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after a decade of failed attempts, David Smith, a self-described shape hobbyist of Bridlington in East Yorkshire, England, suspected that he might have finally solved an open problem in the mathematics of tiling: That is, he thought he might have discovered an “einstein.”

In less poetic terms, an einstein is an “aperiodic monotile,” a shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. (The term “einstein” comes from the German “ein stein,” or “one stone” — more loosely, “one tile” or “one shape.”)

Your typical wallpaper or tiled floor is part of an infinite pattern that repeats periodically; when shifted, or “translated,” the pattern can be exactly superimposed on itself

In November of 1947, Albert Einstein offered the United States and the international community advice on how to coexist under the looming threat of nuclear war. An excerpt from his article in The Atlantic, “Atomic War or Peace,” has been animated in the video above.

Today, as the Trump administration appears to be considering nuclear war with North Korea, Einstein’s words resonate once again. In his article, the German-born Nobel Prize-winner cautioned against fear-mongering, which he believed only increases international antagonism. Einstein did condone nuclear programs, but only as a necessary evil for deterrence; he believed the atomic bomb should never again be deployed.

“I am not saying that the United States should not manufacture and stockpile the bomb, for I believe that it must do so; it must be able to deter another nation from making an atomic attack when it also has the bomb,” Einstein said. “To keep a stockpile of atomic bombs without promising not to initiate its use is exploiting the possession of bombs for political ends….Unless there is a determination not to use [atomic bombs] that is stronger than can be noted today among American political and military leaders, and on the part of the public itself, atomic warfare will be hard to avoid.”

A note written by Albert Einstein in 1921 to an Italian scientist who had refused to meet him has sold for $6,100 (£4,300) at an auction in Jerusalem.

"To the scientific researcher, at whose feet I slept and sat for two full days, as a friendly souvenir," the note to Ms Piccini said.

"You know nowadays the 'Me Too' campaign? Probably Einstein would have been in this campaign by leaving such a note to this lady," Gal Wiener, chief executive of Winner's, told the Associated Press news agency.

Less commonly understood, however, is how thoroughly the research into this profound, abstruse and seemingly otherworldly theory was shaped by the messy human dramas of the past century.

Some of the barriers to acceptance were conceptual.

But other obstacles were political. The turmoil and disruptions of World War I, for example, prevented many people from learning and thinking about general relativity

Long, long ago, when the universe was only about 100,000 years old — a buzzing, expanding mass of particles and radiation — a strange new energy field switched on. That energy suffused space with a kind of cosmic antigravity, delivering a not-so-gentle boost to the expansion of the universe.Then, after another 100,000 years or so, the new field simply winked off, leaving no trace other than a speeded-up universe.

astronomers from Johns Hopkins University. In a bold and speculative leap into the past, the team has posited the existence of this field to explain an astronomical puzzle: the universe seems to be expanding faster than it should be.

The cosmos is expanding only about 9 percent more quickly than theory prescribes. But this slight-sounding discrepancy has intrigued astronomers, who think it might be revealing something new about the universe.

Consider two American children, one rich and one poor, both brilliant. The rich one is much more likely to become an inventor, creating products that help improve America’s quality of life. The poor child probably will not.

That’s the conclusion of a new study by the Equality of Opportunity project, a team of researchers led by the Stanford economist Raj Chetty. Chetty and his team look at who becomes inventors in the United States, a career path that can contribute to vast improvements in Americans’ standard of living. They find that children from families in the the top 1 percent of income distribution are 10 times as likely to have filed for a patent as those from below-median-income families, and that white children are three times as likely to have filed a patent as black children. This means, they say, that there could be millions of “lost Einsteins”—individuals who might have become inventors and changed the course of American life, had they grown up in different neighborhoods. “There are very large gaps in innovation by income, race, and gender,” Chetty told me. “These gaps don’t seem to be about differences in ability to innovate—they seem directly related to environment.”

Indeed, exposure to certain specific fields makes children more likely to pursue a career, and a patent, in those fields, the researchers found. This is how they know that exposure, in addition to neighborhoods, is important to innovation: It would be unlikely that growing up in a good neighborhood would inspire many children to patent in the same small field. People who grew up in Minneapolis, where there are many medical-device manufacturers, were especially likely to get patents in medical devices, for instance. Among people living in Boston as adults, those who grew up in Silicon Valley were especially likely to patent in computers. Children whose parents have patents in a specific field—say, antennas—are also likely to patent in exactly the same field as their parents did.

The Event Horizon Telescope collaboration, an international team of radio astronomers that has been staring down the throat of a giant black hole for years, on Wednesday published what it called the most intimate portrait yet of the forces that give rise to quasars

The black hole in question is a monster 6.5 billion times as massive as the sun, and lies in the center of an enormous elliptical galaxy, Messier 87, about 55 million light-years away in the constellation Virgo.

Now, seen through the radio equivalent of polarized sunglasses, the M87 black hole appears as a finely whiskered vortex, like the spinning fan blades of a jet engine, pumping matter into the black hole and energy outward into space.

The vast majority of mayors in American cities do not support sweeping changes to the funding of their police departments, and most say last year's racial justice protests were a force for good in their cities, according to a new survey of more than 100 mayors from across the U.S.

Eighty percent of the mayors who responded to the Menino Survey of Mayors say they believe their police budgets last year were "about right." Most mayors said they did not support reallocating many, or some of their police department's resources and responsibilities.

The findings come in the early days of the Biden administration, as the president seeks to make good on campaign promises to rein in police abuse and dismantle systemic racism. The country's divisions over race, criminal justice and policing are some of the most significant domestic challenges facing Biden's administration.

Nxivm sex-cult founder Keith Raniere faces up to life behind bars Tuesday when he is set to be sentenced in the horrific abuse of scores of young women.

running a twisted secret group out of Albany that sexually, physically and mentally abused followers.

“a massive manipulator, a con man and the crime boss of a cult-like organization involving sex trafficking, child pornography, extortion-compelled abortions, branding, degradation and humiliation,” t

an international consortium of research collaborations revealed compelling evidence for the existence of a low-pitch hum of gravitational waves reverberating across the universe.

The scientists strongly suspect that these gravitational waves are the collective echo of pairs of supermassive black holes — thousands of them, some as massive as a billion suns, sitting at the hearts of ancient galaxies up to 10 billion light-years away — as they slowly merge and generate ripples in space-time.

Each pair of supermassive black holes is generating a different note, Dr. Siemens said, “and what we’re receiving is the sum of all those signals at once.”

The Colombian establishment is lining up behind Rodolfo Hernández, a populist businessman with an incendiary streak, to defeat the leftist former rebel Gustavo Petro.

For months, pollsters predicted that Gustavo Petro, a former rebel-turned-senator making a bid to be the nation’s first leftist president, would head to a June presidential runoff against Federico Gutiérrez, a conservative establishment candidate who had argued that a vote for Mr. Petro amounted to “a leap into the void.’’

Rodolfo Hernández, a former mayor and wealthy businessman with a populist, anti-corruption platform whose outsider status, incendiary statements and single-issue approach to politics have earned him comparisons to Donald Trump.

Various books I’ve been reading lately have me thinking about 1966. I have often said that the history of Black America could be divided between what happened before and after that year.

It was a year when the fight for Black equality shifted sharply in mood, ushering in an era in which rhetoric overtook actual game plans for action

The difference between Black America in 1960 and in 1970 appears vaster to me than it was between the start and end of any other decade since the 1860s, after Emancipation

Unlike Einstein, who was urging the US to get ahead, these distinguished authors want everyone to slow down, and in a completely rational world that is what we would do

But, very much like the 1940s, that is not going to happen. Is the US, having gone to great trouble to deny China the most advanced semi-conductors necessary for cutting-edge AI, going to voluntarily slow itself down? Is China going to pause in its own urgent effort to compete? Putin observed six years ago that “whoever becomes leader in this sphere will rule the world”. We are now in a race that cannot be stopped.

Now we have to get used to capabilities that grow much, much faster, advancing radically in a matter of weeks. That is the real reason 1,100 experts have hit the panic button. Since the advent of Deep Learning by machines about ten years ago, the scale of “training compute” — think of this as the power of AI — has doubled every six months

The evenhanded approach of Louis Menand, who won a Pulitzer Prize for “The Metaphysical Club,” is like a breath of fresh air. “The Free World” sparkles. Fully original, beautifully written, it covers the interchange of arts and ideas between the United States and Europe in the decades following World War II

Menand is no cheerleader; his assessment of America’s failures can be withering. But his larger point, backed by a mountain of research and reams of thoughtful commentary, is that American culture ascended in this era for the right reasons. “Ideas mattered. Painting mattered. Movies mattered. Poetry mattered,”

Much of this was the result of the forced migration of intellectual talent after Mussolini and Hitler came to power. We tend to remember the scientists who fled — like Albert Einstein — much more than the composers, performers, writers, poets, philosophers and political theorists. At a time when immigration to the United States had all but ended, the door remained ajar for those with unique résumés. “Getting into the United States was like getting into a highly selective college,” Menand writes.

The Foundation, which is affiliated with the German Green party, founded the prize not to honor Arendt but to “honor individuals who identify critical and unseen aspects of current political events and who are not afraid to enter the public realm by representing their opinion in controversial political discussions”, withdrew its support, causing the city of Bremen to withdraw its support, leading to an initial cancellation

The Foundation said Gessen’s comparison was “unacceptable”, but has since backtracked and has now said that they stand behind the award.

The comparison is not a one-to-one argument, but rather a barometer for urging individuals – and countries – to think about their support for Israe