Rufus Wainwright has defended his musical Opening Night, which was forced to close early after mixed reviews, saying West End audiences lack “curiosity” after Brexit and the British press had turned on the project because it was “too European”.

Opening Night was Wainwright’s first musical and is an adaptation of John Cassavetes’ 1977 film about an actor struggling to cope, who is played by Sheridan Smith. Directed by Ivo van Hove, it opened in March at the Gielgud theatre but a month later announced it would be closing two months early.

Some audience members reportedly walked out during the performance or left during the interval. The musical included a scene where Smith staggers out into the streets of the West End while being filmed and projected back on to the stage.

Wainwright said the experimental elements of the show were too much for conservative audiences, and seeing Smith – who is a mainstream star – in something more avant garde was anathema to certain critics and audience members.

“I do feel that since Brexit, England has entered into a darker corridor where it is a little more narrow in its outlook and the vitriol because we put ‘English rose Sheridan Smith through this ordeal of European theatre’ felt a little bit suspect to me,” he told the Guardian. “I was a little surprised by that.”

Opening Night did get some positive reviews. The Guardian gave it four stars and said it was “the most unusual thing on the London stage right now”, while Time Out called Smith “superb”. But other critics weren’t convinced.

The New York Times critic Houman Barekat said the adaptation “desecrated” Cassavettes’ original film, while he dismissed Wainwright’s songs as “algorithmically bland”. The New Statesman said it was a “chaotic and masochistic project”, while Attitude called it a “missed opportunity sorely lacking in camp”.

Although Wainwright admits the show “wasn’t perfect by any means” and that there “were mistakes made on many fronts”, he believes the negative reaction to the show was partly because Britain has become more insular since the 2016 Brexit referendum.

“There’s a lack of imagination and curiosity about change,” he said. “All of the reviews from Europe were incredible for this piece; the staging and the rhythm is more European and there was a vitriolic reaction against that. I don’t think it was perfect and that I don’t deserve criticism, but this thing of shutting it down if it’s not exactly what you want is not really the theatrical lane that I want to live in.”

Opening Night’s producers, Wessex Grove, said “what is sure-fire and safe has its place” but it was proud to have taken a “risk”, when it announced the show was ending prematurely.

“In a challenging financial landscape, Opening Night was always a risk and, while the production may not have had the life we had hoped for, we feel immensely proud of the risk we took and of this extraordinary production,” they said.

Van Hove said it was “always sad” when a show was cut short.

Wainwright defended Smith, who told the Guardian she “had something to prove” because – like the character she plays in Opening Night – she had unravelled on stage in 2016. “People were saying be careful, we have to be delicate with her, and it couldn’t have been further from the truth,” he said.

“She was always excited and giving her full – I have nothing but admiration and love for her.”

The songwriter, who is the child of two famous folk singers, Loudon Wainwright III and Kate McGarrigle, and whose sister Martha is also a famous artist, has written two operas and 11 studio albums.

Wainwright said he was “a little beaten up by” the experience but was glad the production was ambitious and stood out from what he thinks is a conservative landscape on the West End. “I think the West End has got pretty staid,” he said.

“The main objective I have is that people think about it for days and days and look: people have thought about Opening Night now for weeks. It has remained in the psyche of the press and the public … it does endure for better or for worse.”

Wainwright said he was working on the cast album of the show, which he hopes can give it another life. The final performance of Opening Night in the West End will take place on 18 May.

Israeli military forces have taken control of the Palestinian side of the Rafah crossing between Gaza and Egypt, a key strategic objective and the sole gateway between Egypt and Gaza for humanitarian aid, Israeli military officials have confirmed.

“At the moment we have operational control of the Gazan side of the Rafah crossing and we have special forces scanning the crossing … That is what is happening in the upcoming hours. The operation is not over … I can’t give a timeline,” a military official said on Tuesday morning.

The spokesperson of the Gaza border authority on Tuesday confirmed the presence of Israeli tanks at the Rafah crossing. Aid officials in the territory said that the flow of aid through the crossing has been halted.

The Israeli operation comes as ahead of a new round of indirect negotiations on a ceasefire in Cairo following an announcement by Hamas leaders on Monday night that they would accept a recent proposal for a deal. Israeli officials say they will send a delegation for further talks although the deal did not meet its core demands and vowed to push ahead with an often threatened assault on Rafah.

“Israel is receiving Hamas response … an Israeli delegation will soon be in Cairo,” the military official said.

The promise of continued talks left a glimmer of hope alive for an agreement that could bring at least a pause to the seven-month-old war that has devastated Gaza.

The Israeli military said late on Monday it was conducting targeted strikes against Hamas in Rafah. The city’s Kuwaiti hospital said on Tuesday that 11 people had been killed and dozens of others injured in Israeli strikes.

After having vowed for weeks to push into the southern border town, Israel on Monday called for Palestinians in eastern Rafah to leave for an “expanded humanitarian area” ahead of a ground incursion.

The military official said the target was “terrorist infrastructure”, after the launch of rockets at Israeli troops at the Kerem Shalom earlier this week.

“We were able to operate in this manner and quickly because of the vast majority of people evacuating and moving and we were able to operate in a very specific area within a specific areas. We are only talking about the Gaza side of the crossing,” the official said.

The Rafah gate is a vital aid lifeline and particularly sensitive for Egypt, which is anxious to avoid a mass migration of Palestinians into its Sinai desert.

The more than 1 million Palestinians taking refuge in Rafah were thrown into confusion by the day’s events, with Israel’s evacuation order triggering an exodus of thousands of people.

In a private meeting on Monday, Jordan’s King Abdullah told US president Joe Biden that an Israeli offensive in Rafah would lead to a “new massacre” of Palestinian civilians and urged the international community to take urgent action.

In a phone call on Monday, Biden pressed Israeli prime minister Benjamin Netanyahu not to go ahead with a large-scale offensive. Biden has been vocal in his demand that Israel not undertake a ground offensive in Rafah without a credible plan to protect Palestinian civilians.

US state department spokesperson Matthew Miller said the US had not seen such a plan, adding that Washington could not support an operation in Rafah as it is currently envisioned.

Miller said American officials were reviewing the Hamas response to the ceasefire proposal “and discussing it with our partners in the region.”

It was not immediately known if the proposal Hamas agreed to was substantially different from one that US secretary of state Antony Blinken pressed the group to accept last week, which Blinken said included significant Israeli concessions.

Talks in Cairo had appeared to stall at the weekend over Hamas’s insistence that Israel should commit to making the ceasefire permanent at the outset of the agreement, rather than to negotiate its duration after the truce had taken hold.

An account in Haaretz suggested that the deal Hamas agreed to does not include an immediate demand for a permanent ceasefire, but also changes other elements of the Egyptian deal proposal, such as the requirement that it free 33 hostages in the first phase. It also reportedly takes away Israel’s right of veto on which Palestinian detainees are released in exchange.

On Monday night, hundreds of Israelis rallied around the country calling for the government to agree to the terms of the deal that Hamas had accepted.

About 1,000 protesters gathered near the defence headquarters in Tel Aviv, while in Jerusalem, about 100 protesters marched toward Netanyahu’s residence with a banner reading, “The blood is on your hands.”

Two women have sprayed the words “MeToo” on a 19th-century painting of a woman’s vagina by French artist Gustave Courbet in a stunt by a performance artist, a museum and the artist said.

“The Origin of the World”, a nude painted from 1866, was protected by a “glass pane” and the police were on site to assess the damage, the Centre Pompidou in the north-eastern city of Metz told AFP on Monday.

The work had been on loan to the Centre Pompidou-Metz from the Musee d’Orsay in Paris as part of an exhibition centred on French psychoanalyst Jacques Lacan, who once owned the painting.

Metz prosecutor Yves Badorc said two women born in 1986 and 1993 had been arrested after five works in total, including Courbet’s nude, had been sprayed with the words “MeToo”.

A third person – who has not been detained – is believed to have stolen another artwork, he said.

The stolen piece – red embroidery on white material by French artist Annette Messager – is called “I Think Therefore I Suck”.

French-Luxembourgish performance artist Deborah de Robertis told AFP she had organised the spray painting in red, carried out by two other people, as part of a performance titled: “You Don’t Separate the Woman from the Artist”.

In a video sent to AFP by de Robertis, one woman tags Courbet’s famous painting with red paint and then another painting.

They then chant “MeToo” before being dragged away by security guards.

De Robertis explained that she wanted to “challenge the history of art”, in particular by tagging “MeToo” on the famous painting “because women are the origin of the world”.

In an open letter, de Robertis denounced the behaviour of six men in the art world, describing them as “predators” and “censors”.

She said the actions were a feminist performance, carried out because “the very closed world of contemporary art has remained largely silent until now”.

The artist said they had also targeted another work by Austrian artist Valie Export.

De Robertis already had work on display at the venue – a photograph of a 2014 performance at the Musee d’Orsay in which she posed showing her vagina underneath Courbet’s painting.

Culture minister Rachida Dati wrote on X: “To ‘activists’ who think that art is not powerful enough to carry a message alone … An artwork is not a poster to colour in with the day’s message.”

Metz mayor Francois Grosdidier condemned what he described as “a new attack on culture, this time by fanatic feminists”.

Courbet’s nude was first owned by a Turkish-Egyptian diplomat called Khalil Bey, a flamboyant figure in 1860s Paris who put together an art collection celebrating the female body before he was ruined by his gambling debts, according to the Musee d’Orsay.

It belonged to Lacan before it entered the museum’s collection in 1995.

A French court in 2020 sentenced de Robertis to pay a 2,000-euro ($2,150) fine for appearing naked in 2018 in front of a cave in the town of Lourdes in southwest France, a Catholic pilgrimage site for those who believe the Virgin Mary appeared there.

A case against her was dropped in 2017 after she showed her vagina in front of Leonardo da Vinci’s Mona Lisa at the Louvre museum in the French capital.

Pro-Palestinian protesters who had been blocked by police from accessing an encampment at the Massachusetts Institute of Technology on Monday broke through fencing, linked arms and encircled tents that remained there, as Columbia University canceled its university-wide commencement ceremony following weeks of pro-Palestinian protests.

Sam Ihns, a graduate student at MIT studying mechanical engineering and a member of MIT Jews for a Ceasefire, said the group had been at the encampment for the past two weeks and that they were calling for an end to the killing of thousands of people in Gaza.

“Specifically, our encampment is protesting MIT’s direct research ties to the Israeli Ministry of Defense,” he said.

Protesters also sat in the middle of Massachusetts Avenue, blocking the street during rush hour in the Boston area.

The demonstrations at Columbia have roiled its campus and officials said on Monday that while it would not hold its main ceremony, students would be able to celebrate at a series of smaller, school-based ceremonies this week and next.

The decision comes as universities around the country wrangle with how to handle commencements for students whose high school graduations were derailed by Covid-19 in 2020. Another campus shaken by protests, Emory University, announced on Monday that it would move its commencement from its Atlanta campus to a suburban arena. Others, including the University of Michigan, Indiana University and Northeastern University, have pulled off ceremonies with few disruptions.

Columbia’s decision to cancel its main ceremony, scheduled for 15 May, saves its president, Minouche Shafik, from having to deliver a commencement address in the same part of campus where police dismantled a protest encampment last week. The Ivy League school in upper Manhattan said it had made the decision after discussions with students.

“Our students emphasized that these smaller-scale, school-based celebrations are most meaningful to them and their families,” officials said.

Most of the ceremonies that had been scheduled for the south lawn of the main campus, where encampments were taken down last week, will take place about five miles north at Columbia’s sports complex, officials said.

Speakers at some of Columbia’s still-scheduled graduation ceremonies include the Pulitzer Prize-winning playwright James Ijames and Dr Monica Bertagnolli, director of the National Institutes of Health.

Columbia had already canceled in-person classes. More than 200 pro-Palestinian demonstrators who had camped out on Columbia’s green or occupied an academic building were arrested in recent weeks.

Similar encampments sprouted up elsewhere as universities struggled with where to draw the line between allowing free expression while maintaining safe and inclusive campuses.

On Monday evening, a group of students at the Rhode Island School of Design in Providence used tables and chairs to barricade the entrance to the second floor of a building on campus, preventing police from getting in, according to a report from the Brown Daily Herald, a student publication at nearby Brown University.

The protest was organized by Risd Students for Justice in Palestine, who said they would not leave the building until president Crystal Williams met their demands for fiscal transparency around investments, “holistic” divestment from groups involved with “sustaining Israel apartheid”, establishing a student oversight committee for investments and publicly condemning Israel’s actions in Gaza as a genocide.

The University of Southern California earlier canceled its main graduation ceremony. Students abandoned their camp at USC on Sunday after being surrounded by police and threatened with arrest.

Other universities have held graduation ceremonies with beefed-up security. The University of Michigan’s ceremony was interrupted by chanting a few times on Saturday. In Boston on Sunday, some students waved small Palestinian or Israeli flags at Northeastern University’s commencement in Fenway Park.

At the University of California, San Diego, police cleared an encampment and arrested more than 64 people, including 40 students, on Monday.

The University of California, Los Angeles, moved all classes online for the entire week due to continuing disruptions following the dismantling of an encampment last week. The university police force reported 44 arrests on Monday but there were no specific details, the UCLA spokesperson Eddie North-Hager said in an email to the Associated Press.

Schools are trying various tactics from appeasement to threats of disciplinary action to get protesters to take down encampments or move to campus areas where demonstrations would be less intrusive.

A group of faculty and staff members at University of North Carolina at Chapel Hill asked the administration for amnesty for any students who were arrested and suspended during recent protests. UNC Faculty and Staff for Justice in Palestine said in a media advisory that it would deliver a letter on behalf of more than 500 faculty who support the student activists.

Other universities took a different approach.

Harvard University’s interim president, Alan Garber, warned students that those participating in a pro-Palestinian encampment in Harvard Yard could face “involuntary leave”. That means they would not be allowed on campus, could lose their student housing and might not be able to take exams, Garber said.

If Erik ten Hag’s future at Manchester United remained up for debate then surely this removed any lingering doubts for Sir Jim Ratcliffe. Even amid a season in which his team have lurched from one disaster to another, a scintillating performance from a Crystal Palace side inspired by the magical feet of Michael Olise delivered one of the most embarrassing evenings of the Dutchman’s tenure.

United’s European aspirations for next season may now have to rely on them beating Manchester City in the FA Cup final after two goals from Olise, Jean-Philippe Mateta’s ninth in 11 since the appointment of Oliver Glasner and another from Tyrick Mitchell gave Palace a league double over their opponents for the first time in Premier League history. The scant consolation for Ten Hag was that Palace could not find a fifth to match their record victory over United back in December 1972 after the substitute Odsonne Édouard hit a post late on. For reference, that result led to the sacking of the manager, Frank O’Farrell, three days later.

Ten Hag should at least make it through to the end of the season but faces a mammoth task to lift his despondent players after this chastening defeat in south London. Palace have now picked up four victories in their last five matches under Glasner and look like a team who don’t want the season to end. But while Gareth Southgate – watching on from the stands at his former club – would have been impressed with Eberechi Eze and pleased to see Marc Guéhi make his return as a substitute as he aims to prove his fitness in time for the Euros after three months out, it was Olise who stole the show.

The former Reading forward has opted to play for France Under-21s, although he remains eligible for England. Having now been directly involved in 13 goals in his last nine starts here, the 22-year-old would certainly be under consideration if he ever changes his mind.

In the absence of the sidelined Bruno Fernandes and Harry Maguire, the extent of United’s injury list meant that two of the substitutes were goalkeepers and four had never made a senior appearance. Jarred Gillett, the referee, made history by wearing a head-mounted ­RefCam, with ­footage to be broadcast at a later date, and his first decision was to wave away Mitchell’s appeals for a penalty after a challenge from Jonny Evans.

It was not long until Palace found a way through United’s porous defence as the familiar failings returned, however. A sublime piece of skill from Olise after he received Daniel Muñoz’s throw-in left Casemiro sprawling in the centre circle as the forward sped away before clipping a precise shot past André Onana from the edge of the penalty area. “Professionals shouldn’t allow this,” was Ten Hag’s verdict. “It’s not the first time this season it has happened.”

The electric Olise could have had a hat-trick inside the first 23 minutes had Mateta not blocked his goalbound shot after he was again set up by Muñoz before shooting straight at Onana. The visitors’ hopes of a quick equaliser were dashed when Gillett ruled Rasmus Højlund had impeded Dean Henderson, the former United goalkeeper, as he jumped for the ball.

United were fortunate Olise could not capitalise on a slip from Kobbie Mainoo that left him clean through on goal. Onana then almost came unstuck when trying to clear under pressure from Mateta and sliced the ball out of play to the delight of the home fans. But United’s luck could not hold forever and Ten Hag looked on forlornly when Chris Richards fed Mateta after winning possession. The in-form striker powered past the helpless Evans before smashing his shot into the net.

United’s players were sent out into the rain early for the second half but Palace continued where they left off as Eze volleyed Nathaniel Clyne’s cross straight at Onana. Casemiro thought he had pulled one back when he stabbed home after his header came back off a post, only to be flagged offside by almost a metre.

That only seemed to provoke Palace as a wonderful backheel by Olise through the legs of Casemiro teed up Eze to curl just wide before Mitchell and then Will Hughes were denied by Onana. United were clearly there for the taking and Adam Wharton’s brilliant cross allowed Joachim Andersen to set up Mitchell to tap home from close range. Ten Hag’s response was to replace Antony with Sofyan Amrabat in an attempt to keep the score respectable. But only Casemiro will know why he allowed Muñoz the opportunity to steal the ball near the byline and free Olise to hammer home a fourth.

The double substitution of Olise and Eze to a standing ovation ended the torment of United’s defenders for the evening. To their credit, the away supporters kept singing until the bitter end but it remains to be seen if their manager can survive beyond this campaign.

Things had been tense at the University of California, Los Angeles, with some ugly jibes and the occasional shove exchanged between students who support Israel’s war on Gaza and those who have set up encampments to call for a permanent ceasefire and the university’s divestment from companies that arm and otherwise profit from Israel’s occupation and military incursions in the Palestinian territories.

But what happened in the middle of the night last Tuesday was no scuffle. It was not even one more of the outsized, excessively brutal raids that college administrations have invited the police to inflict on their students.

Since the previous Thursday, groups of ever-more aggressive counter-protesters had beset the Palestine solidarity tent village on UCLA’s Dickson Plaza. Then, just before 11pm on 30 April, at least a 100 masked young men stormed the camp. They announced their presence by blasting the sounds of screaming babies from loudspeakers. They shined strobe lights, sprayed irritant gases and launched firecrackers at the encampment. One landed in the middle of the tents, eliciting screams from the occupants. The besieged protesters called for help – at least five people were already injured – but none came.

The mob breached the metal barricades around the camp, kicked in its plywood walls, and began stomping and beating the campers with fists and poles. At this point, a two-sided melee began. The Daily Bruin, the student paper, reported that some blasts of gas appeared to come from inside the camp. A text from the UC Divest Coalition sent around 1140pm, however, said that the encampment members do not possess teargas and were using “community defense” and wearing goggles to protect themselves.

Unlike at other colleges – such as New Hampshire’s Dartmouth College, where cops alerted by the administration mustered in riot gear practically before students pitched their tents – UCLA, in the persons of its security guards and campus police, watched the chaos and did nothing. Unarmed guards hired by the university retreated to a campus building and locked the doors behind them. A handful of UC police officers showed up at 11.13pm and left less than 10 minutes later. John Thomas, the UCPD chief, said that officers came under attack while trying to help an injured person and left. The Los Angeles police department did not arrive until around 1.30am or quell the violence until after 3.00am. A video posted at around 3.30am caught UC security standing a distance away, filming the action on their phones.

Twenty-five members of the encampment were hospitalized overnight. No attackers were arrested. In an editorial addressed to the UCLA chancellor the next day, the Bruin asked: “Will someone have to die tonight for you to intervene?”

On Thursday, UCLA intervened. It called in the LAPD and highway patrol, who arrived early in the morning in body armor, face shields and helmets. They tore down the plywood, shooting flash bangs and at least one rubber bullet. The protesters sprayed fire extinguishers back at them. In contrast to the nights before, this time the cops braved the blows and accomplished their tasks efficiently. By mid-morning, more than 200 students had been arrested, booked and released from custody, the encampment was dismantled and trash was cleared from the site.

The foreign press called the attacks what they were. Al Jazeera described the event as an “assault” that “followed days of harassment”. The BBC, indicating that the evidence spoke for itself, simply posted a video under the headline, “Watch: Counter-protesters attack UCLA pro-Palestinian camp.”

Most of the US press refrained from assigning blame. They called the events “clashes” and described the assaults in the passive voice. “Barriers were breached,” said CBS News. The New York Times reported that “fistfights broke out, chemicals were sprayed into the air and people were kicked or beaten with poles.”

Since the start, Fox News had openly blamed the members of the encampments, many of them Jewish, for victimizing Jews around campus and applauded the police crackdowns. But with the police uncharacteristically absent and the campers unmistakably the victims, it was hard to control the narrative. Even Fox’s Jew-on-the-scene, student Eli Tsives, slipped, calling the attackers a “mob”.

Joe Biden weighed in from the White House. In a statement, he strung together diverse acts –“vandalism, trespassing”, “forcing the cancellation of classes and graduations”, “threatening people”– ending each list with “This is not peaceful protest. It’s against the law.” He added: “We are not an authoritarian nation where we silence people and squash dissent … but neither are we a lawless country.”

Like the press and the police, the president performed several sleights of rhetoric. He mixed violent acts with non-violent acts. He conflated school policy with law and illegality with lawlessness, a word connoting anarchy. Apparently, he has not heard of non-violent civil disobedience – lawbreaking in resistance to unjust laws or policies – which Henry David Thoreau called a “duty” to democracy. In fact, the campus occupations are versions of the sit-ins of the Black civil rights movement, illegal trespass that has since been sacralized in the annals of American freedom.

Biden also declined to specify who committed any of the acts he condemned, letting the impression float that the culprits are the anti-war protesters.

Who were these UCLA counter-protesters? Tsives said they looked to be in their late 20s and claimed that they were locals who had “had enough” of antisemitism. Another witness, Sean Beckner-Carmitchel, a videographer who has covered political actions around Los Angeles, knew them better. “I saw people that I’ve seen at Trump rallies,” he told Al Jazeera. “I’ve seen them at anti-LGBTQ protests.” Unlike the pro-Israel students who gather during the day, these guys were not wearing yarmulkes or carrying blue-and-white flags. They were chanting “USA! USA!” At Columbia, the Proud Boys founder Gavin McInnes was spotted trying to enter the Gaza Solidarity Encampment.

The media’s focus on the encampments, simultaneously obsessive and blurry, has diverted attention from the war itself and the protesters’ message, which they repeat whenever they speak: the Palestinian death toll is approaching 35,000. After six months of merciless onslaught, Israel will receive $15bn in unconditioned US military aid. Netanyahu has announced plans to invade Rafah, where an estimated 1.5 million people are sheltering, even if a hostage deal is reached. UN workers in Gaza have coined a new term for the psychological state of the people: rather than post-traumatic stress disorder, or PTSD, they are suffering CTSD –constant traumatic stress disorder.

But something else is sliding past popular attention: the meaning of the events at UCLA. Vigilantes staged an assault on unarmed civilians and the state let it happen. This has occurred many times before in US history, particularly when the victims were African American. Still, it is historic.

Is this the mayhem Trump promises at every rally? Is this what we can expect if he loses the election – or if he wins? Have the brownshirts been unleashed? Whatever it augurs, the eve of May Day 2024 must be marked. While across the nation law enforcers are being ordered to commit violence against peaceful, unarmed citizens, in LA they tacitly deputized a mob to police the political speech – and people – that both the police and the mob despise. And by action or inaction, speech or silence, educational leaders, civil authorities and the president condoned this police-enabled civilian violence, this real anarchy.

At UCLA we witnessed legally sanctioned lawlessness. It is more terrible and more politically momentous than anything a civilian can ever do.

• Judith Levine is a Brooklyn journalist and essayist, a contributing writer to the Intercept, and the author of five books

Two college freshmen who, during their final year of high school, found a new way to prove Pythagoras’s theorem by using trigonometry – which mathematicians for generations thought was impossible – have since uncovered multiple more such proofs, they revealed in a national interview on Sunday.

“We found five, and then we found a general format that could potentially produce at least five additional proofs,” Calcea Johnson said on CBS’s 60 Minutes, a little more than a year after she and Ne’Kiya Jackson collaborated on an accomplishment that earned them international recognition.

Nonetheless, in comments that stunned their interviewer, Bill Whitaker, the two graduates of St Mary’s Academy in New Orleans denied seeing themselves as math geniuses and dismissed any interest in pursuing careers in mathematics.

“People might expect too much out of me if I become a mathematician,” Jackson said, shaking her head. Johnson, for her part, added: “I may take up a minor in math, but I don’t want that to be my job job.”

Sunday’s conversation on CBS’s popular Sunday evening news magazine were perhaps their most extensive, widely broadcast remarks to date on the new ground that they broke with respect to the Pythagorean theorem.

The 2,000-year-old theorem established that the sum of the squares of a right triangle’s two shorter sides equals the square of the hypotenuse – the third, longest side opposite the shape’s right angle. Countless schoolchildren taking geometry have memorized the notation summarizing the theorem: a² + b² = c².

For 2,000 years, mathematicians maintained that any alleged proof of the Pythagorean theorem that was based in trigonometry would constitute a logical fallacy known as circular reason – in essence, trying to validate an idea with the idea itself.

But the bonus question on a math contest that Johnson and Jackson took home to complete during the Christmas break of their final year at St Mary’s served as the impetus for them to plot out a new way to demonstrate that one could indeed use trigonometry to prove Pythagoras’s theorem.

Their work was so compelling that the pair went to a regional meeting of the American Mathematical Society in Atlanta in March 2023 to outline their findings. At the organization’s recommendation, Jackson and Johnson have submitted their discoveries for final peer review and publication – as well as working on additional proofs while that process is pending, as 60 Minutes noted.

The 60 Minutes interview gave Johnson and Jackson occasion to reflect on the intense reaction caused by initial media reports on their innovative work at St Mary’s, a Catholic high school that has been dedicated to educating Black girls since its founding shortly after the US civil war.

Some of it was negative. Some in the math community smarted at claims in a press release issued by St Mary’s that asserted Jackson and Johnson’s research was “unprecedented”. And they flocked to social media demanding that a 2009 trigonometry-based proof for Pythagoras’s theorem get its due.

Yet a lot of the reaction to Johnson and Jackson was positive, especially as mathematicians who picked apart their work confirmed that – by all indications – they had arrived at a valid new proof, a celebration-worthy accomplishment.

Michelle Obama wrote a post on social media that linked to a story about Johnson and Jackson, adding the text: “I just love this story. … Way to go, Ne’Kiya and Calcea! I’m rooting for you and can’t wait to see what you all do next.”

They also received a commendation from Louisiana’s then governor as well as symbolic keys to the city of New Orleans.

Asked on 60 Minutes why they thought people were so impressed with what they had done, Jackson said she thought the public was surprised young Black women could author such a feat.

“I’d like to be celebrated for what it is,” Jackson said. “Like – it’s a great mathematical achievement.”

Jackson is now attending New Orleans’ Xavier University and enrolled in its pharmacy department. Meanwhile, Johnson – who graduated from St Mary’s as its valedictorian – is now an environmental engineering student at Louisiana State University in Baton Rouge.

Perched over a small bay, the village of Binibeca Vell on the Spanish island of Menorca has long been a magnet for tourists looking to wander along its winding, narrow lanes lined with whitewashed villas.

But as its popularity swells on social media, setting off a stampede for selfies snapped along its cobblestone streets, residents are threatening to stop access to the village all together.

“The problem isn’t tourists,” said Óscar Monge, who heads the group representing Binibeca Vell’s 195 property owners. Instead, he pointed the finger at officials, who he said had forsaken residents as they grappled with the noise generated by the constant parade of visitors and the rubbish that piled up daily.

“Binibeca Vell is not a place of adventure, but it’s a private housing development where people reside,” Monge added.

It’ is a debate playing out across Spain and much of Europe as residents call on officials to more when it comes to striking a balance between their needs and soaring tourist numbers.

As mentions of Binibeca Vell multiplied on social media, the number of visitors has rocketed to about 800,000 a year, with most of them arriving between May and October, said Monge. This year residents are bracing for as many as 1 million visitors, he added.

“If the administration continues to leave us abandoned, in August we’ll carry out a vote among owners on whether we should close up the development,” he said.

The threat follows years of complaints by residents. Speaking to the news website ElDiario.es last month, one resident vented her frustration over how tourists had behaved while visiting the village. “They went into homes, they sat on chairs, they take things, climb on our walls, they have outdoor drinking parties,” she said. “If this isn’t regulated, it will happen every summer.”

Residents began cracking down last year, asking tourists to visit only during certain hours. The schedule was tightened this month to ask that tourists stop by only between 11am and 8pm. “We want to have breakfast peacefully on our terraces and sleep peacefully without noise,” said Monge.

The request on the village’s website also asks tourists to refrain from “entering homes” and “climbing balconies”. The request is accompanied by a series of photos depicting one tourist splayed out on a stairwell and another sitting in the chair of a resident.

Seemingly at the heart of the residents’ stance is a lapsed deal with local officials. Last year, residents were given €15,000 (£12,850) to help with rubbish removal, while officials committed to better training for tour guides that visit the area and curbs on public transport into the area.

So far the deal has not been renewed. As both sides lay blame on each other, they are scheduled to meet in the coming days. “We’re going with very little hope, to be honest,” said Monge.

The head of tourism for the Menorcan government, Begoña Mercadal, did not reply to a request for comment. But speaking to Eldiario.es, she confirmed that the village was within its right to curtail visits. “We fully acknowledge that it is private property and, therefore, if they want to close it, that is their right,” Mercadal said.

Monge was swift to acknowledge that the decision to do so, however, would probably harm the 100 or so families in the region whose hotels, bars and souvenir shops depend on local tourism. “Of course it’s a difficult decision but we’re being pushed into it,” he said.

He described the closure as a last resort. “From the coast you would still be able to visit the perimeter of the village, but you wouldn’t be able to enter the interior lanes,” he added. “And that’s the charming photo that everyone wants for Instagram.”

There has been widespread condemnation of an attack on a man who was found nailed to a fence in a car park in Bushmills, County Antrim.

The victim, in his 20s, was discovered with nails in both hands and injuries to his nose in the Dundarave Park area. He was taken to hospital for treatment in the early hours of Sunday.

Two vans, one belonging to the injured man, were found on fire nearby and crews from the Northern Ireland fire and rescue service were called to the scene. Graffiti on the wall of public toilets in the vicinity was being linked to the violent attack and arson.

About 20 visitors in campervans and mobile homes were reported to have been in the area at the time of the assault.

Some local people said privately they believed loyalist paramilitaries were responsible.

The Police Service of Northern Ireland said the victim of the “brutal” and “sinister” attack had been left with life-changing but not life-threatening injuries.

The PSNI also said paramilitary involvement was one of the lines of inquiry being investigated.

It called on anyone with information or video footage to contact them as part of the police investigation.

The assistant chief constable Bobby Singleton told the BBC: “This criminal and violent behaviour cannot be tolerated in a peaceful community and has to be condemned.”

Local politicians said people were shocked by what happened.

The Alliance party assembly member (MLA) Sian Mulholland told a local radio station there was no place for vigilantism in Northern Ireland in 2024.

“If people do have concerns, the police and the justice system are the routes we have to follow,” she said, “otherwise we are in the wild west.”

A local Traditional Unionist Voice MLA, Jim Allister, said: “It is for the lawful authorities to deal with law-breaking. Mob rule has no place in our society.”

The last reported incident of a similar attack was more than 20 years ago.

In 2002 a 23-year-old man from west Belfast was found “crucified” and with broken legs in a loyalist area in the south of the city. Harry McCartan had to undergo surgery to remove wooden splinters that remained in his hands after the 6in nails were removed.

There was a time, not so long ago, that Donald Trump did not seem to be very familiar with the Bible.

When he first ran for the nomination of the very Christian Republican party, Trump was unable to name a single Bible verse. Early in his 2016 presidential campaign he referred to the eucharist as a “little cracker”. In a subsequent church visit, as he attempted to prove his religious credentials, he put cash in a plate that was meant to hold the communion.

How times have changed.

“All Americans need a Bible in their home, and I have many. It’s my favorite book,” Trump declared in March, in a video posted on Truth Social. “I’m proud to endorse and encourage you to get this Bible. We must make America pray again.”

In the video, Trump, who has a long history of endorsing and selling things, is clutching the God Bless the USA Bible – a “patriotic” take on the holy text that Trump is now hawking for $59.99.

“I want to have a lot of people have it,” Trump continued. “You have to have it for your heart and for your soul.”

Well, who am I to defy a one-term, twice-impeached, former president who is currently on trial over hush-money payments to a porn star. I bought it.

Buying something from Donald Trump is fraught with danger. Trump is known for not following through on business agreements: in the run-up to the 2016 election, literally hundreds of people, including lawyers, carpenters and painters, came forward to accuse Trump of not paying them for their work.

Happily the Bible, which cost $83.37 after tax and shipping, eventually arrived. I eagerly tore open the packaging, held the bag upside down, and out plopped what is essentially a Christian nationalist’s fantasy: a Bible that is all American flags and bald eagles, with founding documents and lyrics to a patriotic anthem slotted in alongside the holy text.

The front of the Bible has an embossed USA flag. In the back are glossy pages bearing some of America’s most sacred documents: the Declaration of Independence; the Pledge of Allegiance; and the lyrics to Lee Greenwood’s God Bless the USA, a song which is played on repeat at Trump’s political rallies.

These pages are illustrated with the American flag and some of the country’s best-regarded things: the bald eagle, yes, but also the Statue of Liberty, what appears to be a musket, and the Capitol building, which somewhat ironically was attacked by supporters of Trump three years ago.

One of the more intriguing questions in the FAQ section of the Trump bible website asks: “What if my Bible has sticky pages?”

My Bible did indeed have sticky pages. But no bother: the FAQ guidance explains that sticky pages are a common problem with new bibles, and directs the reader to “a YouTube video that does a wonderful job of explaining how to break your new Bible in”.

That video is six minutes long. It shows a man unboxing what is objectively a better-looking Bible than the God Bless the USA version, then flipping through the entire book, page by page. “Separating the pages is a somewhat tedious process,” the man says.

He was right. The Trump Bible, which uses public domain text from the King James version, has 1,350 thin-to-the-point-of-translucent pages, and I wasn’t about to go through the entire thing. But all the good stuff appears to be in here: there’s Noah desperately bundling animals onto a big boat, Job having his life ruined because of what amounts to a wager between god and the devil, and the book of Leviticus – much of which is given over to the correct way to sacrifice animals. (For a bullock, sprinkle its blood round the altar and wash its innards before setting it on fire; if you’re offering up a pigeon, be sure to wring off its head before plucking.)

You don’t have to pay $59.99 for that kind of content. Search “free Bible” online and there are hundreds of places that are literally giving it away. But this Trump-endorsed Bible represents something special to his supporters, said Kristin Du Mez, a professor at Calvin University whose research focuses on the intersection of gender, religion and politics.

“My sense is, most people aren’t buying this Bible to read it,” Du Mez said. “They’re buying the Bible to have it, and to participate in this kind of shared identity. To put $60 down to say: ‘Yes, this is my guy and and I’m committed to this, and this is my faith.’”

The shared identity is one of embracing the “myth of Christian America”, Du Mez said: “The idea that America was founded as a distinctly Christian nation: a proto conservative, white evangelical version of the country, which never really existed. It’s that shared vision of a mythical past, and commitment to restoring some semblance of that kind of mythical order in the present.”

After those early fumbles as he attempted to appeal to Christians, Trump was ultimately embraced by the evangelicals who make up much of the GOP – the same GOP taking a hatchet to church-state separation. In fact, the former president’s relationship with the religious right has now deepened to the extent that Trump is comfortable with comparing himself to their messiah.

Further cementing that bond goes some way towards explaining Trump’s decision to promote the God Bless the USA bible. But there’s also the financial aspect.

Trump owes more than $500m as a result of civil court convictions. He has been charged with more than 90 felony crimes, in five different jurisdictions, and lawyers cost money (unless you don’t pay them).

While the God Bless the USA Bible website says that the Bible is “not owned, managed or controlled by Donald J Trump”, it adds that the venture “uses Donald J Trump’s name, likeness and image under paid license from CIC Ventures LLC”.

Trump, according to a financial disclosure report filed last year, is the manager, president, secretary and treasurer of CIC Ventures LLC.

Happy days for Trump then. Although this Bible wheeze has not gone down well with everyone.

“Blasphemous” and “disgusting”, was the verdict of pastor Loran Livingston, a conservative evangelical who leads the Central church in North Carolina. A pastor in South Carolina said the Bible was a “commandment violation”, while Raphael Warnock, the Democratic Georgia senator and a pastor himself, also wasn’t happy.

“The Bible does not need Donald Trump’s endorsement,” Warnock told CNN.

“And Jesus in the very last week of his life chased the money changers out of the temple, those who would take sacred things and use them as cheap relics to be sold in the marketplace.”

It is unclear how many of these “cheap relics” have been sold. As of early May, God Bless the USA Bibles were still available for sale online – unlike the Trump-licensed sneakers that he was hawking earlier this year.

After the failure of Trump Steaks, Trump Vodka, Trump Mortgage, Trump Magazine, various Trump casinos and the Trump board game, perhaps the former president has finally given his name to a winning product. At $59.99 a pop for what is, objectively, quite a poorly printed, rather sticky book, the God Bless the USA Bible looks like a fairly safe bet. Maybe those lawyers will get paid after all.