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Ex-presenter of BBC Radio 4 show complains in Guardian of ‘gratuitous gratitude’ and ‘gushing’ between host and guest

For more than three decades, John Humphrys delighted and infuriated listeners in equal measure as he confronted the nation’s politicians in his trademark, pointed style on the Today programme.

Now a listener himself, the former presenter of the BBC’s flagship radio news show is just as pointed in his assessment of the current incarnation of the programme. His verdict? It’s irritating.

То, что свет нельзя обогнать, сложение скоростей, замедление времени — всё это стоит на обычном школьном синусе, которому угол сделали мнимым. Не метафора и не «похоже» — буквально та же функция.Давайте убедимся в этом сами.

Это финал серии. В первой синус был показан тенью вращающейся стрелки, во второй — каталогом из сорока с лишним мест, где эта тень лежит. А в конце каталога была ремарка, что у синуса есть гиперболический двойник, за которым стоит ещё пол-математики.

В основе всей статьи один ход, которому двести с лишним лет: подставить в синус мнимый угол. Операция законна с тех пор, как Эйлер переписал синус через экспоненту: ряду всё равно, веществен ли аргумент. Этим ходом Лобачевский построил свою геометрию, а Минковский — пространство-время; пройдём его тем же ходом. Итак: что такое sin(iθ)?

Путь: ход Эйлера → корень всего → круг и гипербола → геометрия Лобачевского → эмбеддинги нейросетей → относительность → малые углы → чёрная дыра → бонус: слово «синус» → итог

Spain and France will meet Tuesday in Arlington, Texas, in a matchup anticipated for years. Neither team has lost at this year's World Cup.

(Image credit: Mark J. Terrill)

Dwayne Johnson and Catherine Laga’aia star in the latest Disney animation to get the live-action treatment, and the model-actor-singer proffers more of her signature lush soft rock

Moana
Out now
The 2016 Disney animation gets the “live action” treatment with a more-or-less remake starring Dwayne Johnson and newcomer Catherine Laga’aia, joined by, as you’d expect, animated versions of various critters, including Tamatoa the coconut crab (once more voiced by Jemaine Clement).

Trump made the comments on his Truth Social after U.S. officials demanded that Iran make a public statement saying the Strait of Hormuz is open.

(Image credit: Iranian Supreme Leader Office)

From the Battle of Santiago and The Miracle of Bern to Nasa and Woman in the Moon, test your knowledge with the Saturday quiz

1 Which 90s duo only released three singles, all chart toppers?
2 Betsy Ross is traditionally credited with designing and making what?
3 Based in Cambridge, which geographical research organisation is the BAS?
4 Which wetland sedge is important in the history of writing?
5 What did Nasa borrow from the 1929 Fritz Lang film Woman in the Moon?
6 What 1,000-year-old Sherwood Forest resident died in 2026?
7 Which country’s national museum burned down in 2018?
8 Which magazine was named after the sound of a “guitar being struck with force”?
What links:
9 E, H, I and S; June Brown; Kendrick Lamar, formerly?
10 White (bow); red (sword); black (pair of scales); pale (nothing)?
11 Robert Mitchum, 1962; Robert De Niro, 1991; Javier Bardem, 2026?
12 Hetty Feather; Tom Jones; Oedipus; Oliver Twist; Superman?
13 Cadbury Castle; Danebury; Maiden Castle; Vespasian’s Camp?
14 Abhakshya; haram; tabu; treif?
15 Maracanaço; Miracle of Bern; Battle of Santiago; Disgrace of Gijón?

Thinktank urges prospective prime minister to reclaim UK’s role as an international leader on development

Influential backbenchers are calling on Andy Burnham to reclaim Labour’s leadership on international development and chart a course back to spending 0.7% of national income on overseas aid.

In a collection of essays to be published soon by the New Economics Foundation (NEF) thinktank, MPs lay out proposals for a Burnham-led government to rethink foreign policy.

Child who ate smuggled-in homemade sandwich kicks off latest skirmish over private resorts

As lunchtime approaches at Il Tirreno, a private beach club in Montalto di Castro on the Lazio coast, Beatrice Bordo, sitting in the shade of a blue umbrella, unwraps a slice of pizza.

A pranzo al sacco, or packed lunch, has become the latest skirmish in Italy’s long-running beach disputes after a woman was confronted over the clandestine consumption of a homemade sandwich at a private establishment in Puglia.

Недавно я прошёл несколько технических собеседований, и меня удивил один момент. Для всех вакансий требуется навык работы с AI-инструментами. Но на самих собесах меня просили написать рабочий код в текстовом редакторе без подсветки синтаксиса и решать алгоритмические задачи.

Возник вопрос: почему так происходит и нормально ли это для 2026 года?

The country’s coastline is one of the shortest in Europe, but it packs a punch with unspoilt nature reserves, vibrant Venetian towns and a thriving foodie scene

I’m riding a salt-coloured horse through the Dragonja valley, deep in the green hills of Slovenian Istria. Electric-blue dragonflies zip over the river as we gallop past olive trees and vineyards. The landscape rises steeply in a series of grassy terraces, and at the top of the hill we rein in the sweating horses to take in the view. Far below, the huge grids of solinas (salt pans), glittery and light-blue in the early morning light, look strange and somehow elegant against the wild, expansive sea beyond.

The Istrian peninsula is the largest in the Adriatic Sea, with 90% of it in Croatia and smaller portions in Slovenia and Italy. I’ve come to explore the Slovenian section. At just 29 miles (47km), the country’s coastline is one of the shortest in Europe, from the Italian city of Trieste down to the Croatian border, but it boasts colourful seaside towns, hilltop villages and an emerging gastronomy scene.

Teachers call for schools to be urgently adapted for hot weather amid reports of nausea, fainting and heatstroke

The extreme heat that has hit the UK twice in the past few weeks has left teachers struggling to cope as temperatures in some classrooms climb above 40C, with pupils and staff suffering from heatstroke, nausea and headaches.

Teachers say they have been desperately trying to keep children safe, with some covering younger pupils in wet paper towels as they lie on the floor, while older students have been given trays of water under their desks to put their feet in.

Leapfrogging the roofs of lorries, slipping in and out of different personae to evade capture, The Queen’s Gambit star is audacious in this reluctant last stand drama

This is a story about a girl named Lucky. Early morning, she wakes up – knock, knock, knock, on the door. It’s the FBI, and they’re pursuing her across the country because she’s stolen $10m. Don’t make the mistake I did, imagining this new Apple TV thriller (from Wednesday), starring Anya Taylor-Joy, to be a dramatisation of the song Lucky by Britney Spears. I’ve tried to find a connection between the two and, as you can see, it’s a stretch.

The seven-part show falls into the “one last heist” genre – but intriguingly, starts the morning after it. Our antiheroine stands on the roof of a Las Vegas casino hotel, having successfully stolen millions, toasting to a new, legitimate life. Within hours, Lucky appears to have been betrayed by the man she loves. She’s forced to run, penniless, from both the authorities and the murderous enforcers of a crime boss – who are collecting on a different debt incurred by her career criminal father. I guess what happens in Vegas doesn’t stay there.

After years of one-sided commitment, revisiting her hit song Casual finally gave me a reality check

‘Sadie,” I say. “I would call our daughter Sadie. Or I like Leo for a boy.” I’ve been on the phone for two and a half hours, speaking about our hypothetical children to a man who has explicitly said that he does not want a relationship. At the same time, he’s said things like: “I told my mum about you. She wants to meet you.” When he makes those comments, I can’t help dreaming – in the words of a certain song – of us in a year: maybe we’ll have an apartment, and he’d show me off to his friends at the pier?

That’s the fantasy Chappell Roan imagines in her 2022 hit Casual. My own vision looks a little different: instead of a pier there is an apartment (where the now familiar sound of his key in the door still excites me), and his friends say things like: “I’ve never seen him act like this with anyone else before.” But crucially, in this fantasy, we’ve made a commitment to each other. The first time I heard Casual, I was in a committed relationship. I listened to it often, singing along loudly in the bedroom I shared with my boyfriend to “Knee deep in the passenger seat, and you’re eating me out”. (Roan was nervous about that line – “it’s crass,” she said – but fans loved it.) I also loved the song’s sense of unrequited yearning, but I couldn’t really relate to it. Not yet.

Reports of falling sperm counts and testosterone levels have fuelled fears over chemicals, pollution and modern lifestyles. But how much do scientists agree on what is affecting male fertility?

The world is unwittingly walking into a male reproductive crisis, scientists warned this week as they presented data that revealed an apparent halving of average male testosterone levels over the past 50 years.

“It is mind-blowing that testosterone has declined by 50%,” Prof Hagai Levine, who led the work, told the Guardian. “This is a lot. Wake up people. Wake up.”

Teachers call for schools to be urgently adapted for hot weather amid reports of nausea, fainting and heatstroke

The extreme heat that has hit the UK twice in the past few weeks has left teachers struggling to cope as temperatures in some classrooms climb above 40C, with pupils and staff suffering from heatstroke, nausea and headaches.

Teachers say they have been desperately trying to keep children safe, with some covering younger pupils in wet paper towels as they lie on the floor, while older students have been given trays of water under their desks to put their feet in.

Thinktank urges prospective prime minister to reclaim UK’s role as an international leader on development

Influential backbenchers are calling on Andy Burnham to reclaim Labour’s leadership on international development and chart a course back to spending 0.7% of national income on overseas aid.

In a collection of essays to be published soon by the New Economics Foundation (NEF) thinktank, MPs lay out proposals for a Burnham-led government to rethink foreign policy.

Devon and Cornwall police say 26-year-old man no longer part of investigation after former MP found dead at home in Haytor

A 26-year-old man who was arrested on suspicion of the murder of the former MP Ann Widdecombe has been released from custody and is no longer part of the investigation, Devon and Cornwall police said early on Saturday.

In a statement, assistant chief constable Matt Longman said: “Our priority remains identifying those responsible and ensuring that all available evidence is thoroughly examined.

The Trump administration finalized a rule Friday that changes how agencies enforce the Endangered Species Act. The administration narrowed the definition of "harm" under the landmark law.

(Image credit: Carolyn Kaster)

Devon and Cornwall police say 26-year-old man no longer part of investigation after former MP found dead at home in Haytor

A 26-year-old man who was arrested on suspicion of the murder of the former MP Ann Widdecombe has been released from custody and is no longer part of the investigation, Devon and Cornwall police said early on Saturday.

In a statement, assistant chief constable Matt Longman said: “Our priority remains identifying those responsible and ensuring that all available evidence is thoroughly examined.

Ahead of the census in August, campaign group suggests current poll design overstates the nation’s religiousness

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Australia would no longer be a majority religious country if the format of a question in the census was changed, according to a new survey.

The Essential Media poll tested the existing census format, where people choose from a list that includes the most common religions, “no religion” and “other”.