As the billionaire retires, he leaves memorable advice from his annual letters that include pithy takes on bubbles, discipline and long-term goals

Warren Buffett, the billionaire investor who is retiring at the end of 2025, has entertained and educated shareholders in his Berkshire Hathaway conglomerate for many years with his pithy annual letters outlining the firm’s performance.

Every year since 1965 he has updated his investors on the journey as Berkshire morphed from a “struggling northern textile business” with $25m of shareholder equity when he took over, to an empire worth more than $1tn.

Though the price I paid for Berkshire looked cheap, its business – a large northern textile operation – was headed for extinction.

My error caused Berkshire shareholders to give far more than they received (a practice that – despite the biblical endorsement – is far from blessed when you are buying businesses).

Woody Allen once explained why eclecticism works: ‘The real advantage of being bisexual is that it doubles your chances for a date on Saturday night.’

When such a CEO is encouraged by his advisers to make deals, he responds much as would a teenage boy who is encouraged by his father to have a normal sex life. It’s not a push he needs.

Andrew destroyed a few small insurers. Beyond that, it awakened some larger companies to the fact that their reinsurance protection against catastrophes was far from adequate. (It’s only when the tide goes out that you learn who’s been swimming naked.)

In our view, however, derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal.

Participants seeking to dodge troubles face the same problem as someone seeking to avoid venereal disease: it’s not just whom you sleep with, but also whom they are sleeping with.

From this irritating reality comes the first law of corporate survival for ambitious CEOs who pile on leverage and run large and unfathomable derivatives books: modest incompetence simply won’t do; it’s mind-boggling screw-ups that are required.

When downpours of that sort occur, it’s imperative that we rush outdoors carrying washtubs, not teaspoons. And that we will do.

Naturally, I was delighted to attend Mrs B’s birthday party. After all, she’s promised to attend my 100th.

She sold me our interest when she was 89 and worked until she was 103. (After retiring, she died the next year, a sequence I point out to any other Berkshire manager who even thinks of retiring.)

The candidates are young to middle-aged, well-to-do to rich, and all wish to work for Berkshire for reasons that go beyond compensation.

(I’ve reluctantly discarded the notion of my continuing to manage the portfolio after my death – abandoning my hope to give new meaning to the term ‘thinking outside the box’.)

From long exposures of motor racing to remote-operated cameras at football matches, here’s how our favourite sports images were made

• Tom Jenkins’s best sport photographs of 2025

• How one of the best tennis photos was taken

We’ve received more than 500,000 sports photographs in the past year, with some absolute belters among them. Here are some of the fleeting moments, wild celebrations and creative compositions that caught our eyes – accompanied by explanations and technical info from the photographers themselves.

Chloe Kelly celebrates by Florencia Tan Jun (1/200th sec, f/2.8, ISO 2500)

Either say you can’t make it well in advance or keep stumm

As New Year’s Eve looms, I implore you to heed this party etiquette advice. There are only two correct times to decline a party invitation: well in advance or not at all. The last thing any stressed-out host wants to receive, in the moments before their big event begins, is a sudden flood of 11th-hour RSVPs from guests announcing that they’re not coming. And yet, as anyone who regularly organises large parties in Britain knows, that’s exactly what they tend to be sent. It needs to stop.

Having an invitation turned down in advance stings a little, but it is genuinely helpful. It provides a sense of potential turnout to help gauge catering and expectations. A decline on the day, however, is infuriatingly useless. Food and booze will already long since have been ordered, and it’s way too late to invite another friend to make up the numbers.

Phineas Harper is a writer and curator

The best and worst of 2025 – featuring devotion in DC, late-night tweeting and the fly that sank a birdie

The White House, issuing a communique to reporters covering April’s global market meltdown over tariffs as US losses hit $6.6tn (£4.9tn) in two days. “The President won his second round matchup of the Senior Club Championship today in Jupiter, FL, and advances to the Championship Round tomorrow.”

The Guardian’s sex advice columnist has answered countless questions over the last two decades. As the column ends, here’s what has struck and surprised her

People find it so hard to talk about sex, so if someone takes the time to sit down and write a question, then send it to the Guardian for me to answer, I always regard that as a great privilege. In the 20 years of writing the column, I have been reminded how many people are still out there, living their lives in quiet desperation about something that’s really troubling them sexually. Often the solution is more education; they just need to learn something, or be helped to be more open about a problem.

So many people grow up without the message that sex is healthy and important for a person’s quality of life, and they feel guilty every time they have sex, or think a sexual thought. They haven’t been able to enjoy sexuality and discover who they really are. Sometimes, it’s not the sexuality that is causing someone’s problem, it’s societal notions – prioritising monogamy, for instance – that makes life difficult. One of the things I would have liked to have addressed more was sexuality when people have serious disabilities or illness. Many people think they can’t continue to be sexual beings, and often that idea is pushed by people around them – that, to me, is tragic.

Minutes of travel expenses of former Duke of York as UK trade envoy withheld from National Archives

• Blair pressured officials over case of UK soldiers accused of beating Iraqi man to death, files show

The Cabinet Office has been accused of covering up for the royal family after the release of documents including some relating to travel expenses for the former Duke of York as UK trade envoy were withheld at the last minute.

Files released to the National Archives include documents relating to the death of Diana, Princess of Wales, and a grovelling apology from John Major’s office after an official birthday telegram to the Queen Mother was addressed in an “improper manner”.

From a jewel heist to crumbling galleries, it’s been a dire year for the world’s most visited museum. At least France has woken up to its predicament

Long before Versailles dazzled the world, the Louvre rose from the banks of the Seine as a royal residence. Charles V kept his celebrated library here; Henri IV installed his cabinets of paintings, objets d’art and arms, and created within its walls a veritable city of artists, where cabinetmakers, tapestry-makers, painters and armourers lived and worked. Under Louis XIII, coins, medals and the Louvre’s printing press were added; under Louis XIV came casts, antiquities and the academies of architecture, the arts and the sciences.

The Enlightenment demanded that the masterpieces of the art world be made public; the revolution answered. On 8 November 1793, ordinary citizens were admitted to the Louvre’s Salon Carré and Grande Galerie for the first time, transforming a royal palace into a national art museum. Continually evolving through redesign, reconstruction and reinvention, it has survived revolutions, arson and Nazi occupation. Within its labyrinthine galleries, audacious thefts have unfolded in broad daylight, while secret acts of bravery left barely a trace in history. The Louvre is a place of enduring mystery and fantasy, belonging to both France’s collective memory and the world’s imagination. This year, however, a succession of thefts, leaks and infrastructure failures has forced the French to look again at what the Louvre has become – and what it risks losing.

Agnès Poirier is a political commentator, writer and critic for the British, American and European press

Exclusive: Scientists uncovered biological strands using artificial intelligence and hope discovery will revolutionise treatment

Scientists have discovered two new subtypes of multiple sclerosis with the aid of artificial intelligence, paving the way for personalised treatments and better outcomes for patients.

Millions of people have the disease globally – but treatments are mostly selected on the basis of symptoms, and may not be effective because they don’t target the underlying biology of the patient.

When BT earmarked the kiosk for closure in January, Derek Harris began to campaign. The fight gave him purpose at a difficult time in his life

• ‘I don’t want it to die’: one man’s battle to save the last phone box in his village

The caller display flashes up: “Derek in the K6” it reads. On the line is Derek Harris, ringing from the red phone box he saved for his village. When he saw, on the agenda for the parish council meeting, that BT had earmarked it for closure, Harris knew he had to fight it. “It’s fighting for what is valuable, cherished,” he told me when I went to meet him in February, sitting over coffee in a cafe near Sharrington, the Norfolk village that has been his home for more than 50 years, and the phone box for longer. It’s a K6, for Kiosk No 6, designed in 1935 by Sir Giles Gilbert Scott.

For a few weeks, Harris, then 89, became a media star. One of the criteria for keeping a phone box in use is that at least 52 calls have to be made from it in a year (fewer than 10 had been made in 2024). As the campaign picked up speed, one day a queue of people made more than 230 calls from the K6. Harris sparked a national conversation about the continuing need for kiosks in an age of mobiles. Behind the scenes, he was a tenacious activist, sending constant emails to his MP, councillors, and of course, BT. Some of them included photographs he had taken of BT vans whose engineers were working nearby, as proof the phone box could be easily maintained. In March, BT decided to reverse its decision.

US president says Chinese leader didn’t notify him of the large-scale military drills, which continued with live missile launches into the Taiwan Strait

• Taiwan-China tensions – explained in 30 seconds

Donald Trump has said he is not worried by China’s live-fire military drills surrounding Taiwan and that he has a great relationship with the Chinese leader Xi Jinping, who “hasn’t told me anything about it”.

The US president made the comments one day into the surprise attack simulation launched by the People’s Liberation Army (PLA) on Monday, and which continued into Tuesday with live missile launches into the Taiwan Strait.

Coral Adventurer, separately being investigated for allegedly leaving behind passenger who died on Lizard Island, ordered not to leave PNG waters

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A cruise ship that ran aground off Papua New Guinea has been “detained” out of concern it’s unseaworthy “due to potential damage”, amid an investigation into how it became stuck on Saturday morning.

The Coral Adventurer remained stuck on a reef off the north coast of Papua New Guinea, about 30km from PNG’s second-largest city, Lae, on Tuesday, as efforts to refloat it continue.

Ukrainian president calls latest talks with Trump productive; Zelenskyy says attack on Putin’s residence is ‘lies’. What we know on day 1,406

Volodymyr Zelenskyy has said Ukraine cannot win its war against Russia without US support and accused Moscow of trying to sabotage peace talks after the Kremlin said it had foiled a Ukrainian drone attack on Vladimir Putin’s residence. Zelenskyy described the claim as “typical Russian lies” after his two-hour meeting on Sunday with Donald Trump in Florida, Luke Harding and Sammy Gecsoyler report. The Ukrainian president said Russia was “at it again” and using “dangerous statements” to undermine “diplomatic efforts” with the US to end the conflict. He added: “This alleged ‘residence strike’ story is a complete fabrication intended to justify additional attacks against Ukraine, including Kyiv, as well as Russia’s own refusal to take necessary steps to end the war.”

Zelenskyy later said his Sunday meeting with Trump was productive. “Can we win without American support? No,” Zelenskyy told Fox News, before laying out the difficulties that would be posed by a lack of US backing. He also said: “I don’t trust Putin and he doesn’t want success for Ukraine.”

Vladimir Putin has told his army to press on with a campaign to take full control of the Zaporizhzhia region in southern Ukraine after a Russian commander said Moscow’s forces were 15km (9.3 miles) from its biggest city. Col-Gen Mikhail Teplinsky told the Russian president at a televised meeting with top military officials at the Kremlin on Monday – a day after Putin spoke with Trump about Ukraine – that Russian forces were getting closer to the city of Zaporizhzhia. Moscow controls about 75% of Ukraine’s wider Zaporizhzhia province, one of four Putin annexed in 2022 in a move denounced by Kyiv and the west as illegal. Gen Valery Gerasimov, the chief of Russia’s general staff, earlier told Putin that Moscow’s forces were advancing along nearly the entire frontline, while Kyiv’s forces were focused on defence and attempting to counterattack. The battlefield reports could not be independently verified.

Russia’s foreign minister said the west must understand that Russia holds the strategic initiative in Ukraine as discussions move forward on a possible settlement. Sergei Lavrov told state news agency RIA that Kyiv and western countries had to come to terms with the fact that Russia held the initiative on the battlefield as the fourth anniversary of its 2022 invasion approaches. “Our principled position remains unchanged. The strategic initiative rests wholly with the Russian army and the west understands this.” Ukraine and the west, Lavrov said, had to take account of the realities on the ground.

Power line repairs near Ukraine’s Zaporizhzhia nuclear power plant have been successfully completed, the International Atomic Energy Agency cited its director general, Rafael Grossi, as saying on Monday. An IAEA team was monitoring repairs near the plant after a local ceasefire brokered by the agency began, with the work expected to last several days.

A historic theatre in the Russian-occupied Ukrainian city of Mariupol has opened its doors more than three years after it was destroyed in a Russian airstrike that killed hundreds of civilians sheltering inside. Moscow-installed authorities marked the rebuilding of the Donetsk Academic Regional Drama Theatre with a gala concert on the building’s new main stage Sunday night. The original theatre was destroyed when it was targeted by a Russian airstrike in 2022 as Moscow’s forces besieged the city. Mariupol’s Ukrainian city council, which left the city when it was occupied for Ukrainian-controlled territory, called the rebuilding and the opening of the theatre “singing and dancing on bones”.

Zia’s archrivalry with Sheikh Hasina defined the country’s politics for a generation

Former Bangladeshi prime minister Khaleda Zia, whose archrivalry with Sheikh Hasina defined the country’s politics for a generation, has died, her political party said on Tuesday. She was 80.

“The BNP chairperson and former prime minister, the national leader Begum Khaleda Zia, passed away today at 6am, just after the Fajr (dawn) prayer,” the Bangladesh Nationalist party (BNP) said in a statement.

Jewish safety after Bondi will only be found by tackling radicalisation across Australia head on

What would it take for me to feel safe wearing a kippah (a Jewish head covering) on a daily basis? This is a question I have been asking myself since 14 December. Which is not to suggest that I felt safe – or maybe comfortable is a better adjective – being Jewish in public before the Bondi massacre, but is to say that the question has suddenly become far more urgent.

I do not feel safe wearing a kippah because I fear that to many Australians this would be interpreted as a sign that I support Israel. I do not want people to make assumptions about my politics based on my appearance. And, more prosaically, in terms of my fear, I do not want to be shouted at when I’m going to the shops. I do not feel safe wearing a kippah because all of my life I’ve overheard non-Jewish people sharing antisemitic conspiracy theories. Greedy, cheap, power hungry, in control of the media. A host of conscious and unconscious biases inform how people react to Jews – to wear a kippah is to invite these reactions.

Two men killed in Hegseth-led attack on boat suspected of carrying drugs in international waters, Pentagon says

The US military announced the killing of another two men in “a lethal kinetic strike”on a boat suspected of carrying drugs in international waters in the eastern Pacific Ocean on Monday.

The Pentagon released video of the strike, which brings the total number of known naval attacks on suspected drug smugglers to 30 since September, and raises the death toll to at least 107 people, according to US military figures.

Australian federal police are reviewing security camera footage from the duo’s month-long trip to Davao in November

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The alleged Bondi attack shooters did not receive training or come into contact with a broader terror cell while visiting the Philippines, according to current assessments by federal police, with initial investigations indicating the father and son acted alone.

The police assessment came as the prime minister, Anthony Albanese, continued to reject calls for a federal royal commission into the Bondi massacre and antisemitism in Australia despite growing demands from families of the shooting victims, Jewish community leaders and the Coalition opposition.

• Littler’s missed doubles cheered in win over Rob Cross

• Champion denies being bothered in unconvincing style

They say you either die a hero, or live long enough to become the villain. At a feverish and hostile Alexandra Palace, the same crowd that cheered Luke Littler on as a 16-year-old boy now jeers him to victory as an 18-year-old man. The character arc has come full circle; the heel turn complete. He is three matches from retaining his world title, and remains the overwhelming favourite to do so. But from this point, he’s going to have to do it on his own.

As he finally skewered the winning dart to beat the spirited Rob Cross 4-2, he spun around to rebuke the audience that had done everything in its power to rattle him, from cheering his missed doubles to singing for Michael van Gerwen instead. “NOW WHAT?” he screamed at the sea of rented fancy dress, once and then twice. The heckling continued, surged even, and had still not abated by the time Littler gathered for his stage interview.

Former PM’s team suggested initial less-politicised drafts seemed patronising and appealed to ‘fuddy-duddy Britain’

• Brown’s allies could wreck Labour’s 2005 election hopes, Mandelson warned

Tony Blair’s key advisers agonised over the writing of his notoriously ill-judged speech to the Women’s Institute (WI) which saw the then prime minister heckled and slow hand-clapped before 10,000 members at Wembley Arena, newly released documents reveal.

Despite the WI explicitly warning they were “wary of anything that smacked of capital P politics”, Blair’s aides were critical of his first draft and bombarded him with additions to inject more policy.

Grammy-winning artist joins husband Jay-Z and artists like Taylor Swift following the success of Cowboy Carter tour

Beyoncé is now a billionaire, according to a report from Forbes – becoming the fifth musician to obtain the status.

The Grammy award-winning artist, 44, has joined the world’s wealthiest people following the success of her Cowboy Carter tour, which grossed more than $400m in ticket sales, and an additional $50m in merchandise sales. Her previous Renaissance world tour brought in about more than $579m.

Israeli prime minister said he will award Trump with Israel prize, highest civilian honor, while visiting Mar-a-Lago

Donald Trump has warned that Hamas will have “hell to pay” if it fails to disarm while offering full-throated support to Benjamin Netanyahu during a meeting with the Israeli prime minister in Florida.

In a bravura display of mutual admiration, Netanyahu announced that the US president would be awarded the Israel prize, the country’s highest civilian honour, which since its inception in the 1950s has never before been given to a non-Israeli person.

Some things just aren’t resolvable ...

• See more of Fiona Katauskas’s cartoons here

Trump also repeated false claims about renovation costs for the Fed headquarters during a Monday press conference

Donald Trump launched another attack against Federal Reserve chair Jerome Powell on Monday, calling the central banker a “fool” and once again suggesting he would like to fire him.

Trump launched his latest attack on Powell during a press conference with Israel’s prime minister Benjamin Netanyahu, repeating false claims about the cost of a renovation of the central bank headquarters, and told reporters that he might file a lawsuit against Powell for “gross incompetence”.

Meera Syal also made dame while England women’s football and rugby winners feature prominently

The actors Idris Elba and Meera Syal have been made a knight and a dame in the new year honours list, with top awards also going to the ice skaters Jayne Torvill and Christopher Dean.

The former head of NHS England, Amanda Pritchard, was also made a dame and there were knighthoods for Patrick McCabe, a former UN official responsible for clearing unexploded bombs in Gaza; Tristram Hunt, the former Labour MP and now director of the V&A, for services to museums; and Roy Clarke, creator of the sitcoms Last of the Summer Wine, Open All Hours and Keeping Up Appearances.

Kenneth Kirsch, 65, and Michael Greenberg, 71, died after the Sunday middair collision near Hammonton airport

Two men who died after their helicopters collided midair in New Jersey over the weekend both earned their private pilot licenses over a decade ago and would often have breakfast together at a cafe near the crash site before taking to the skies from the local airport.

Authorities on Monday identified the two New Jersey men as Kenneth Kirsch, 65, and Michael Greenberg, 71. Witnesses told police that the two helicopters they were piloting Sunday were flying close together just before they crashed in a farm field near the airport in Hammonton, about 35 miles (56km) south-east of Philadelphia.