Features

Will the toughest problem in maths ever be solved?

For many, not just mathematicians, the Riemann hypothesis is the very definition of a supremely difficult problem that might be forever beyond our intellect. Most mathematicians had given up on it, being pessimistic about making any headway. But recently, the first progress – although not a solution – in more than 50 years has been made. The 165-year-old hypothesis was bequeathed to us by German mathematician Berhard Riemann. It deals with prime numbers – numbers that can only be divided by themselves and 1. For example, 2, 3, 5, 7, 13, 17, 19 and so on to infinity. Has our universe taken only one pathway out of a possible mathematical multiverse? They first appeared in 300 bc with Euclid. His work Elements is like reading poetry using numbers.

Are you a hotel buffet bandit?

Last week, on a Swedish train somewhere between Linkoping and Mjolby, as I struggled to open a bag of cheesy doofers that was to serve as my lunch, my travel companions began unwrapping their own picnics. Some, like me, had made hasty and unappetising purchases at the station. Others had carefully curated lunches, assembled earlier in the day from our hotel’s lavish breakfast buffet. Well-filled rolls, pieces of fruit, pastries. In they tucked. Germans may be on the march at dawn, annexing sun loungers, but it’s the Brits who secrete breakfast goods I was suddenly aware of a frisson of stance-taking rippling through our group. There were those who regarded buffet plundering as theft and those who defended it as plain common sense.

There’s still everything to play for in America’s election

The first presidential debate of 2024 changed history by killing off Joe Biden’s career. The second presidential debate was nowhere near as dramatic, for the simple reason that it did not feature the President. Instead, Kamala Harris, Biden’s Vice President and now the Democratic party’s nominee, stood on stage at the National Constitution Center in Pennsylvania on Tuesday night and presented herself as a sort of change candidate for continuity, or perhaps a continuity candidate for change. This audacious move ought to be highly implausible, yet so far she seems to have got away with it. Certainly, by any fair measure, she won the debate and was duly rewarded with an endorsement from Taylor Swift and her cat on Instagram.

Why are Chinese students giving up on architecture?

I recently convened an urban studies summer school in a top university in Shanghai and asked the assembled class of architectural master’s students: ‘Who wants to be an architect?’ Not one hand was raised. This was not the typical reticence of Chinese youngsters; this was a class of architectural students who have given up on architecture. They are all hoping to escape architectural education, so that they might progress to classes in AI, digital transformation or some other hi-tech sector where they believe jobs exist. For them, architecture is a dead end. As my Chinese students are discovering, there are too few jobs in the sector, the pay is low and the work is unappealing.

Xi speech warrior: Elon Musk’s love affair with China

Elon Musk revels in the role of ‘free speech absolutist’. Last week, for instance, he jumped to the defence of Pavel Durov, the head of the messaging and social media app Telegram, after he was arrested by the French police. But while Musk claims he is a defender of free speech, he frequently kowtows to the Chinese Communist party, for whom the concept is alien. Musk is now the CCP’s favourite western capitalist. So although he is eager to tell his 196 million Twitter followers that ‘Britain is turning into the Soviet Union’, he has avoided antagonising China. He has echoed CCP talking points on contentious issues, such as Taiwan and artificial intelligence, while remaining silent on China’s human-rights record.

Is it time to pity restaurant critics?

An atom is made of protons, electrons and neutrons, and protons are made of quarks, and a quark is the size of the violin you’d play for a restaurant critic who complains about their job. It’s the best job in the world: go out for dinner on expenses with a friend or a lover, then bash out a thousand words. Why, then, might we feel some pity for our restaurant critics? One reason could be that the Grim Reaper is hovering. Last week, the Evening Standard’s restaurant critic Jimi Famurewa announced that his column was being scrapped, as the paper moves to a weekly edition. Another reason, perhaps, is the lifestyle of a restaurant critic. Earlier this year, the New York Times’s Pete Wells left his column for health reasons: ‘I can’t hack the week-to-week reviewing life any more.

The expensive business of quoting poetry

Writers, I hope we can all agree, should be paid for their work. That’s the principle behind the law of copyright, and it has held for more than a century. We owe it to (among others) Charles Dickens and Frances Hodgson Burnett. But what about when their work is quoted by other writers?  You’re allowed to quote only a certain proportion of a work before you need to pay the rights holder This week I published a new book in which I spend a lot of time discussing the work of other writers. The Haunted Wood: A History of Childhood Reading is a canter through children’s literature from Aesop and Anonymous to J.K. Rowling and Julia Donaldson.

The deep sorrow of losing a sibling

My sister died last summer, before her time, at 58. Her death has left me shaken with sorrow and remorse: we did not always get on. The other day I accompanied her daughters and husband to scatter her ashes on the Thames at Greenwich in south London where she and I had grown up. The great muddy waterway would take Clare’s ashes out to sea eventually. People like Liz Truss live in Greenwich now, but in my time the inhabitants were Labour-voting bohemian types. Daniel Day-Lewis (a brattish schoolboy) lived down the road from us on Crooms Hill with his poet father Cecil. At Greenwich Theatre opposite, Max Wall performed his anarcho-comic piano sketches on Friday nights. Claire Tomalin was a near neighbour (as was, later, Jonathan Sumption).

Inside an MP’s inbox

There is nothing so ex as an ex-MP, Tam Dalyell used to say. Now that parliament has returned from recess, and the newly elected MPs are no longer described as ‘newly elected MPs’, it may seem that the old contrarian had a point. But the truth is that being an ex-MP’s staffer is as ex as it gets. I worked for Derek Thomas, the Tory MP for St Ives from 2015 until this year. The day after the election – our man lost to the Liberal Democrat, to make it even more humiliating; like being dumped for a librarian – the emails and the phone calls stopped. Even the woman who rang every day to tell us that the nurses on her ward were working for Isis (and she ought to know, she had been recruited by the CIA as an asset some years ago) had taken us off speed-dial.

Miliband’s empty energy promise

Though not quite up there with history’s great political texts, Ed Miliband’s letter this week to the director of the ESO, which runs Britain’s national grid, is a rather important document. It reveals – or confirms – that Labour has committed itself to decarbonising Britain’s electricity system by 2030 without really having any idea of how that can be done. Miliband described this letter as a ‘formal commission… to provide practical advice on achieving clean power’. That is all very well, except shouldn’t Miliband have sought this advice months ago, before pledging to achieve net zero on domestic energy by 2030? This week was supposed to be the big reveal: we would learn how this target – considered unreachable by many – is going to be hit.

How big business pushed up vet bills

I was on my way to a Pilates class when I spotted Paul waving at me urgently from across the road at the bus stop. ‘Can you help, Miss,’ he said. ‘It’s Gladys, she’s in a bad way.’ I looked down at his Staffordshire bull terrier and immediately saw what he meant. The 16-year-old dog was trembling, panting and appeared to be struggling to stand. She’d also lost a lot of weight. I’ve known Paul and Gladys for the past eight years, running into them on the street near my home in east London. Paul is not wealthy and has a couple of disabilities. He always calls me Miss. ‘She’s got bad in the past few days,’ he said. ‘She’s not eating, she just paces and can’t lie down. I took her to a vet yesterday. I think it’s time for her to go.

What will become of George Orwell’s archives?

The news that a vast cache of material by and concerning George Orwell is about to be cast to the four winds in the wake of a corporate sell-off has stirred predictable fury among Orwell buffs. As in all the best literary rows, the contending roles seemed to be clearly defined from the outset. There were the heroes (Orwell and his many acolytes); there was a principal villain – the publisher Hachette, which had decided to unload its archive, only to find that no single bidder could meet the asking price; there was the agent of their devilry (more about him in a moment); and even some subsidiary baddies, in the shape of a clutch of rare book dealers who are now hard at work flogging off the individual lots.

Save our steam engines!

Last week, if you’d known what to listen for, you might have heard a chorus of miniature whistles in gardens across the UK. Other sounds too: the whirr of pistons, the hissing of steam from valves. Up and down the nation, enthusiasts were fuelling up their model traction engines and steamrollers and raising steam not in celebration, but in mourning. It was a tiny mechanical wake for Mamod, the Birmingham firm which has made model steam engines since 1936, and which has announced that it is ceasing production. It’s estimated that more than 2.5 million engines have been sold by the company over the years. As commerce and government push our behaviours down digital channels, older hobbies don’t register When a beloved brand perishes, there’s rarely a single reason.

What China wants from Russia

On the face of it, the ‘no limits’ partnership between Russia and China declared weeks before Vladimir Putin invaded Ukraine in February 2022 appears to be going from strength to strength. Last week, Chinese Premier Li Qiang spent four days in Moscow and signed off on what Putin described as ‘large-scale joint plans and projects’ that would ‘continue for many years’. Russia’s trade with China has more than doubled to $240 billion since the invasion, buoying the Kremlin’s coffers with oil money and substituting goods sanctioned by the West. Moscow and Beijing have also stepped up joint military exercises.

The death of free speech in Britain

In Michel Houellebecq’s satirical novel Soumission, the French elite submits to Islamic rule rather than accept a National Front government. Nine years after its publication, submission seems more imminent on this side of the English Channel. My American friends are surprised to learn there’s no equivalent to the First Amendment in Britain. They have forgotten a free press was one of the things their ancestors rebelled to establish in the US. Free speech is a much more recent thing in the UK. If it was born in the 1960s, it seems to be dying in the 2020s. If free speech in the UK was born in the 1960s, it seems to be dying in the 2020s After the recent riots, people were given prison sentences for posting words and images on social media.

Is Germany’s far right about to go mainstream?

‘We need to deport, deport, deport!’ Björn Höcke, leader of the Alternative für Deutschland in Thuringia, emphasises each word with a clenched fist. It’s a hot Saturday evening in the small town of Arnstadt and Höcke is launching the AfD’s state election campaign. His branch of the party has been categorised as ‘indisputably far right’ not just by the press but by German domestic intelligence. Nonetheless, it’s leading in the polls ahead of three east German state elections, two of which take place on Sunday. Höcke could well end up ‘Minister President’ of Thuringia.

An American’s love letter to Britain

My wife and I relocated to the UK a few months ago after spending the past 37 years in the United States, and I cannot stop comparing the two countries. I oscillate wildly between my irrational exuberance at America’s superior market efficiencies and my sheer amazement at how orderly and polite you all are. These reactions surprise me, as I am hardly new to these shores. I attended graduate school at Oxford, worked for a while in London, married a beautiful and talented Essex girl (TOWIE indeed), and have consulted for the UK government in Northern Ireland for the past eight years. But now I actually live here, there are so many things that I am seeing with new eyes and deeply appreciate about the UK. Let’s start with the major ones. No guns.

Is the CCRC fit to decide on Lucy Letby’s appeal?

Whatever happened to the likes of the BBC’s Rough Justice and Channel 4’s Trial and Error? Why did human rights organisations such as Liberty and Justice stop campaigning on behalf of UK prisoners wrongfully jailed? Why are there fewer MPs plugging away on behalf of constituents they believe to have been victims of miscarriages of justice? All this activity seemed to be wound down after the Criminal Cases Review Commission (CCRC) began its work in 1997. Outsiders were no longer needed to look into the criminal justice system, many believed, now that we had a one-stop shop for prisoners protesting against their convictions for crimes they insist they did not commit.