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“I said, ‘Bibi, this is your chance for victory,’” Mr. Trump related, referring to Mr. Netanyahu by his nickname. “He was fine with it,” Mr. Trump continued, adding, “He’s got to be fine with it. He has no choice. With me, you got to be fine.”

Mr. Netanyahu is in no position to defy Mr. Trump while facing international censure over Israel’s conduct in the war and growing international isolation, analysts say, increasing its reliance on the United States.

“Trump doesn’t threaten Netanyahu; he orders him,” wrote Nahum Barnea, a prominent Israeli political columnist, in Sunday’s Yedioth Ahronoth, a mainstream Hebrew daily, in an article with the headline “He’s the Boss.”

The turn of events in recent days “clearly illustrated that state of affairs to everyone,” Mr. Barnea continued, referring to Mr. Trump’s ultimatum to Hamas on Friday to accept the proposal, followed hours later by the president’s interpretation of a highly qualified acceptance by the militant group as an unqualified yes.

Israelis then learned from Mr. Trump, via a social media post on Saturday, that Israel had already agreed to an initial withdrawal line within Gaza for the first phase of the deal, which proposes exchanging about 20 living hostages and the bodies of about 28 believed to be dead for 250 Palestinian prisoners serving life terms and hundreds more Gazans detained during the war.

Once Hamas signs on, Mr. Trump announced in the same post, a cease-fire would “IMMEDIATELY” go into effect.

For months, Mr. Netanyahu has been engaged in a delicate balancing act. He has been determined to fulfill his pledge of total victory over Hamas, whose attack on Israel on Oct. 7, 2023, ignited the war, and to ensure his own political survival by appeasing his far-right coalition partners who oppose any deal that leaves Hamas standing.

At the same time, the humanitarian crisis in Gaza, where tens of thousands of Palestinians have been killed and hunger has run rampant, has stirred global wrath. Polls have shown that a majority of Israelis, long skeptical of the chances of a “total victory,” favor ending the war in order to get the hostages back. And Mr. Trump’s patience appears to have worn thin.

“It doesn’t look like Hamas is leaving, and it doesn’t look like the total victory he promised,” Mitchell Barak, an Israeli pollster who worked as an aide to Mr. Netanyahu in the 1990s, said of the prime minister. “I think he realized his credit with Trump ran out.”

Unlike the defiant stance Mr. Netanyahu often took against the Biden administration or President Barack Obama, Mr. Barak said, “For the first time, Netanyahu cannot disregard the wishes of an American president, because of the way Trump operates. Trump is unpredictable and will not fall in line with the Israeli position.”

That has become more evident in recent days as Mr. Trump has weighed his relations with Mr. Netanyahu against his interests and ties with other countries in the region, including Turkey, whose leader, President Recep Tayyip Erdogan, has used harsh rhetoric against Israel, and Qatar, a country that Mr. Netanyahu recently accused of harboring terrorists.

Only two months ago, Mr. Netanyahu’s government approved a plan to expand the war by taking control of Gaza City, a risky decision that went against the recommendations of the Israeli military. Israeli leaders described the city as one of Hamas’s last bastions and presented the operation as an essential step toward wiping out the group’s military and governing capabilities.

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Prime Minister Benjamin Netanyahu of Israel at the White House following a meeting with President Trump last week.Credit…Doug Mills/The New York Times

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How would you go about answering the question “How many people have ever lived on this planet?” If you type that into Google or an artificial intelligence chatbot, you’ll get an answer pretty quickly—usually 117 billion. That number, at least in my opinion, seems far too small. After all, the world’s population is currently estimated at 8.2 billion people. That means we make up about 7 percent of all people ever born.

The 117-billion figure includes every person who has ever seen the light of day—including those who died young. Life expectancy has increased globally over time, however. As a result, there are other strange population questions to consider. For example, a 2014 article in the Economist stated that half of all people who have ever been age 65 or older are alive today. Can that really be true? And how do you even calculate something like that?

Demographers have been asking such questions for decades. One of the biggest challenges they face is from the data: you need to know how many people have lived at different times, as well as the average life expectancy or birth rate. Such numbers are available today (though records are not always reliable), but less so for centuries past. Statistical analyses and censuses have not been routinely carried out everywhere and across all societies. Demographers must therefore rely heavily on estimates.

And then there are a few fundamental questions to consider. What exactly is meant by “human”? Do we mean all members of the genus Homo who have walked our planet or just Homo sapiens in particular? Given the challenges, it’s astonishing that when estimating all the people who have ever lived, we are usually only presented with one number, 117 billion, rather than a range with a low and a high estimate. I argue that that is entirely appropriate from a scientific point of view and signals that the result is an approximation. The order of magnitude may seem plausible, but the question cannot be answered exactly.

Modeling Population Growth

To realistically assess the 117-billion-person estimate, you first need data. From the 20th century to the present, you can find lots of population figures, thanks to regular censuses conducted in many countries since the 1850s.

Looking further back in history, the number of people living can be roughly estimated based on the size of cities and population density. For even earlier times, archaeological remains offer clues.

Nevertheless, some sources put the world population in the year C.E. 1 at 170 million people and others at 300 million, almost double that number. There is also the question of how far back we should even look. There are estimates in which demographers go back as far as 4.5 million years to consider all members of the genus Homo. Others, however, focus on Homo sapiens and look back between 50,000 and 200,000 years.

Over the years, not only the number of living humans but also the corresponding rate of population growth has changed significantly. The world’s population used to increase very slowly, but seems to have grown faster in recent centuries. That’s because the birth rate has decreased while the death rate has decreased even more—a combination that can be difficult to model.

The growth rate can be assumed to be constant for small time intervals, however. Demographers use that assumption to estimate the number of all living people in a given time interval. You have to divide the period under consideration into different sections; for example, you can start 50,000 years before our era and end in the year 2025. The more subdivisions you make, the more accurate the result.

If we now assume that the birth rate g and death rate s are constant within a section of that timeline, then the population size N changes according to the following differential equation:

Given that g and s are assumed to be constant within an interval, the population size in this area can be modeled using an exponential function: N(t) = N₀e^kt, where the parameters k (the net growth rate) and N₀ (the population size when time t = 0) are determined by the data points.

To determine how many people have ever lived, you have to add up the number of all living people at each point in time t. This can be done by calculating the integral of the piecewise-defined function over t in the respective section:

This approach overestimates the actual answer, though. Think of it this way: If you are reading this article, then you are currently alive; you were most likely already alive 10 years ago, however, and also contributed to the world population back then. The integrated result must therefore be divided by the respective life expectancy of the people who lived during the period in question. At the end, you can add up the results for all time periods and—ta-da!—the result should correspond to the total number of people who have ever lived.

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01 of 25

Frosted and fabulous cupcakes

In Season 3 of Sex and the City, Carrie and Miranda stop by Magnolia Bakery for a treat, creating a moment that launched a million cupcakes. It catapulted Magnolia Bakery to fame and upgraded cupcakes from forgettable kid food to crave-worthy adult indulgence. 

Cupcake-only bakeries popped up across the country, which included Sprinkles (which rolled out cupcake ATMs in 2012), Baked by Melissa (miniature cupcakes), and the now-closed chain Crumbs (giant cupcakes). And while the long tail of the Sex and the City universe seems to have reached its conclusion with the series finale of And Just Like That, the sweet trend it spawned lives on, in every flavor from classic chocolate to pickle. —Karen Shimizu

02 of 25

The legendary roast chicken

In 2002, Judy Rodgers published The Zuni Café Cookbook, which revealed the secrets to her cult-status roast chicken, the signature dish served at her San Francisco restaurant. The recipe gave cooks the roadmap to reproduce the dish seamlessly at home. A deceptively simple approach, to dry-brine the bird with salt a day or two before it’s roasted in a blazing-hot oven, yielded the crispiest skin and juiciest meat. It produced restaurant-level results perfect for weeknight cooking, yet impressive enough for special occasions. The recipe quickly became, and remains, the definitive roast chicken. —Cheryl Slocum

In 2004, David Chang’s Momofuku Noodle Bar reset America’s ramen expectations. Packets of noodles gave way to slow-simmered pork broth, pork belly, and fresh, colorful toppings. Tonkotsu’s luxe richness became the emblem of that shift with its opaque broth, which also coincided with the rise of bone broth. Ramen moved from cheap filler to high-end comfort food. Its rise made way for a slew of new restaurants and recipes devoted to the art of the comforting soup noodles. —Breana Killeen

03 of 25

Ramen, but make it luxe: tonkotsu ramen

In 2004, David Chang’s Momofuku Noodle Bar reset America’s ramen expectations. Packets of noodles gave way to slow-simmered pork broth, pork belly, and fresh, colorful toppings. Tonkotsu’s luxe richness became the emblem of that shift with its opaque broth, which also coincided with the rise of bone broth. Ramen moved from cheap filler to high-end comfort food. Its rise made way for a slew of new restaurants and recipes devoted to the art of the comforting soup noodles. —Breana Killeen

04 of 25

Brussels sprouts steal the show

The Brussels sprouts that cropped up on restaurant menus in the mid-2000s were different from the boiled brassicas many grew up eating. Farmers had bred out much of the bitterness by the early 2000s, and chefs leaned on methods like roasting and frying to turn them into crispy, craveable sides that rivaled even French fries. 

New York Magazine name-checked the sprouts in 2005 after they appeared at trendy restaurants like The Spotted Pig and Del Posto. Not long after, David Chang made them a signature dish at Momofuku — pan-roasted with kimchi purée — before he eventually took them off the menu. “Every single table ordered them.” —Audrey Morgan

05 of 25

No-knead, no-problem bread

With its crackling, chewy crust, airy, flavorful crumb, and no need to knead, Jim Lahey’s simple bread recipe took home baking by storm when published in Mark Bittman’s The New York Times column in 2006. Though not the first no-knead bread recipe under the sun (in fact, a No Need to Knead cookbook by baker Suzanne Dunaway had been published in 2000), it was Lahey’s technique that captured the nation’s imagination. 

The ingredients — flour, water, salt, yeast, and cornmeal — were ones that most cooks had readily at hand. The tools to make it were simple: no pizza stones, cloches, or baskets required. Just an ovenproof pot to bake the bread in, which mimicked the radiant heat of a domed brick oven. And perhaps most appealingly, the process was nearly all hands-off. Instead of kneading, the bread got its structure (as well as a satisfying, sourdough-like tang) from an unusually long first rise. 

Nearly 20 years on, it remains a peerless gateway bread recipe, the surest way to give first-time bakers the confidence to bake artisanal loaves at home. And for those who want to build on the basics, it’s also adaptable, easily incorporating flavors like rosemary and roasted garlic. —Karen Shimizu

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Credit:  Food & Wine / Photo Illustration by Janet Maples

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Just north of the Las Vegas Strip lies a graveyard of relics that recalls the boomtown’s lofty ambitions.

Dented metal signs, neon bulbs humming, lie in the desert dust, welcoming you to a city as varied as its defunct businesses: the bright pink feathers of the original Flamingo Las Vegas Hotel and Casino; the Red Barn’s crimson cherry in a martini glass, homage to one of the city’s first gay bars; the dancing “Happy Shirt” of Steiner Cleaners, Liberace’s one-time laundry.

They are reminders of long-closed places in a city that has reinvented itself time and time again.

According to its brochure, the Neon Museum preserved these mementos to celebrate Las Vegas’s “vibrant past, present and future.” But for many, the word that describes the city’s present is not quite “vibrant.”

Mark Rumpler, 66, an Elvis impersonator for almost two decades, had a different word: “Rough.”

“It was a turbulent summer,” said Sean McBurney, the chief commercial officer of Caesars Entertainment, which operates multiple Strip casinos and resorts, including Caesars Palace.

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Mark Rumpler, an Elvis impersonator for almost two decades, greets visitors at Las Vegas’s iconic welcome sign.

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The US government shut down at 12:01 a.m. et on 1 October, after lawmakers in Congress failed to agree on a funding bill to keep the government running. Threats of federal shutdowns have become routine in the past decade, but this closure could be different: US President Donald Trump’s administration has encouraged mass firings of federal workers — a group that includes tens of thousands of scientists — during the lapse in funding.

“When you shut it down, you have to do lay-offs. So, we’d be laying off a lot of people that are going to be very affected,” Trump said on 30 September. It’s not clear when such lay-offs would begin, whether they would survive legal challenges or how extensive they would be. Even without any shutdown-driven lay-offs, the Trump administration projects that it will cut 300,000 people from the roughly 2.4-million-person federal workforce by the end of the year as part of its efforts to downsize the government.

In the meantime, the federal government has stopped non-essential operations. Science-agency staff members have been sent home, their research suspended. The US National Institutes of Health (NIH) had planned to halt its in-house basic research and stop admitting new people to the NIH hospital in Bethesda, Maryland. If the shutdown lasts more than a few days, it will directly affect non-government researchers: both the US National Science Foundation (NSF) and the US Environmental Protection Agency (EPA) would stop awarding new grants.

Shutdowns “can have a significant impact on the scientific research enterprise, and a lot of that does depend on how long a shutdown is”, says Joanne Padrón Carney, the chief government-relations officer at the American Association for the Advancement of Science, a non-profit organization in Washington DC.

It’s unclear how long the shutdown could last. The first Trump administration (2017–21) featured a 35-day closure, the longest in US history, that cost roughly US$5 billion and led to disruptions across most US science agencies. There is no set date for the parties to meet for negotiations.

The White House did not respond to Nature’s questions about mass layoffs and the shutdown’s effect on science.

Shutdown showdown

In March, a small group of Senate Democrats voted with Republicans to pass a bill to keep the government open. But this time, Democratic lawmakers have voiced concerns about loss of health-care subsidies and a range of other issues, including attacks on free speech.

Although many scientists worry about the effect of a shutdown, some, including some federal researchers, see this as an opportunity for Congress to derail the Trump team’s activities, which have already included substantial lay-offs, budget cuts and disruption to research.

At a public protest in Washington DC on 29 September, federal employees spoke out against the actions of the Trump administration. “American science, the gold-standard and world-leading science and innovation enterprise, is being destroyed,” said Mark Histed, a neuroscientist at the NIH in Bethesda. “Congress has a rare moment of leverage to check Trump’s executive overreach and it must stand up and do so.”

Drastic reductions

No previous shutdowns carried the threat of mass firings, officially called reductions in force (RIFs). According to guidance issued by the White House Office of Management and Budget (OMB), the office has directed agencies to consider issuing RIF notices to all employees who are working on certain projects: those whose Congressional funding lapsed on 1 October and whose goals are not “consistent with the President’s Priorities.” Carney says that the memo could be used to close programmes, leading to a loss of institutional knowledge at science agencies.

Agencies whose budgets are cut have discretion to cut staff, but it’s unclear whether that authority applies during shutdowns, says Nick Bednar, a legal scholar at the University of Minnesota Twin Cities in Minneapolis. “We are in largely uncharted territory,” he says. The administration has already faced legal push-back on previous mass firings. In September, a judge ruled that the termination of 25,000 federal workers earlier this year was unlawful, but that too much time had passed since the termination to mandate their reinstatement. On 30 September, two unions sued the administration to block any RIFs.

Scanty details

Nature contacted multiple federal agencies about their shutdown plans. None provided information about potential RIFs. But huge numbers of federal employees at science-heavy agencies are already on unpaid leave.

According to plans disseminated before the government closed, the NSF intended to furlough roughly 75% of its staff. The US National Oceanic and Atmospheric Administration was expecting to furlough 54% of its personnel, halting “most research activities”. At NASA, in which 83% of staffers were furloughed, a skeleton crew will keep active satellites operational.

The US Department of Energy’s website did not have a detailed contingency plan and an agency spokesperson declined to provide specifics about furloughed staff. At the EPA, 86% of the staff are to be furloughed, but ongoing experiments will be preserved.

A contingency plan for the NIH specified a furlough of 78% of workers, preserving only crucial functions such as care for existing patients. The US Centers for Disease Control and Prevention will furlough 64% of its staff.

One set of activities has been authorized to continue across all agencies during the shutdown: on 28 September, the Office of Personnel Management published guidance stating that activities related to administering RIFs — such as sending termination notices — are exempted from shutdown-related freezes.

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