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‘Ahead of his time’: AI helps unlock discoveries hidden in notebooks of man who transformed maths

Kurt Gödel left 1,009 pages of densely written text – much of it in an obsolete shorthand – which is now said to contain hundreds of proved theoremsThe Austrian logician Kurt Gödel was one of the most original thinkers of the 20th century. His two incompleteness theorems, published in 1931, transformed mathematics and paved the way for the digital age.After his seminal results of the 1930s, Gödel published only a few papers. His unpublished work, however, runs to tens of thousands of pages, and is of great interest to historians of science. Continue reading...

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SpaceX to use its giant 'chopsticks' to catch booster and spacecraft after latest space mission

SpaceX's latest flight planned for Friday will mark the first attempt to catch the Starship spacecraft at its South Texas launch site upon its return to Earth.

Trump insists ‘nobody’s been killed’ as he admits dragging out war for ‘investors’: report

President Donald Trump reiterated a sweeping claim about U.S. troops in the war he's waging while revealing who's really setting its pace.In a pair of interviews that aired Thursday, Trump told conservative radio host Hugh Hewitt that "nobody's been killed in the last five months" in the war against Iran. He then told sports commentator Stephen A. Smith that he's stretching out the conflict because Middle Eastern nations he described as "tremendous investors" in the United States asked him to do so, The Washington Post reported Friday."We haven't lost a soldier in five months, and we control the Gulf," Trump told Hewitt.Pentagon figures cited by the Post show 23 American service members have died in the Middle East during the war with Iran, with 11 deaths coming from enemy fire and the other 12 in nonhostile circumstances. In July, an enemy attack on an air base in Jordan killed three soldiers, while another died during a controlled drone detonation at a base in Iraq and a Navy captain was killed in an emergency landing in the Arabian Sea, the Post reported. Two airmen supporting the war died in October in incidents not involving combat, according to Pentagon figures reported by Air & Space Forces Magazine.The remarks aired a day after Trump attended a Veterans Day ceremony alongside Vice President JD Vance.In his conversation with Smith, Trump insisted he has the power to wrap up the war quickly but is holding back because neighboring countries prefer a slower approach. He said those nations "would rather have me do it the way I'm doing it now.""I could end it immediately, but at the request of the nations that I'm looking to protect, we are doing it a little bit longer way," Trump said. "All of them would much prefer the waiting period...So, they've asked me to do that...I'm not sure I agree with it."

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Espionage arrests up while threats become increasingly complex

The FBI's counterintelligence operation has increased arrests for spying 53% over the past 21 months as espionage threats intensify from China, Russia and Iran pursuing American military secrets, advanced technology and intelligence about U.S. government operations.

Dutch prime minister holds hours of crisis talks as coalition acrimony erupts over tax package

Dutch Prime Minister Rob Jetten is trying to prevent his coalition government from collapsing