting of 44 digits. Ordinary calculators typically provide only 10 digits, which is why they round the numerical values up or down. With a more accurate calculator or computer program, you will find that 3,987¹² + 4,365¹² does not actually equal 4,472¹².

In fact, what “The Wizard of Evergreen Terrace” proves is that many of the creators of The Simpsons have a surprisingly deep knowledge of mathematics. Many of its writers have had backgrounds in computer science, mathematics or physics, including David X. Cohen, who was responsible for the Fermat joke. He had written a computer program specifically to spit out a near solution for this purpose. That he chose Fermat’s great theorem may not have been pure coincidence: in fact, as a student, Cohen attended lectures by mathematician Ken Ribet, who had done some of the preliminary work for Wiles’s proof.

And that’s far from the only Simpsons episode with a slyly placed nerdy Easter egg. In his book The Simpsons and Their Mathematical Secrets, mathematician Simon Singh presents many more examples. If nothing else, the show invites you to take a closer look during a cozy evening TV viewing—and perhaps make a mathematical discovery in the process.

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