Marriage killers you won't see coming: TRACEY COX reveals the 5 factors that can unexpectedly derail even the strongest couples - and how to protect your relationship
TRACEY COX: We all know the classic relationship destroyers: affairs, money problems, growing apart. But there's a sneakier category of marriage-enders that nobody warns you about.
Brit, 24, is 'instantly paralysed' after breaking his neck in belly flop into Turkish hotel pool as 'wrong insurance' leaves him with £50k bill
A young British holidaymaker has been 'instantly paralysed' after breaking his neck while 'belly flopping' in the pool while on holiday with his girlfriend.
CHARLOTTE GRIFFITHS: Did 'paranoia' over secrecy cause Harry and Meghan's Diana dinner to be cancelled?
There is a big mystery in royal circles after a highly anticipated fundraising dinner for the Diana Award was suddenly cancelled.
REBECCA ENGLISH: Following in his dad's footsteps, a calm Prince George starts at Eton
He walked in both as a king-in-waiting and a nervous teenager about to embark on a thrilling new chapter of his life.
Common stomach bug linked to unwashed lettuce could be behind at least 1 in 5 bowel cancers, study suggests
A common bacteria found in the stomachs of millions of people in the UK could be to blame for the disturbing rise in bowel cancer cases, new research has suggested.
Unravelling the mystery of the Devil's Arrows: Study reveals how prehistoric builders hauled 25-tonne rocks 11 miles across Yorkshire to build the landmark 5,000 years ago
Each weighing around 25 tonnes and standing at almost 23ft (seven metres) tall, how the enormous stones got there has remained unclear - until now.
Former Essex Police officer who faces 'child sex offence' allegation is named
He has now been charged with 'arranging or facilitating the commission of a child sexual offence'
Stansted Airport provide UPDATE as disruption continues for second day
Stansted Airport has provided an update as passengers across the UK face a second day of disruption after an air traffic control issue.
Stansted Airport provide UPDATE as disruption continues for second day
Stansted Airport has provided an update as passengers across the UK face a second day of disruption after an air traffic control issue.
Alan Carr breaks down in tears after receiving Special Recognition gong as fans laud NTAs performance by pals Amanda Holden and Paloma Faith as 'the campest thing they've ever seen'
Alan Carr broke down in tears as he was awarded the Special Recognition gong at the National Television Awards on Tuesday.
OpenAI Says It Has Cracked One of Math's 'Millennium Problems'
An anonymous reader quotes a report from The New York Times: OpenAIsaid on Tuesday that its newest artificial intelligence technology had solved one of the "Millennium Problems," a collection of important unanswered math questions meant to push the world's leading mathematicians to new heights. The announcement is an another clear sign that A.I. is fundamentally changing the upper reaches of mathematics, which have long been viewed as a pinnacle of human achievement. The change has excited some mathematicians, while stirring concern among others.
Over the past year, A.I. systems successfully solved a wide range of problems that have bedeviled mathematicians for decades. But these problems were not as complex, nor as closely watched, as the one that OpenAI's technology has solved over the past several days. The Millennium Problems are among the most heavily researched in the field. "This is a spectacular culmination of the arc we have seen over the past twelve months," OpenAI researcher Sebastien Bubeck said of the company's new solution.
The company announced that one of its latest models, which has not yet been released to the public, needed just 88 hours to solve what mathematicians call "the Navier-Stokes existence and smoothness problem." This problem involves a series of equations that are often used to predict the weather. The equations describe the movement of water and other fluids. The Navier-Stokes problem, which has no clear practical value, asks whether these equations completely break down in certain situations. OpenAI's proof claims to have defined just such a situation.
This would imply, at least theoretically, that the laws of physics themselves would break down under certain conditions: that, for example, water could be made to spontaneously explode. But mathematicians and physicists do not believe that this mathematical breakdown could really lead to such an outcome in the physical world. The Navier-Stokes problem was one of seven "Millennium Problems" selected by the Clay Mathematics Institute in the year 2000 as a way of tracking the progress of mathematics in the new millennium. The institute, founded by an American businessman named Landon T. Clay, offered a million dollars for the first correct solution to each problem. Before OpenAI's announcement, only one of the problems had been solved. OpenAI says it managed to solve the Navier-Stokes problem by coordinating as many as 10,000 AI agents, an extremely expensive process that may have cost millions of dollars in computing power.
For those curious about the findings, the company has released a paper (PDF) and formal Lean proof.
Read more of this story at Slashdot.
The 'prime location' near the A12 in Colchester where enormous Lidl could be built
A large plot of land was purchased by the supermarket giant
I ordered a £3,000 wig but it's the wrong colour and slips. Why can't I get a full refund? SALLY SORTS IT
In August 2025, I commissioned a bespoke £3,077 wig from Raoul, a London wig maker. It required a deposit of £1,455.
Katie Price shocks with scary heavy makeup look as she turns heads on the NTA red carpet - as she covers her black eye from getting face filler and new breast implants just hours earlier
Katie Price shocked fans with a scary heavy makeup look as she turned heads on the NTA red carpet on Tuesday night.
The Voice UK plagued by toxic in-fighting, 'fix' accusations and a never-ending parade of coaches - as Tom Jones' sacking is another bum note for struggling show
It's the latest in a long line of scandals to befall the show, which launched in 2012 with an average viewership of over seven million, but this year had its lowest launch figure to date - just 1.9 million
Recap as Stansted Airport flights cancelled
Passengers at Stansted Airport face a second day of disruption today after an issue with air traffic control.
Recap as Stansted Airport flights cancelled
Passengers at Stansted Airport face a second day of disruption today after an issue with air traffic control.
Katie Price opts for tiny lace hot pants and displays the results of her recent surgeries while Amanda Holden wears a garish pink gown as they lead the worst dressed on the National Television Awards red carpet
The National Television Awards is typically a night for glamorous gowns and eye-catching dresses, but not every star hits the mark with their looks.
Another Microsoft team admits it’s struggling to handle flood of AI-generated code
Increase in vibe-coded browser extensions sees Edge team automate quality assessments
Gordon Ramsay shares pictures with wife Tana and son Jesse - in her Victoria Beckham dress - before they hit the NTA red carpet
Gordon Ramsay and his wife Tana put on a glamorous display as they got dolled up for the NTAs on Tuesday night.