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Like many of you I've hardly been able to think about anything else these past ten days apart from the war in Ukraine. So today's puzzles are a celebration of Lviv, Ukraine's western city, which played an important role in the history of 20th century mathematics. During the 1930s, a remarkable group of scholars came up with new ideas, methods and theorems that helped shape the subject for decades.The Lwów school of mathematics – at that time, the city was in Poland – was a closely-knit circle of Polish mathematicians, including Stefan Banach, Stanisław Ulam and Hugo Steinhaus, who made important contributions to areas including set-theory, topology and analysis .These friends had unconventional working habits. Much of their time was spent in cafés, in particular the Scottish Café, wh...

One of the standout scenes in HBO's "Winning Time," which aired its first episode Sunday, features a tense one-on-one pickup game between Lakers veteran guard Norm Nixon (played by his real-life son DeVaughn Nixon) and apparent superstar Magic Johnson (Quincy Isaiah).This is one time in the celebrated series about the Showtime Los Angeles Lakers where the onscreen friction wasn't acting.Nixon, 38, explains that he built up tension on the set to help the scene, even pulling an improvised showboat move that Isaiah wasn't expecting during the filming. "I wanted to create that fury and anger, that fight" between a veteran player and a rookie who is seemingly gunning for his job, Nixon says. "And that's exactly how it was read on the screen."Sky hooks, no-look passes: The casting magic of H...

When Ghislaine Maxwell was convicted last December of procuring minor teenagers for the disgraced financier Jeffrey Epstein to sexually abuse, their victims expressed joy and relief that long-delayed justice had finally been served.Less than one week later, however, a juror's comments revealed that he apparently did not disclose childhood sexual abuse during jury selection – sparking a chain of events that could now potentially undermine the trial's outcome.Following prosecution and defense requests to investigate the juror Scotty David's comments – and Maxwell's calls for a retrial – Judge Alison Nathan said that she will question him under oath on Tuesday.While David said he would invoke his fifth amendment right against self-incrimination, prosecutors are seeking immunity for him whi...

Rresearch shows that people in wealthier, high-consuming countries can help avert climate breakdown by making six relatively straightforward lifestyle changes, creating a society of “less stuff and more joy”.Experts say if enacted these “shifts” would account for a quarter of the required emissions reductions needed to keep the global heating down to 1.5C and increase pressure on government and the private sector to make the necessary far-reaching systemic change.Founder of the Jump campaign Tom Bailey. Photograph: Andy Hall/The ObserverThe research has inspired the Jump campaign, urging people to sign up to make the changes. Tom Bailey, one of its co-founders, said if pledging to make all six shifts is too daunting, just making a start on some of them can make a difference.end clutter...

The Galaxy S22+ is Samsung's big-screen premium phone for 2022, offering top specs and good quality hardware, but little in the way of novel or exciting features. It's a safe, solid device.With an RRP of £949 ($999/A$1,549) that doesn't mean low cost, but it is £200 cheaper than the all-singing, all-dancing £1,149 S22 Ultra superphone with its Galaxy Note-like design. Shop around, though, and you should soon be able to find it for less.The back of the phone is smooth, frosted glass with colour-matched aluminum sides and camera housing, here shown in 'pink gold' colour. Photograph: Samuel Gibbs/The GuardianThe S22+ is similar to last year's S21+ with a flat glass front and back and solid-feeling aluminum sides. It looks and feels refined rather than flashy, and while it has a big 6.6i...

People in well-off countries can help avert climate breakdown by making six relatively straightforward lifestyle changes, according to research from three leading institutions.The study found that sticking to six specific commitments – from flying no more than once every three years to only buying three new items of clothing a year – could rein in the runaway consumption that is partially driving the climate crisis.The research carried out by academics at Leeds University and analyzed by experts at the global engineering firm Arup and the C40 group of world cities, found that making the six commitments could account for a quarter of the emissions reductions required to keep the global heating down to 1.5C.The study was published on Monday alongside the launch of a new climate movement t...

Use your fridge and freezerAbout £2.1bn-worth of fresh fruit and vegetables is thrown away in UK homes each year because it has gone soft, moldy or is out of date.How fresh produce is stored is key to its fate, and if you stow it in your fridge you will buy yourself more time. Apples, for example, can last for more than 100 days, much longer than in a fruit bowl.“In my house the only things that are in the fruit bowl are bananas,” says Helen White, a special adviser for household food waste at the sustainability charity Wrap.But before you start rejigging your fridge, check how cold it is. The average UK fridge is running at 6.6C when it should be below 5C. If you don't know how to adjust the temperature, the Love Food Hate Waste website has a guide. It also has a handy AZ of food s...

The ukrainian war is causing a mass exodus of citizens fleeing Russian attacks. Since the beginning of the invasion on February 24, 1.7 million people have fled the country, according to the latest balance of the United Nations Refugee Agency (UNHCR). This figure is increasing every hour as the Kremlin steps up the offensive. More than half of the refugees have gone to Poland and some thousands have already arrived in third countries, such as the Czech Republic, where there is a significant Ukrainian community, according to UNHCR chief Filippo Grandi. ...