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She was referring to a plan to end the war and bring home the hostages that President Trump unveiled last month, being discussed in Egypt this week. And Ms. Zangkauer was expressing a sentiment shared by many.

“Everyone wants it to happen,” President Trump said on Monday evening at a briefing in the White House, speaking of his peace proposal. “Even Hamas.”

But much still remains unresolved.

The indirect talks between Israel and Hamas, mediated by the United States, Qatar, and Egypt, are likely to focus on two aspects of Mr. Trump’s 20-point proposal: exchanging Israeli-held Palestinians for captives, and an Israeli pullback from parts of Gaza.

Israel believes that about 20 hostages are still alive in Gaza, and also seeks the remains of about 25 others. Secretary of State Marco Rubio told Fox News Sunday that Hamas had “agreed to the president’s hostage release framework.”

Under that plan, the hostages will be exchanged for 250 Palestinians prisoners serving life sentences and 1,700 Gazans jailed by Israel during the war. For every hostage whose remains are released, Israel will also release the remains of 15 Gazans.

While the plan calls for the release of the hostages within 72 hours of Israel agreeing to it, that would be logistically difficult, experts say. And the two sides have yet to agree on which Palestinian prisoners will be released.

The White House press secretary, Karoline Leavitt, told reporters at a briefing on Monday that the teams were in Egypt to discuss that exchange. “They’re going over the list of both the Israeli hostages and also the political prisoners who will be released, and those talks are underway,” she said.

“All sides of this conflict agree that this war needs to end,” she said, “and agree to the 20-point framework that President Trump proposed.” The talks, she added, were an “incredible achievement.”

On Friday, Hamas said it was willing to release the hostages. But Hamas has not addressed major points in the American peace plan, among them demands that it has objected to in the past. The proposal, for example, calls on the group to disarm and for it to have no role in the governance of Gaza — both key Israeli positions that Hamas has long rejected.

Questions also remain about the withdrawal of Israeli forces from positions in Gaza.

In a social media post on Saturday, Mr. Trump said that Israel had already agreed to an initial withdrawal line within Gaza for the first phase of the deal.

“When Hamas confirms, the Ceasefire will be IMMEDIATELY effective, the Hostages and Prisoner Exchange will begin, and we will create the conditions for the next phase of withdrawal,” he pledged.

But Hamas may still seek to negotiate those lines.

In previous talks on ending the conflict, Hamas agreed to Israeli troops withdrawing into a buffer zone near Gaza’s border with Israel. But Mr. Trump’s plan would leave Israeli forces deeper in Gaza, and Hamas has signaled that it may object to elements of the plan.

In a speech to Israelis over the weekend, Prime Minister Benjamin Netanyahu tried to cast the Trump plan as a victory. He said the stage for a possible deal to end to the war had been set by his decision to keep up the pressure on Hamas with a devastating military campaign, which drew condemnation from much of the world. He also cited diplomatic efforts.

Members of Mr. Netanyahu’s far-right coalition have long objected to a deal and have threatened to dissolve his government if he agrees to one. The prime minister has sought to appease them, but he is also under pressure from many Israelis who want a hostage deal and an end to the conflict, as well as from the international community, not least Mr. Trump.

On Saturday, Mr. Trump posted images of Israelis rallying in Tel Aviv for a hostage deal. He added no comments, but the images appeared to speak for themselves.

Defying Mr. Trump does not appear to be an option, even for Mr. Netanyahu. By Saturday, the Israeli military was limiting its actions to what Israeli officials called defensive operations and responses to immediate threats.

Hamas, too, is under pressure to end the war.

Many Palestinians in Gaza see the Trump proposal as their best hope after nearly two years of extreme privation and repeated displacement. Much of Gaza has been destroyed, tens of thousands of Palestinians have been killed, including thousands of children, and Mr. Trump has said that Israel will have a green light to destroy Hamas if the group does not agree to a deal.

Mr. Trump demanded on social media that Israel stop bombing Gaza to allow the agreement with Hamas to move forward. The Israeli military instructed its forces to focus on defense, curbing military operations in the Gaza Strip, according to Israeli officials.

The fighting on the ground has nonetheless continued. The Israeli military said that it launched multiple attacks on Sunday against what it described as militants threatening troops. Emergency workers in Gaza said that they had been unable to reach some of those killed because they were in combat zones.

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Scientists moved a step closer to understanding the complex causes of autism this week. Although all of the headlines went to US President Donald Trump’s poorly evidenced statements that the painkiller acetaminophen is linked to the neurodevelopmental condition, his White House autism event brought welcome — and largely overlooked — news to scientists: the US National Institutes of Health (NIH) is investing US$50 million in an unusual autism-research effort.

Trump and Jayanta Bhattacharya, director of the NIH, announced on 22 September that 13 research groups will receive funding under the Autism Data Science Initiative (ADSI), a Trump administration programme to fund studies that explore how interacting genetic and environmental factors contribute to autism. “This is where the field needs to be going in searching for the complex causes of autism,” says Helen Tager-Flusberg, who studies autism at Boston University, Massachusetts.

The funded projects range from studies on environmental exposures during pregnancy to experiments on brain cells. Funding was also awarded to efforts to replicate the projects’ results and so ensure that they are robust.

Researchers, although pleased by the aims of the funded work and the rigour of the methods, have some concerns about the project. Several ADSI-funding recipients say that they are expected to complete their projects relatively quickly — within three years instead of the usual five — and some say that they are alert to political interference with their results. Trump prompted fierce pushback from scientists with his statements about acetaminophen earlier this week, given the lack of convincing evidence to support a link with autism. “We should wait until the research happens before announcing an answer,” says Jason Stein, a neuroscientist at the University of North Carolina, Chapel Hill, who received an ADSI grant.

“This is not political interference, but rather a bold, science-driven effort to deliver meaningful answers more quickly,” said a spokesperson for the US Department of Health and Human Services (HSS), which oversees the NIH.

Quick turnaround

The NIH announced the ADSI in May and invited researchers to submit grant applications for research into the causes of autism, its growing prevalence, and potential interventions. Some researchers expressed concern that applicants had only a month to submit proposals — much less time than usual — and it was unclear who was reviewing the grants and with what criteria. Some worried that the funding would be channelled to researching the discredited idea promoted by Trump’s health secretary, Robert F. Kennedy Jr, that vaccines are linked to autism. “Some people thought: maybe we should steer clear of this,” says Judith Miller, a psychologist who studies autism at the Children’s Hospital of Philadelphia in Pennsylvania.

In the end, nearly 250 research teams applied, and no awards were granted to projects that focus explictly on autism and vaccines.

Several of the projects will involve exposomics: the study of the array of environmental factors to which a person is exposed. Miller is leading a three-year, $4.3-million project combining genome and exposome data to seek factors associated with autism. The project will draw on previously collected data on more than 100,000 children, including about 4,000 autistic children, and connect those to maternal-health records. The research team plans to use information on where participants live to add in data on air quality, access to green spaces, and other environmental markers. “We haven’t been able to bring this type of data all together in a clinical population,” before, Miller says.

Replication requirement

Stein and his team, by contrast, are examining autism using brain organoids grown from the stem cells of autistic and non-autistic children. The researchers plan to expose the tissue to substances that epidemiological studies have linked to autism — such as valproic acid, a drug used to treat epilepsy — and examine how this affects gene activity.

The team expects to be asked by the NIH to look at acetaminophen or other substances, too, says Joseph Piven, a psychiatrist at University of North Carolina, Chapel Hill, who is also working on the organoid project. “As long as they have some detectable level of epidemiological evidence, I think that’s a valid question to go forward,” he says.

The ADSI is building in replication efforts from the start. Judy Zhong, a population-health scientist at Weill Cornell Medicine in New York City, has received around $5 million from the ADSI for a centre that will require other ADSI-funded investigators to hand over their computer models so that their results can be independently replicated. “It is very unusual,” Zhong says.

Collaborative approach

But researchers are still worried about political interference in autism research. Some point to the announcement earlier this month that the HHS would award a contract to Rensselaer Polytechnic Institute in Troy, New York, to search for an association between vaccines and autism in databases. “Is this the best use of funds to support another investigation, on what appears to be a largely settled question?” says Craig Newschaffer, an autism researcher at Pennsylvania State University in University Park.

Some researchers would like to see more funding for research that helps autistic people to lead healthy and fulfilling lives — a primary focus of only 2 of the 13 ADSI grants. Katharine Zuckerman, a paediatrician at Oregon Health & Science University in Portland, will be using her $4.25-million grant to look for factors in childrens’ lives — such as regular doctor’s visits or attending quality schools — that correlate with outcomes that autistic people say are important to them, such as sleep or good mental health. Like the other ADSI projects, this will be done in consultation with the autism community.

“Looking at the cause of autism is important, but I think that it’s also important that we address the concerns of autistic people who are here today and what we could do to improve their lives,” Zuckerman says.

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Most founder stories begin with a business plan, a pitch deck, or a stint in a Silicon Valley accelerator. Mine started in a garage, working as a mechanic before moving into large-scale solar construction. That unconventional path gave me a perspective I believe many entrepreneurs share: The best ideas rarely follow a straightforward path. They come from connecting unexpected skills and experiences. Whether you build in energy, finance or technology, the real opportunity lies in spotting links that others overlook.

As industries evolve, founders are increasingly asked to combine insights from different fields. The next breakthrough can come from anywhere. My story is one version of that pattern: years in construction, side ventures in cycling and crypto, as well as a growing conviction that blockchain and renewable energy could merge into something bigger. The important point is that these connections are available to anyone willing to look for them

NFTs beyond the hype

For me, the clearest connection between seemingly separate paths came in the form of NFTs. They showed how a digital tool could unlock real-world solutions when applied differently.

For many, NFTs are shorthand for speculation and hype. They recall headlines of digital art selling for millions during a bubble, but at their core, NFTs are simply verifiable certificates of ownership. They are secure, transparent and impossible to counterfeit. Those qualities give them value far beyond collectibles.

Renewable energy is a prime example. Historically, solar infrastructure has been locked behind institutional walls. You needed significant capital, specialized contracts, and relationships in a closed network. By linking NFTs to renewable projects, individuals could hold digital certificates that represent direct participation in the infrastructure powering their communities. Instead of being abstract shareholders in a utility, people could have verifiable claims tied to specific assets — be it a solar farm in Spain or a wind project in Japan.

This points to a broader principle for founders: Technologies often outgrow the reputations they start with. Something like NFTs, which were dismissed as frivolous in one context, can become transformative in another. The pattern is common. Artificial intelligence was once a niche academic field before becoming the backbone of entire industries. Cloud computing was once seen as insecure and unreliable, but today no modern business can operate without it. Hype cycles can distract, but they can also be early signals of where long-term value will emerge. Leaders must learn to separate noise from substance and recognize when a tool is finally ready for serious application.

Blockchain as an equalizer

Blockchain itself grew from speculation, but its biggest benefit lies in offering access. Traditional finance and infrastructure projects often operate like exclusive clubs, requiring large amounts of money, insider knowledge, and legal support. Blockchain lowers these barriers. It makes processes transparent, allows direct participation, and removes unnecessary intermediaries.

In renewable energy, that means individuals and small groups can help finance and accelerate the transition alongside corporations and governments. Participation is no longer limited to the few who already sit inside the system. That is the equalizing force blockchain brings — and it is the type of structural change founders should be looking for in their own industries.

Advice for founders

From my own journey, three lessons stand out for anyone looking to apply their expertise to new frontiers:

1. Draw on your background, however unconventional. Skills picked up in unrelated fields often prove essential later. Steve Jobs famously credited a college calligraphy class with shaping the typography of the Macintosh. In my case, running construction sites taught me how to manage risk, coordinate teams, and solve problems under pressure — skills that proved invaluable when I later moved into blockchain. Founders often underestimate their own experience, but the truth is that most breakthroughs are not born from a blank slate. They are built on layers of past knowledge, applied in new ways.

2. Stay focused on the mission. Every industry has hype cycles, but blockchain is especially noisy. New tokens, fads, and shortcuts appear daily. The temptation to chase quick wins is strong, but they rarely build lasting businesses. Innovation requires a clear mission and the patience to execute it. Founders who withstand the noise are those who anchor themselves to a long-term vision. That discipline not only creates stronger companies, but it also builds credibility with partners, regulators, and investors who are looking for stability in a volatile field.

3. Curate expertise early. Great founders are not experts in everything; they are curators of expertise. To bring my project to life, I brought in specialists from day one. Identifying gaps early and filling them before they become roadblocks is essential. It saves time, prevents costly mistakes, and accelerates execution. The best founders see themselves less as lone visionaries and more as architects — assembling the right team and letting them excel in their respective domains.

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Bad Bunny, the season premiere host, was announced as the Super Bowl LX halftime show headliner, drawing the ire of government officials like Kristi Noem, the secretary of homeland security, who said that “ICE enforcement” would attend the Super Bowl and would be “all over” the event.

And — oh yes — the category of late-night TV comedy became unexpectedly volatile: In July, CBS announced that “The Late Show With Stephen Colbert” would go off the air next May, citing economic factors. And Disney pulled the ABC late-night show “Jimmy Kimmel Live!” for a few broadcasts in September, amid controversy over remarks that Kimmel made on the show about the fatal shooting of Charlie Kirk, the right-wing activist.

“S.N.L.” addressed some of these controversies in its opening sketch, in which the Weekend Update co-anchor Colin Jost played Secretary Hegseth, speaking to U.S. military officers at Marine Corps Base Quantico in Northern Virginia. (“Thanks to failed liberal policies, our Army has never been gayer,” Jost said in his speech. “And yet, it’s also never been fatter. Make that make sense.”)

Jost’s lecture was soon overtaken by Johnson, who declared that “S.N.L.” had “better be careful, because I know late-night TV like the back of my hand.” As he said this, Johnson turned over his hand to show what looked like a bruise noticeably disguised by makeup.

“Not looking great right now,” he said, quickly clasping that hand with the other. “Oops! Don’t look at that. Gonna cover this up for the rest of my life.” Johnson also warned that “S.N.L.” would have to be on its “best behavior” or else it would have to answer to his “attack dog,” the F.C.C. chairman, Brendan Carr. (Mikey Day played Carr in a brief appearance, boogieing onto the stage to Rockwell’s “Somebody’s Watching Me.”)

As its 51st season got underway, Johnson said that “S.N.L.” should have “called it at 50, right?”

“It’s so sad to see something get old and confused and yet still demand your constant attention,” he said. “Oh well.”

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James Austin Johnson, returning as President Trump and stealing the spotlight from Defense Secretary Pete Hegseth (Colin Jost), who was lecturing a gathering of generals and admirals.Credit…NBC Universal, via YouTube

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The U.S. Southeast will likely avoid the worst effects from Tropical Storm Imelda—all thanks to another tropical cyclone.

Imelda and Hurricane Humberto have been churning over the northeastern Caribbean, between the Bahamas and Bermuda, for several days. Last Friday, the forecasts were highly uncertain about Imelda’s path and future strength: the possibilities ranged from the storm making landfall in the Carolinas, which would bring torrential rain and floods, to it not making landfall in the U.S. The latter now looks to be the likely scenario. That’s because Imelda dawdled in its development while Humberto quickly exploded into a major hurricane, which has influenced how much the two storms “feel” each other—essentially a flavor of what is called the Fujiwhara effect. (The East Coast will still feel rip currents from Imelda, though, and the storm could pose a threat to Bermuda as it takes a sharp eastward turn in the coming days.)

The higher-than-usual level of forecast uncertainty can be explained partly by the fact that storms in the Atlantic don’t typically form this close to each other. Tropical cyclones are influenced by the larger atmospheric environment, and adding another storm system makes that environment more complex. Meteorologists were also unclear about exactly where the center of Imelda would ultimately form, which made it difficult to know how that center would interact with other features in the atmosphere.

To get a sense of the atmospheric picture last Friday, it’s helpful to remember that the atmosphere is three-dimensional, with various low- or high-pressure areas or wind currents at various altitudes. In this case, there was a low-pressure area higher up in the atmosphere over the Southeast, an area of high pressure that is quasi-permanently centered roughly over Bermuda, and the two storms—Humberto and what would become Imelda, then called Potential Tropical Cyclone Nine. What wasn’t clear was whether Imelda would form quickly enough and in the right place for it to interact with that upper-level low, which would push it more rapidly north and toward a U.S. landfall. “Hurricanes are governed by the surrounding wind flow, and the quicker [the storm] gets stronger, the more it gets influenced by winds higher up in the atmosphere,” says Alan Gerard, a retired National Weather Service meteorologist, who runs the consulting company Balanced Weather.

But Imelda was very slow to become organized into a full tropical storm, so it has crept northward slowly, leaving it in the perfect spot to feel the pull of Humberto. “Essentially what happens is: you’ve got [westerly] winds around Humberto from the cyclone, and Imelda just gets caught up in that and follows behind,” Gerard says.*

This is a form of the Fujiwhara effect, says University of Miami hurricane researcher Brian McNoldy. In 1921, Japanese meteorologist Sakuhei Fujiwhara theorized that two vortices spinning through fluid (which is exactly what tropical cyclones are) could come close enough to each other to begin orbiting a common central point. If such storms move even closer, they can eventually merge into one, which happened with Hurricanes Hilary and Irwin in the eastern Pacific in 2017.

Imelda and Humberto aren’t close enough for that to happen, but the Fujiwhara effect can take other forms once the distance between two storms is within about 800 miles, and each can “feel” the other, McNoldy says. “The centers of Imelda and Humberto are now just 600 miles apart, and their outer circulations are already communicating,” McNoldy wrote in an e-mail to Scientific American. “Model forecasts bring them even closer together in the coming couple of days.”

Humberto is weakening the quasi-permanent ridge over Bermuda and opening up a path to pull Imelda behind it. Essentially, “Imelda is caught up in Humberto’s wake,” Gerard says.

Though this reduces the risks to the U.S., the interaction could mean that Imelda will pose more of a direct threat to Bermuda than Humberto will; the latter will travel a few hundred miles to the north of the islands.

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Hmmmm… Does Trump want civil war?

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Confidence among Trump supporters about the nation’s trajectory is slipping, according to new polling.

YouGov/Economist polling shows that at the start of September, 75 percent of Trump voters said the country was headed in the right direction, while just 17 percent believed it was on the wrong track. By the end of the month, those numbers shifted to 70 percent and 22 percent, respectively—a net negative swing of 10 points.

The YouGov/Economist poll is not the first to show that Republicans are growing increasingly pessimistic. The latest Gallup poll showed a fall in optimism about the direction of the country among Republicans to 68 percent in September, from 76 percent in August.

And according to AP-NORC, the share of Republicans saying the U.S. is headed in the wrong direction has surged from 29 percent in June to 51 percent in September. Among Republicans under 45, that number leapt by 30 points to 61 percent.

A Marquette poll from this month also reflected declining optimism, showing Republican satisfaction with the country’s direction falling from 79 percent in July to 70 percent in September.

The drop in optimism comes after a turbulent September for the Trump administration. The killing of conservative activist Charlie Kirk rattled parts of the movement, while the White House faced backlash over what critics described as a crackdown on free speech following the decision by ABC News to take the Jimmy Kimmel show off air after his remarks about Kirk. The month closed with a bitter standoff in Washington that led to a government shutdown, fueling further uncertainty.

Concerns About Political Violence

The death of Charlie Kirk has ignited concerns among Republicans about political violence, according to polling.

A Quinnipiac poll found that a majority of Republicans (60 percent) believe the U.S. is in a political crisis. YouGov polling also found that 67 percent of Republicans think political violence is a very big problem.

And a Marquette survey shows that Republicans see political violence as a serious problem, but they overwhelmingly blame the left for it. More than half of Republicans (57 percent) say left-wing violence is the bigger issue, while only 3 percent point to right-wing violence. At the same time, they are less likely than Democrats to connect aggressive political language to an increased risk of violence—just 39 percent of Republicans say heated rhetoric makes violence much more likely, compared to 63 percent of Democrats.

Meanwhile, Gallup polling shows that the fallout from Kirk’s assassination has shifted Americans’ sense of national priorities. Gallup found mentions of crime or violence as the country’s top problem rose from 3 percent in August to 8 percent in September, the highest in five years. Concern about national unity doubled from 5 percent to 10 percent, the highest since the aftermath of January 6.

But partisan divides are clear. Republicans drove most of the increase in concern about crime, jumping from 6 percent to 14 percent, while independents fueled the spike in unity concerns, climbing from 5 percent to 13 percent.

Republicans have responded with near-uniform outrage and grief to the assassination of Kirk, describing his killing as both a personal tragedy and a political turning point.

Trump was among the first to speak out, calling Kirk’s death a “dark moment for America” and praising him as “a tremendous person” who devoted his life to the conservative cause.

Within days, he ordered flags to be flown at half-staff and announced that Kirk would receive the Presidential Medal of Freedom posthumously. At a memorial service in Arizona, Trump elevated Kirk as a “martyr for American freedom” and placed blame on the “radical left” for creating what he described as the climate of hostility that led to the shooting.

Other Republican lawmakers struck similar notes. Senate Majority Leader John Thune and Senator Mike Lee both praised Kirk’s influence on the conservative movement and condemned the violence that ended his life, calling the assassination a reminder of America’s increasingly dangerous political climate.

Vice President JD Vance also echoed Trump’s framing, urging supporters to treat the killing not just as an act of violence, but as part of a broader cultural battle, warning that those who mocked Kirk’s death online were contributing to the same climate the president condemned.

But Peter Loge, director of the Project on Ethics in Political Communication at George Washington University, told Newsweek that it is exactly this kind of rhetoric that is contributing toward the growing sense of dissatisfaction with the country’s trajectory.

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President Donald Trump walks from Marine One after arriving on the South Lawn of the White House, Tuesday, Sept. 30, 2025, in Washington. (AP Photo/Alex Brandon)

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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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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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