Tens of thousands of handwritten pages by one of the 20th century's greatest mathematicians, Alexander Grothendieck, many of which the eccentric genius penned while living as a hermit...

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In my attempt to keep my hair healthy, I’ve tried all the gimmicks; I’ve chewed hundreds of gummy hair vitamins and done all the serums, but have zero recommendations for you. Through years of testing the product trends, I have found some effective hair treatments. For instance, I started using pre-shampoo oils to help with dry scalp and I put a Jolie filter on my shower head to soften my hard water and hair.

The Washington, DC region is bracing for disruption to the local economy when federal funding lapses at midnight

Max Verstappen faces a fight to take pole position at the Singapore Grand Prix after calling his Red Bull “unacceptable” in final practice. As Carlos Sainz raced to the top of the time charts at the Marina Bay Circuit, Verstappen finished fourth. The Dutchman is on an unprecedented 10-race winning streak with his Red Bull team unbeaten at the 14 rounds of the season so far. But Verstappen bemoaned the handling of his car in the city-state, describing the upshifts in his Red Bull machinery as “unacceptable”. He added: “These upshifts, what the f***. I am just struggling for rear grip. If I competed in drifting, I might win the race.” Verstappen returned to the track in the closing moments of the one-hour running, ringing the neck of his Red Bull to move from sixth to fourth, 0.313 sec slower than Sainz. But his struggles will give the chasing pack hope of finally stopping Verstappen and Red Bull with Ferrari holding the upper hand heading into qualifying later on Saturday. Sainz and team-mate Charles Leclerc traded top spot in the two practice sessions here on Friday, with the former again fastest in the concluding running before the fight for pole. Leclerc looked set to eclipse Sainz only to make a mistake in the second sector before backing out of his speediest lap, finishing fifth. George Russell took an encouraging second for Mercedes, just 0.069 sec slower than Sainz, with Lando Norris third in his McLaren. Lewis Hamilton was sixth for Mercedes, within half-a-second of Sainz. Verstappen’s team-mate Sergio Perez, who won here last year, finished eighth, 0.719 sec back. Qualifying for the 15th round of 22 takes place at 2100 local time (1400 BST). Read More Charity boss speaks out over ‘traumatic’ encounter with royal aide Ukraine war’s heaviest fight rages in east - follow live Max Verstappen struggles in Singapore practice under the lights On this day in 2021: George Russell joins Lewis Hamilton at Mercedes Ferrari’s Carlos Sainz gets goosebumps after landing pole for Italian Grand Prix

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The destruction of the Nova Khakhovka dam will likely turn Ukraine’s southern fields “into deserts” within the year – sparking a global food security crisis, top Ukrainian officials have warned. Ukraine’s emerency services are carrying out rescue operations across dozens towns and villages in the wake of the dam – which is under Russian occupation – unleashing the waters of one of Europe’s largest reservoirs across the war-torn south. The deluge has destroyed homes, drowned animals, severed clean water supplies and forced thousands of people to evacuate. The sudden emptying of the reservoir has crippled key irrigation systems in three surrounding regions. That has stopped the water supply to nearly 600,000 hectares of agricultural land, and endangered the production of 4 million tonnes of grain and oil crops, Ukraine's agricultural ministry wrote in a statement. “The fields in the south of Ukraine may turn into deserts as early as next year,” the ministry said, adding that the surrounding countryside and water supplies have also been destroyed and fish stock killed. “In total, according to preliminary calculations, the losses from the death of all biological resources will amount to [$285 million dollars],” it concluded. Mykhailo Podolyak, a chief advisor to President Zelenksy, warned this “global ecological disaster” could impact worldwide food supplies, as Ukraine, nicknamed the bread basket of the world, is a major producer of grains and oils. “The instantaneous death of a large number of fish and animals, the waterlogging of drained lands and the change in the climatic regime of the region will later be reflected in the food security of the world,” he told The Independent. Ukraine holds the western bank of the Dnipro River near the dam - where some 16,000 people were affected by the flood. Russia controls the eastern side, which is lower and more vulnerable to flooding and where some 22,000 people are impacted. About 3,000 people have already been evacuated from flooded areas on both sides of the river, officials said. The Ukrainian military has blamed Moscow for the attack, saying Russia wants to prevent an advance by Ukrainian forces. The Kremlin denies the accusations saying Kyiv is seeking to distract from a “failing” counteroffensive, that is ongoing. The Kakhovka hydroelectric dam and reservoir are essential for drinking water and irrigation for a huge area of southern Ukraine and the Crimean Peninsula, which has been occupied by Russia since 2014. It lies in a part of the Kherson region that has been controlled by Moscow's forces for the past year since President Vladimir Putin launched his invasion. On Wednesday the authorities and charities rushed to get drinking water and food supplies to the flooded areas and to help save those who are stranded. In the city, people used boats and rafts to try to find missing inhabitants, while others waded through knee-deep water clutching their belongings. “There were people standing on the street just in their underwear because the water had come in too fast and submerged their homes and belongings,” said Yuliya Konovalova, an aid worker who works for Ukrainian animal charity Hachiko. She had spent the day bringing hot meals and water to the inhabitants of Kherson, and rescuing and feeding stranded pets. "The water was rising so fast we hope those people manage to escape,” she added. She said in the centre of the city trains were leaving every two hours despite the flooding and the shelling to ferry people to the nearby city of Mykolaiv “It is a disaster, it is a catastrophe, it is difficult to understand how it is possible.” “It was a really painful day, on the way back I was crying,” she added breaking down in tears. Ukrainian President Volodymyr Zelensky said that Russian soldiers were shooting from a distance while rescue attempts were in progress. "As soon as our helpers try to save them, they are shot at," he told German newspapers Bild and Die Welt and also Politico. The country’s deputy prime minister, Oleksandr Kubrakov, also warned of drifting landmines unearthed by the flooding. "Water is disturbing mines that were laid earlier, causing them to explode," Mr Kubrakov said. “As a result of the flooding, infectious diseases and chemicals were getting into the water,” he added. Mr Zelensky said later said on Telegram he had spoken to French President Emmanuel Macron about the environmental and humanitarian situation in the Kherson region. "I laid out Ukraine's general needs in dealing with the disaster. And we discussed the possibility of involving international mechanisms to investigate its causes," the president said. Meanwhile, in his first public comments on the disaster, President Putin repeated Moscow's line that Ukraine is to blame for destroying the Kakhovka dam. In a call with Turkish President Recep Tayyip Erdogan, Mr Putin alleged that Kyiv authorities had escalated "war crimes, openly using terrorist methods and staging acts of sabotage on the Russian territory," the Kremlin said in its account of the call. Read More Ukraine-Russia war news – live: Exploding mines float through floodwater after Kherson dam attack ‘Hard to control emotions’ amid Kherson flooding, says Ukrainian aid worker A dam bursts, but this barbaric attack will not halt Kyiv’s ‘big push’ Ukraine’s long-term future to be on agenda at Sunak and Biden meeting The Body in the Woods | An Independent TV Original Documentary The harrowing discovery at centre of The Independent’s new documentary

It turns out the hack Reddit suffered back in February may have resulted in a