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Matt's mathematical mind mashMathematicsWin a million dollars with maths, No. 4: The Hodge ConjectureTo get a handle on the Hodge Conjecture – and claim your $1m – you could start by thinking about shapes drawn on doughnuts. But then things are likely to get a bit more complicated ...Mathematicians' compulsion to make things more and more complex is both a blessing and a curse. Their urge to take an idea and stretch it as far as possible can yield fascinating new insights.

Opioids'I could get 500 tablets a month': the ease of buying opiates onlineHelen, 26, ordered codeine from several pharmacies while addicted to the painkiller UK online pharmacies accused of ‘aggressive’ tactics to sell opiates Helen*, 26, used online pharmacies to buy codeine for about three years, although she no longer has a dependency. She began ordering the painkiller in 2016 after her partner killed himself. “Someone gave me codeine at work one day when I was unwell and I enjoyed the sensation of it – and then I went to France and at the time you could get strong painkillers over the counter.

TattoosWhether it is to commemorate a lost loved one, bask in their independence or mark a new stage of life, many people now get inked when they are older. Six tell their stories For many older people, tattoos came with baggage. Now, social mores have changed and for those in their 60s, 70s and 80s: “The stigma associated with prisoners’ tattoos, or sailors or misfits getting them, has disappeared,” says Louise Krystahl, a tattoo artist.

Mark Meadows This article is more than 4 months oldMark Meadows testifies in bid to move Georgia election case to federal courtThis article is more than 4 months oldTrump’s White House chief of staff argues he acted in capacity as federal officer and that case should be moved to federal court The sprawling 41-count indictment of Donald Trump and 18 other defendants in Fulton county had its first test on Monday as Mark Meadows, the former White House chief of staff, took the stand before a federal judge over his request to move his Georgia election interference case from state to federal court.

BusinessNY analyst sues over Borat filmBorat's efforts to glean cultural learnings from the US have upset a New York financial analyst, who is suing 20th Century Fox over a scene in which he was chased down the street by the spoof Kazakh journalist. Jeffrey Lemerond, a former healthcare analyst at the Carlyle Group , who now works for SAB, a hedge fund in New York, has filed a lawsuit claiming he suffered "

Peaky Blinders: episode by episodePeaky BlindersTommy Shelby is keeping busy with his own moonshine business and more dangerous liaisons with the other side, but will Polly betray him? When Peaky Blinders commits to overstuffing a plotline it does so wholeheartedly and with verve. This episode managed to cram a tense stand-off, a mafia shoot-out, a Communist meeting, at least two betrayals, a modest proposal graciously refused, a possible (probable) pregnancy, and any number of threats.

WomenThis ever-evolving crime rages almost unchecked. Three women talk about the devastating effect it had – and still has – on them Ruth King (not her real name) can still remember the call coming through on her mobile. She thinks of that moment as “the start of hell”. “It was four years ago, but I remember it clear as day,” she says. “It was my friend warning that there were videos of me everywhere.

Albania holidaysA new airport and new routes may take pressure off creaking buses – but at what cost to a valuable wetland for flamingos and other birds? Black smoke billows from the front of the bus. With no air-conditioning besides the sympathetic wafting of a folded map from another passenger, I’m five hours into a bus journey from Tirana to Sarandë. Has the engine exploded? I’m not too sure. But judging by the groans of the driver and other passengers, this is far from ideal.

A-League Women This article is more than 3 months old‘Full circle moment’: Matildas striker Kyah Simon returns to A-League WomenThis article is more than 3 months oldAustralian back at Central Coast Mariners where career startedVeteran forward offered first full-time 12-month contract in ALWMatildas’ striker Kyah Simon is returning to where it all started, 15 years after she began her professional career with the Central Coast Mariners. The deal that brought Simon home is the first full-time, 12-month contract in A-League Women history, which will see her continue to work for the club in an off-field role after the season concludes in April.