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The quality of mathematics research in the United States today is the envy of the scientific world. This is a direct result of the openness and inclusivity of the profession.

According to our own experiences at the universities where we teach, an overwhelming majority of American students with strong math backgrounds are either foreign-born or first-generation students who have additional support from their education-conscious families. At all levels, STEM disciplines are more and more dependent on a constant flow of foreign talent.

The Organization for Economic Cooperation and Development compares mathematical proficiency among 15-year-olds by country worldwide. According to its 2018 report, America ranked 37th while China, America’s main competitor for world leadership, came in first.

This is despite the fact that the United States is the fifth-highest spender per pupil among the 37 developed OECD nations

This massive failure of our K-12 education system trickles through the STEM pipeline.

At the undergraduate level, too few American students are prepared for higher-level mathematics courses. These students are then unprepared for rigorous graduate-level work

Can Americans maintain this unmatched excellence in the future? There are worrisome signs that suggest not.

There are many reasons for this failure, but the way that we educate and prepare teachers is particularly influential. The vast majority of K-12 math teachers are graduates of teacher-preparation programs that teach very little substantive mathematics

This has led to a constant stream of ill-advised and dumbed-down reforms. One of the latest fads is anti-racist mathematics. Promoted in several states, the bizarre doctrine threatens to further degrade the teaching of mathematics.

Another major concern is the twisted interpretation of diversity, equity, and inclusion (DEI).

Under the banner of DEI, universities are abandoning the use of standardized tests like the SAT and GRE in admissions, and cities are considering scrapping academic tracking and various gifted programs in schools, which they deem “inequitable.”

such programs are particularly effective, when properly implemented, at discovering and encouraging talented children from disadvantaged backgrounds.

This will only lead to a further widening of racial disparities in educational outcomes while lowering American children’s rankings in education internationally.

These measures will not only hinder the progress of the generations of our future STEM workforce but also contribute to structural inequalities, as they are uniquely detrimental to students whose parents cannot send them to private schools or effective enrichment programs.

These are just a few examples of an unprecedented fervor for revolutionary change in the name of Critical Race Theory (CRT), a doctrine that views the world as a fierce battleground for the narratives of various identity groups.

The new 2021 Mathematics Framework, currently under consideration by California’s Department of Education, does away “with all tracking, acceleration, gifted programs, or any instruction that involves clustering by individual differences, without expressing any awareness of the impact these drastic alterations would have in preparing STEM-ready candidates.”

Ill-conceived DEI policies, often informed by CRT, and the declining standards of K-12 math education feed each other in a vicious circle

Regarding minorities, in particular, public K-12 education all too often produces students unprepared to compete, thus leading to large disparities in admissions at universities, graduate programs, and faculty positions. This disparity is then condemned as a manifestation of structural racism, resulting in administrative measures to lower the evaluation criteria. Lowering standards at all levels leads eventually to even worse outcomes and larger disparities, and so on in a downward spiral.

A case in point is the recent report by the American Mathematical Society that accuses the entire mathematics community, with the thinnest of specific evidence, of systemic racial discrimination. A major justification put forward for such a grave accusation is the lack of sufficient representation of Black mathematicians in the professio

the report, while raising awareness of several ugly facts from the long-ago past, makes little effort to address the real reasons for this, mainly the catastrophic failure of the K-12 mathematical educational system.

The National Science Foundation, a federal institution meant to support fundamental research, is now diverting some of its limited funding to various DEI initiatives of questionable benefit.

Meanwhile, other countries, especially China, are doing precisely the opposite, following the model of our past dedication to objective measures of excellence. How long before we will see a reverse exodus, away from the United States?

The present crisis can still be reversed by focusing on a few concrete actions:

Improve schools in urban areas and inner-city neighborhoods by following the most promising education programs. These programs demonstrate that inner-city children benefit if they are challenged by high standards and a nurturing environment.

Follow the lead of other highly successful rigorous programs such as BASIS schools and Math for America, which focus on rigorous STEM curricula, combined with 21st-century teaching methods, and recruit talented teachers to help them build on their STEM knowledge and teaching methods.

Increase, rather than eliminate, tailored instruction, both for accelerated and remedial math courses.

Reject the soft bigotry of low expectations, that Black children cannot do well in competitive mathematics programs and need dumbed-down ethnocentric versions of mathematics.

Uphold the objective selection process based on merit at all levels of education and research.

Sorrentino said the study defined economic impact by the extent that a city's economy was closed -- businesses like restaurants, gyms, salons and airports that would lose business without people's physical presence.

The study took into account both the costs associated with quarantining (which requires supervision costs as well as costs due to lowered productivity) as well as social distancing (which incurs costs only due to productivity).

"But our model shows that even before we achieve herd immunity, we can relax social distancing compared to the situation prior to immunization."

The analysis looked at Seattle, beginning on December 14, 2020, when the vaccine was first being administered. Even with this limited data, the effect of vaccinations was dramatic, impacting the so-called "optimal control solution."

While the optimal interventions would vary depending on a number of factors, we always saw that a gradual relaxation of social distancing was possible after roughly 10% of the population got vaccinated," he said.

After just 20 days, the trend was becoming clear when comparing with the case in which the effects of vaccinations were not incorporated in the model.

Sorrentino emphasizes also that everyone should continue to follow the current policy and health guidelines, and that the relaxing of social distancing should adhere to these guidelines and be gradual. And of course, that guidance may change, based on the rates of spread of the virus and the variants.

He writes with disarming composure about the factors that have led to the disintegration of empires and the abandonment of cities and about the mechanism that, in his view, makes it nearly certain that all states that rise will one day fall

societal collapse and its associated terms — “fragility” and “resilience,” “risk” and “sustainability” — have become the objects of extensive scholarly inquiry and infrastructure.

Princeton has a research program in Global Systemic Risk, Cambridge a Center for the Study of Existential Risk

even Tainter, for all his caution and reserve, was willing to allow that contemporary society has built-in vulnerabilities that could allow things to go very badly indeed — probably not right now, maybe not for a few decades still, but possibly sooner. In fact, he worried, it could begin before the year was over.

Plato, in “The Republic,” compared cities to animals and plants, subject to growth and senescence like any living thing. The metaphor would hold: In the early 20th century, the German historian Oswald Spengler proposed that all cultures have souls, vital essences that begin falling into decay the moment they adopt the trappings of civilization.

that theory, which became the heart of “The Collapse of Complex Societies.” Tainter’s argument rests on two proposals. The first is that human societies develop complexity, i.e. specialized roles and the institutional structures that coordinate them, in order to solve problems

All history since then has been “characterized by a seemingly inexorable trend toward higher levels of complexity, specialization and sociopolitical control.”

Eventually, societies we would recognize as similar to our own would emerge, “large, heterogeneous, internally differentiated, class structured, controlled societies in which the resources that sustain life are not equally available to all.”

Something more than the threat of violence would be necessary to hold them together, a delicate balance of symbolic and material benefits that Tainter calls “legitimacy,” the maintenance of which would itself require ever more complex structures, which would become ever less flexible, and more vulnerable, the more they piled up.

Social complexity, he argues, is inevitably subject to diminishing marginal returns. It costs more and more, in other words, while producing smaller and smaller profits.

Take Rome, which, in Tainter's telling, was able to win significant wealth by sacking its neighbors but was thereafter required to maintain an ever larger and more expensive military just to keep the imperial machine from stalling — until it couldn’t anymore.

This is how it goes. As the benefits of ever-increasing complexity — the loot shipped home by the Roman armies or the gentler agricultural symbiosis of the San Juan Basin — begin to dwindle, Tainter writes, societies “become vulnerable to collapse.”

haven’t countless societies weathered military defeats, invasions, even occupations and lengthy civil wars, or rebuilt themselves after earthquakes, floods and famines?

Only complexity, Tainter argues, provides an explanation that applies in every instance of collapse.

Complexity builds and builds, usually incrementally, without anyone noticing how brittle it has all become. Then some little push arrives, and the society begins to fracture.

A disaster — even a severe one like a deadly pandemic, mass social unrest or a rapidly changing climate — can, in Tainter’s view, never be enough by itself to cause collapse

The only precedent Tainter could think of, in which pandemic coincided with mass social unrest, was the Black Death of the 14th century. That crisis reduced the population of Europe by as much as 60 percent.

Whether any existing society is close to collapsing depends on where it falls on the curve of diminishing returns.

The United States hardly feels like a confident empire on the rise these days. But how far along are we?

Scholars of collapse tend to fall into two loose camps. The first, dominated by Tainter, looks for grand narratives and one-size-fits-all explanations

The second is more interested in the particulars of the societies they study

Patricia McAnany, who teaches at the University of North Carolina at Chapel Hill, has questioned the usefulness of the very concept of collapse — she was an editor of a 2010 volume titled “Questioning Collapse” — but admits to being “very, very worried” about the lack, in the United States, of the “nimbleness” that crises require of governments.

We’re too vested and tied to places.” Without the possibility of dispersal, or of real structural change to more equitably distribute resources, “at some point the whole thing blows. It has to.”

In Turchin’s case the key is the loss of “social resilience,” a society’s ability to cooperate and act collectively for common goals. By that measure, Turchin judges that the United States was collapsing well before Covid-19 hit. For the last 40 years, he argues, the population has been growing poorer and more unhealthy as elites accumulate more and more wealth and institutional legitimacy founders. “The United States is basically eating itself from the inside out,

Inequality and “popular immiseration” have left the country extremely vulnerable to external shocks like the pandemic, and to internal triggers like the killings of George Floyd

Turchin is keenly aware of the essential instability of even the sturdiest-seeming systems. “Very severe events, while not terribly likely, are quite possible,” he says. When he emigrated from the U.S.S.R. in 1977, he adds, no one imagined the country would splinter into its constituent parts. “But it did.”

Eric H. Cline, who teaches at the George Washington University, argued in “1177 B.C.: The Year Civilization Collapsed” that Late Bronze Age societies across Europe and western Asia crumbled under a concatenation of stresses, including natural disasters — earthquakes and drought — famine, political strife, mass migration and the closure of trade routes. On their own, none of those factors would have been capable of causing such widespread disintegration, but together they formed a “perfect storm” capable of toppling multiple societies all at once.

Collapse “really is a matter of when,” he told me, “and I’m concerned that this may be the time.”

In “The Collapse of Complex Societies,” Tainter makes a point that echoes the concern that Patricia McAnany raised. “The world today is full,” Tainter writes. Complex societies occupy every inhabitable region of the planet. There is no escaping. This also means, he writes, that collapse, “if and when it comes again, will this time be global.” Our fates are interlinked. “No longer can any individual nation collapse. World civilization will disintegrate as a whole.”

If it happens, he says, it would be “the worst catastrophe in history.”

The quest for efficiency, he wrote recently, has brought on unprecedented levels of complexity: “an elaborate global system of production, shipping, manufacturing and retailing” in which goods are manufactured in one part of the world to meet immediate demands in another, and delivered only when they’re needed. The system’s speed is dizzying, but so are its vulnerabilities.

A more comprehensive failure of fragile supply chains could mean that fuel, food and other essentials would no longer flow to cities. “There would be billions of deaths within a very short period,” Tainter says.

If we sink “into a severe recession or a depression,” Tainter says, “then it will probably cascade. It will simply reinforce itself.”

Tainter tells me, he has seen “a definite uptick” in calls from journalists: The study of societal collapse suddenly no longer seems like a purely academic pursuit

Societies evolve complexity, he argues, precisely to meet such challenges.

He writes of visions of “bloated bureaucracies” becoming the basis of “entire political careers.” Arms races, he observes, presented a “classic example” of spiraling complexity that provides “no tangible benefit for much of the population” and “usually no competitive advantage” either.

It is hard not to read the book through the lens of the last 40 years of American history, as a prediction of how the country might deteriorate if resources continued to be slashed from nearly every sector but the military, prisons and police.

The more a population is squeezed, Tainter warns, the larger the share that “must be allocated to legitimization or coercion.

And so it was: As U.S. military spending skyrocketed — to, by some estimates, a total of more than $1 trillion today from $138 billion in 1980 — the government would try both tactics, ingratiating itself with the wealthy by cutting taxes while dismantling public-assistance programs and incarcerating the poor in ever-greater numbers.

“As resources committed to benefits decline,” Tainter wrote in 1988, “resources committed to control must increase.”

The overall picture drawn by Tainter’s work is a tragic one. It is our very creativity, our extraordinary ability as a species to organize ourselves to solve problems collectively, that leads us into a trap from which there is no escaping

Complexity is “insidious,” in Tainter’s words. “It grows by small steps, each of which seems reasonable at the time.” And then the world starts to fall apart, and you wonder how you got there.

Perhaps collapse is not, actually, a thing. Perhaps, as an idea, it was a product of its time, a Cold War hangover that has outlived its usefulness, or an academic ripple effect of climate-change anxiety, or a feedback loop produced by some combination of the two

if you pay attention to people’s lived experience, and not just to the abstractions imposed by a highly fragmented archaeological record, a different kind of picture emerges.

Tainter’s understanding of societies as problem-solving entities can obscure as much as it reveals

Plantation slavery arose in order to solve a problem faced by the white landowning class: The production of agricultural commodities like sugar and cotton requires a great deal of backbreaking labor. That problem, however, has nothing to do with the problems of the people they enslaved. Which of them counts as “society”?

Since the beginning of the pandemic, the total net worth of America’s billionaires, all 686 of them, has jumped by close to a trillion dollars.

If societies are not in fact unitary, problem-solving entities but heaving contradictions and sites of constant struggle, then their existence is not an all-or-nothing game.

Collapse appears not as an ending, but a reality that some have already suffered — in the hold of a slave ship, say, or on a long, forced march from their ancestral lands to reservations faraway — and survived.

The current pandemic has already given many of us a taste of what happens when a society fails to meet the challenges that face it, when the factions that rule over it tend solely to their own problems

the real danger comes from imagining that we can keep living the way we always have, and that the past is any more stable than the present.

If you close your eyes and open them again, the periodic disintegrations that punctuate our history — all those crumbling ruins — begin to fade, and something else comes into focus: wiliness, stubbornness and, perhaps the strongest and most essential human trait, adaptability.

When one system fails, we build another. We struggle to do things differently, and we push on. As always, we have no other choice.

Polish international Piotr Zieliński gave Napoli the lead inside the opening 35 minutes and it was an advantage the Italian side held for the remainder of the 90 regulation minutes.

"The poorest city in Italy buys the most expensive player in the world."

Maradona would go on to become their God.

The expansion of security measures to other locations across the nation is based on the Postal Service's awareness of "planned protests or other situations involving large crowds" in key cities and areas

States and cities around the country are preparing for unrest ahead of the January 20 inauguration.

“Subjecting 5-year-olds to this technology will not make anyone safer, and we can’t allow invasive surveillance to become the norm in our public spaces,” said Stefanie Coyle, deputy director of the Education Policy Center for the New York Civil Liberties Union.

When the system is on, Mr. LiPuma said, the software looks at the faces captured by the hundreds of cameras and calculates whether those faces match a “persons of interest” list made by school administrators.

Jayde McDonald, a political science major at Buffalo State College, grew up as one of the few black students in Lockport public schools. She said she thought it was too risky for the school to install a facial recognition system that could automatically call the police.

“I’m not sure where they are in the school or even think I’ve seen them,” said Brooke Cox, 14, a freshman at Lockport High School. “I don’t fully know why we have the cameras. I haven’t been told what their purpose is.”

“If suspended students are put on the watch list, they are going to be scrutinized more heavily,” he said, which could lead to a higher likelihood that they could enter into the criminal justice system.

Days after the district announced that the technology had been turned on, some students said they had been told very little about how it worked.

“We all want to keep our children safe in school,” she said. “But there are more effective, proven ways to do so that are less costly.”

Colonisation exposed us to new ideas that shocked and confused us. Graeber & Wengrow focus on the French coming into contact with Native Americans in Canada, and in particular on Wendat Confederacy philosopher–statesman Kandiaronk as an example of European traders, missionaries, and intellectuals debating with, and being criticized by indigenous people. Historians have downplayed how much these encounters shaped Enlightenment ideas.

this thought-provoking book is armed to the teeth with fascinating ideas and interpretations that go against mainstream thinking

ather than yet another history book telling you how humanity got here, they take their respective disciplines to task for dealing in myths.

“extensive agriculture may thus have been an outcome, not a cause, of urbanization”

this simplistic tale of progress ignores and downplays that there was nothing linear or inevitable about where we have ended up.

ake agriculture. Rather than humans enthusiastically entering into what Harari in Sapiens called a Faustian bargain with crops, there were many pathways and responses

Experiments show that plant domestication could have been achieved in as little as 20–30 years, so the fact that cereal domestication here took some 3,000 years questions the notion of an agricultural “revolution”. Lastly, this book includes many examples of areas where agriculture was purposefully rejected. Designating such times and places as “pre-agricultural” is misleading, write the authors, they were anti-agricultural.

The idea that agriculture led to large states similarly needs revision

correlation is not causation, and some 15–20 additional centres of domestication have since been identified that followed different paths. Some cities have previously remained hidden in the sediments of ancient river deltas until revealed by modern remote-sensing technology.

Its legacy, shaped via several iterations, is the modern textbook narrative: hunter-gathering was replaced by pastoralism and then farming; the agricultural revolution resulted in larger populations producing material surpluses; these allowed for specialist occupations but also needed bureaucracies to share and administer them to everyone; and this top-down control led to today’s nation states. Ta-daa!

There are so many historical details and delights hiding between these covers that I was thoroughly enthralle

These instead relied on collective decision-making through assemblies or councils, which questions some of the assumptions of evolutionary psychology about scale: that larger human groups require complex (i.e. hierarchical) systems to organize them.

e what is staring them in the face

humans have always been very capable of consciously experimenting with different social arrangements. And—this is rarely acknowledged—they did so on a seasonal basis, spending e.g. part of the year settled in large communal groups under a leader, and another part as small, independently roving bands.

Throughout, Graeber & Wengrow convincingly argue that the only thing we can say about our ancestors is that “there is no single pattern. The only consistent phenomenon is the very fact of alteration […] If human beings, through most of our history, have moved back and forth fluidly between different social arrangements […] maybe the real question should be ‘how did we get stuck?

Next to criticism, the authors put out some interesting ideas of their own, of which I want to quickly highlight two.

The first is that some of the observed variations in social arrangements resulted from schismogenesis. Anthropologist Gregory Bateson coined this term in the 1930s to describe how people define themselves against or in opposition to others, adopting behaviours and attitudes that are different.

The second idea is that states can be described in terms of three elementary forms of domination: control of violence, control of information, and individual charisma, which express themselves as sovereignty, administration, and competitive politics.

Asking which past society most resembles today’s is the wrong question to ask. It risks slipping into an exercise in retrofitting, “which makes us scour the ancient world for embryonic versions of our modern nation states”

I have left unmentioned several other topics: the overlooked role of women, the legacy of Rousseau’s and Hobbes’s ideas, the origins of inequality and the flawed assumptions hiding behind that question

And cities did not automatically imply social stratification. The Dawn of Everything fascinates with its numerous examples of large settlements without ruling classes, such as Ukrainian mega-sites, the Harappan civilization, or Mexican city-states.

If you have any interest in big history, archaeology, or anthropology, this book is indispensable. I am confident that the questions and critiques raised here will remain relevant for a long time to come.

I was particularly impressed by the in-depth critique by worbsintowords on his YouTube channel What is Politics? of (so far) five videos

And so Operation Peacemaker was born. Loosely based on an academic fellowship, the ONS program invites some of the most hardened youth into the fold: often teenage boys suspected of violent crimes but whom authorities don't have enough evidence to charge criminally.

They are hooked up with mentors -- the reformed criminals-turned-city workers -- who offer advice, guidance and support to get jobs. If the fellows show good behavior after six months, they can earn a stipend of up to $1,000 a month.

In the media, the fellowship is often dubbed "cash for criminals," which makes Boggan's eyes roll. He laughs because, although it's true, the program is so much more. And it's predicated on the most basic of human elements: "We harass them with love and kindness."

“Moderate rebels” was a sarcastic refrain we heard often, making fun of the Obama administration’s description of groups it backs; the Syrian government calls them terrorists.

“Don’t tell me he died! Don’t!” she shrieked. “I only have this one son.”“He will survive,”

Soldiers there said they did not expect the evacuation deal to work.

A senior military official said simply, “It’s over.”

And in many cases, though not all, people living in areas threatened by severe natural hazards do so by choice. If a risk has not been imposed on us, we take it much less seriously. Though Schulz’s piece certainly made a splash online, it is hard to imagine a mass exodus of Portlanders and Seattleites in response. Hey, they like it there.

They don’t have much to compare the future earthquake to. After all, there hasn’t been an earthquake or tsunami like it there since roughly 1700. Schulz poeticizes this problem, calling out humans for their “ignorance of or an indifference to those planetary gears which turn more slowly than our own.” Once again, this confounds our emotional connection to the risk.

The belief that an unlikely event won’t happen again for a while is called a gambler’s fallacy. Probability doesn’t work like that. The odds are the same with every roll of the dice.

But our “temporal parochialism,” as Schulz calls it, also undoes our grasp on probability. “We think probability happens with some sort of regularity or pattern,” says Ropeik. “If an earthquake is projected to hit within 50 years, when there hasn’t been one for centuries, we don’t think it’s going to happen.” Illogical thinking works in reverse, too: “If a minor earthquake just happened in Seattle, we think we’re safe.”

For individuals and government alike, addressing every point of concern requires a cost-benefit analysis. When kids barely have pencils and paper in schools that already exist, how much is appropriate to invest in earthquake preparedness? Even when that earthquake will kill thousands, displace millions, and cripple a region’s economy for decades to come—as Cascadia is projected to—the answer is complicated. “You immediately run into competing issues,” says Slovic. “When you’re putting resources into earthquake protection that has to be taken away from current social needs—that is a very difficult sell.”​

There are things people can do to combat our innate irrationality. The first is obvious: education. California has a seismic safety commission whose job is to publicize the risks of earthquakes and advocate for preparedness at household and state policy levels.

Another idea is similar to food safety ratings in the windows of some cities’ restaurants. Schulz reports that some 75 percent of Oregon’s structures aren’t designed to hold up to a really big Cascadia quake. “These buildings could have their risk and safety score publicly posted,” says Slovic. “That would motivate people to retrofit or mitigate those risks, particularly if they are schools.”

science points to a hard truth. Humans are simply inclined to be more concerned about what’s immediately in front of us: Snakes, fast-moving cars, unfamiliar chemical compounds in our breakfast cereal and the like will always elicit a quicker response than an abstract, far-off hazard.

The metaphors affected how the students saw the problem, and how they proposed to fix it.

So metaphors can influence opinions and choices, but how strong are their effects really? At the end of their experiments, Thibodeau and Boroditsky asked the students to state their gender and political affiliation. As you might expect, men and Republicans were more likely to emphasise enforcement, while women and Democrats leant towards social reforms. But these factors only created differences of around 8 to 9 percentage points. The metaphors, on the other hand, created shifts of between 18 to 22 percentage points!

it’s virtually impossible to talk about complex issues like crime, the economy, health and so on, without resorting to metaphors.

bad metaphors can do a great disservice to the public understanding of science. The idea of the “evolutionary ladder” perpetuates the myth that evolution is about a steady linear march towards complexity.

But that is exactly what Mr. Grinda did. He moved out of the Bedford house in December 2012, ditched the city apartment and got rid of the McLaren. He donated clothes, sports equipment and kitchen utensils to the Church of St. Francis Xavier in Lower Manhattan. He gave his furniture to Housing Works and he packed a Tumi carry-on suitcase with 50 items, including two pairs of jeans, a bathing suit and 10 pairs of socks.

Once he realized his days as a roving houseguest were numbered, Mr. Grinda decided to shift his approach: He kept traveling, but now he was renting apartments on Airbnb or staying in luxury hotels.

Born in suburban Paris in 1974, Mr. Grinda graduated from Princeton in 1996 with a degree in economics. He worked as a consultant at McKinsey & Company for two years before moving back to France to found an online auction start-up funded by the business magnate Bernard Arnault, which Mr. Grinda sold in 2000.He returned to the United States, where he co-founded Zingy, a mobile phone ringtone and game maker, which fetched $80 million in a 2004 sale. After that, he was a founder of OLX, a Craigslist-like service that has become one of the largest global classified websites.Now he is an entrepreneur and angel investor, with more than 200 investments to date, who visits start-ups in Berlin, Paris, New York, San Francisco and other cities.

He looks (and acts) something like Sheldon Cooper, the oddball science geek played by Jim Parsons on “The Big Bang Theory,” an observation Mr. Grinda himself has made.“Friends, who knew me in my late teens and early twenties, would tell you I had exactly the same delusional sense of self-worth and condescending and arrogant self-centered worldview,” he wrote in a blog post that noted his similarities to the sitcom character.

In all, Mr. Grinda said, he stayed with about 15 friends and family members in the first months of 2013. “Everyone was, like, ‘It’s a great idea. Come over,’ ” Mr. Grinda said. “The problem is, the idea of ‘Great, come over’ and me there 24 hours a day, seven days a week, is very different. Especially when their lives are not in sync with mine.”

“When I looked back at the things that mattered the most to me,” he said, “they were experiences, friendships and family — none of which I had invested much in, partly because I was too busy, and partly because I felt anchored by my possessions.”

He hatched a new plan: His friends and family members would come to him.“Rather than me going to them and disrupting their routine,” he said, “getting everyone together in a setting of vacation makes more sense.”

He invited his parents, his friends, their partners, children and nannies for a two-week stay in Anguilla, an island east of Puerto Rico, where he rented two conjoining houses, at a cost of $240,000, with chefs and full house service (and a total of 19 bedrooms).

Mr. Grinda forgot to consider that not everyone lives as he does.For one thing, he had scheduled the Anguilla vacation during the school year, which meant friends with children couldn’t make it. The island’s remoteness, furthermore, meant some guests were forced to endure a tangle of flight connections, leaving some of them exhausted by the time they arrived.And many of the people he invited, who had jobs and other obligations, could stay only for a long weekend.

Mr. Grinda said he has learned a lot from his very big downgrade. He reconnected with old friends, even if it meant annoying them a little, and he rekindled his relationship with his father.“We spent time talking about his life,” he said. And he is no longer against the idea of having a fixed address; he said he is now in negotiations to buy a two-bedroom apartment on the Lower East Side, which he plans to rent out when he is not in town.

Still, the experiment has taken its toll. “The philosophy is interesting,” he said. “But how do you put it into practice? How do you make it real?”

He recently split up with Otilia Aionesei, a former model who works at technology start-up, whom he had been dating, off and on, for two years. The sticking point was their lack of a shared home.“If you want to be his girlfriend, this is the life you have to lead,” Ms. Aionesei said. “I like simple things, to watch movies on the same couch.”Mr. Grinda had a different view. “We went to the Galápagos,” he said. “We went to Tulum. To St. Barts. We have these wonderful experiences and memories together.”

“My home is where I am,” he said. “And it doesn’t matter if it is a friend’s place or a couch or the middle of the jungle or a hotel room on the Lower East Side. But I realize that most of humanity, especially women, don’t see it that way.”

Here is how it works: Each suitor proposes to his first-choice mate; each woman has her own list of favorites. (The economists worked from the now-quaint premise that men only married women, and did the proposing.) She rejects all proposals except her favorite — but does not give him a firm answer. Each suitor rejected by his most beloved then proposes to his second choice, and each woman being wooed in this round again rejects all but her favorite.

Professor Abdulkadiroglu said he had fielded calls from anguished parents seeking advice on how their children could snare the best match. His advice: “Rank them in true preference order.”

The deferred acceptance algorithm, Professor Pathak said, is “one of the great ideas in economics.” It quickly became the basis for a standard lesson in graduate-level economics courses.

In the case of rejection, the algorithm looks to make a match with a student’s second-choice school, and so on. Like the brides and grooms of Professors Gale and Shapley, students and schools connect only tentatively until the very end of the process.

The courting continues until everyone is betrothed. But because each woman has waited to give her final answer (the “deferred acceptance”), she has the opportunity to accept a proposal later from a suitor whom she prefers to someone she had tentatively considered earlier. The later match is preferable for her, and therefore more stable.

It seems that most students prefer to go to school close to home, and if nearby schools are underperforming, students will choose them nevertheless. Researching other options is labor intensive, and poor and immigrant children in particular may not get the help they need to do it.