The original version of this story appeared in Quanta Magazine. Calculus is a powerful mathematical tool. But for hundreds of years after its invention in the 17th century, it stood on a shaky foundation. Its core concepts were rooted in intuition and informal arguments, rather than precise, formal definitions. Two schools of thought emerged in…
Reuters People have gathered at a stadium in Beirut for a commemoration of Hezbollah leaders Hassan Nasrallah and Hashem Safieddine Large crowds have gathered for the funeral of Hezbollah’s former leader Hassan Nasrallah, who was killed in an Israeli air strike in Beirut in September. Mourners dressed in black flocked to a stadium on the…
Pope Francis has asked Catholics to pray for him, as he continues to receive treatment in hospital for double pneumonia. The pontiff was unable to deliver the traditional Angelus prayer in person for the second Sunday running. But in a message written over the last few days, he said he was “confidently continuing” his hospitalisation…
Keir Starmer is unlikely to set out a plan this week for when the UK will increase its defence spending to 2.5% of GDP, a cabinet minister has indicated. The education secretary, Bridget Phillipson, said the target was ambitious, despite Labour previously claiming it would set out a path to meeting the spending goal after…
As the first phase of the ceasefire between Israel and Hamas in Gaza is meant to be drawing to an end, it has once again been put in doubt. After the last six living Israel hostages due to be released in this phase were freed, more than 600 Palestinian prisoners were due to be released…
Dundee University’s world-leading forensic science research centre, which inspired the hit BBC drama Traces, is under threat of closure as the crisis-hit university attempts to plug a £30m budget deficit. It is feared all 24 jobs will be axed at the Leverhulme Research Centre for Forensic Science, the largest interdisciplinary team in the UK dedicated…
Russia launched a large-scale drone attack on Saturday night, causing civilian casualties across Ukraine, official have said. Yuriy Ignat, spokesman for Ukraine’s Air Force Command, said a “record” 267 Russian drones were launched in a single, coordinated attack. Among them, 138 were intercepted by air defence while 119 disappeared from radars after being jammed and…
The German parliament convenes for its last regular session before the general election. Michael Kappeler | Picture Alliance | Getty Images Germans headed to the polls on Sunday to vote in the 2025 federal election, which is all but guaranteed to result in a new chancellor taking over from Olaf Scholz to lead Europe’s largest…
An Egyptian NHS doctor who “glorified terrorist violence” by mocking Israeli civilians fleeing the Hamas attacks in October 2023 has won a legal challenge against deportation. In one of three social media posts hours after the attacks began, Dr Menatalla Elwan, 34, who worked at an NHS trust in Liverpool, reposted footage of music festivalgoers…
BBC Eye Investigations BBC World Service BBC Mumbai-based Aveo had been selling the addictive combination in West Africa Indian authorities have banned two highly-addictive opioids in response to a BBC investigation which found they were fuelling a public health crisis in parts of West Africa. In a letter seen by the BBC from India’s Drugs…
