Leaked footage shows astonishing first look INSIDE Taylor Swift and Travis Kelce's wedding: See the bride's aisle, altar and couple's personal touches as A-listers vanish through MSG castle's'magic doors' Taylor Swift's '40-page prenup': How $2BILLION in assets divide up... and the one major concession Travis is predicted to have written in as special clause America's most expensive home gets jaw-dropping $63MILLION price cut... but it will still cost you $125m Huge crowds gather in Tehran for funeral of slain Iranian supreme leader Ali Khamenei as millions call for'revenge' against the US Sorry, but Taylor Swift's wedding was a tacky, childish, narcissistic spectacle of utter trash... now we all know what comes next: MAUREEN CALLAHAN Ryan Reynolds shuns Taylor Swift wedding controversy as he shares support for Canada - amid wife Blake Lively's FURY over snub from former pal's nuptials to Travis Kelce Lena Dunham leaves Taylor Swift wedding guests GASPING with shockingly rude dinner ...

The US government wants to get hold of a quantum computer good enough to contribute to scientific breakthroughs in just two years. It will use it to try to accelerate the research and development of new materials, pharmaceuticals and molecules useful in agriculture and manufacturing. Once a dream of theoretical physicists, quantum computers are now undoubtedly real, but have yet to prove unambiguously useful or to have broad commercial value. Their computational power depends on their size - how many components called qubits they comprise - and how reliable they are. Existing devices are still too small and too error-prone.

Science A.I.'s First Big Math Breakthrough Is Not What It Seems But it can help us do genuinely creative work--for a reason you might not expect. Sign up for the Slatest to get the most insightful analysis, criticism, and advice out there, delivered to your inbox daily. Last month, OpenAI announced that its latest version of ChatGPT had solved a major math problem, one that had stumped experts for 80 years. This was considered among the most important unsolved problems in combinatorics, a prominent branch of math and computer science dealing with finite objects and arrangements. As opposed to previous A.I.-powered breakthroughs that involved back-and-forth conversations between a chatbot and a human expert, this was cracked with a single prompt.

Last week, OpenAI shocked the mathematical community by revealing that one of its internal artificial intelligence (AI) models had found a counterexample to a famous conjecture made by legendary Hungarian mathematician Paul Erdős in 1946. The planar unit distance problem, or Erdős problem 90, has intrigued mathematicians for decades. The new result is no mere curiosity. Canadian mathematician Daniel Litt described it as "the first result produced autonomously by an AI that I find interesting in itself". The breakthrough, produced with a general-purpose AI model rather than one specialised for mathematics, also highlights how AI is changing mathematical research itself.

The tech giant says a breakthrough in data-center networking has dramatically accelerated the flow of information through its massive cloud infrastructure. Amazon says it recently achieved a major breakthrough in networking design--and has been quietly deploying the new technology in its data centers since late last year. The company claims it has significantly increased data speeds while reducing energy use, potentially giving the tech giant an edge as companies race to build ever-faster systems in the cloud. The new technology hinges on a "quasi-random" design that combines elements of traditional, structured data networks with the performance advantages of more random architectures. Researchers have explored random networks for decades, but the technology has never been successfully scaled.

Plus: The Pope has called for governments to regulate AI. Despite the growing hysteria over AI's threat to white-collar jobs, there's still scant evidence that the technology has had a large-scale impact on the labor market. Analysis of US labor data shows that unemployment in occupations most exposed to AI is actually lower than in less-exposed jobs. There are also no signs that large numbers of workers are shifting from AI-threatened professions into supposedly safer manual-labor jobs. It's true that things aren't great in the job market--but the question is why. Here's what the data really says about AI and jobs .

Mathematicians stunned by AI's biggest breakthrough in mathematics yet An 80-year-old maths conjecture that has eluded the world's greatest mathematicians has been cracked by an artificial intelligence model built by OpenAI. The result has stunned experts and is being hailed as a seismic moment for AI's mathematical ability. "This is a problem that I didn't expect to see solved in my lifetime," says Misha Rudnev at the University of Bristol, UK. "It's absolutely a bomb." Tim Gowers at the University of Cambridge wrote that the solution is "a milestone in AI mathematics" in a blog post accompanying the work . "If a human had written the paper and submitted it to the and I had been asked for a quick opinion, I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that."

The Download: online safety's future and climate tech's big pivot Plus: SpaceX has filed for an IPO expected to be the largest ever. For months, the Trump administration has been going after researchers who study and try to counter hate speech, harassment, propaganda, and disinformation online. Now, some of those researchers are fighting back. In a new lawsuit, they're seeking to strike down a visa restriction policy against "foreign officials and other persons" announced last year by US Secretary of State Marco Rubio. They say the policy violates the speech and due process rights of foreign-born workers whose "work supports greater moderation of content on the [tech] platforms. Find out how the case could impact online safety and free speech .

OpenAI's Sam Altman, left, is a backer of Rain Neuromophics, one of the companies that received funds from the UK's Aria, the brainchild of Dominic Cummings, right OpenAI's Sam Altman, left, is a backer of Rain Neuromophics, one of the companies that received funds from the UK's Aria, the brainchild of Dominic Cummings, right Exclusive: Brainchild of Dominic Cummings, Aria is aimed at funding'crazy' scientific projects to benefit the UK Britain's "invention agency" has pledged £50m of UK taxpayer money to US tech companies and venture capital projects. Dreamed up by Dominic Cummings to fund "crazy" ideas, the Advanced Research and Invention Agency (Aria) is meant to " restore Britain's place as a scientific superpower ". But a joint investigation by the Guardian and Democracy for Sale, an investigative website, has established that more than an eighth of the agency's £400m in research and development funding over the past two years has gone to 14 US tech companies and venture capital groups, in some cases, with no clear return for the UK or Aria. One of these companies, Rain Neuromorphics, is also backed by the OpenAI chief executive, Sam Altman, and was reported to be near collapse last year, shortly after winning Aria money. It did not respond to a request for comment; two of its founders appear to have left the company.

Ace can read the trajectory of a ball, adjust the racket angle, and respond with strokes that keep the exchange alive with real players. Ace has won three out of five games played under official rules. Ace is a robot that aims high: It wants to become the world champion of table tennis . It was developed by Sony AI researchers who, in a new study published in Nature, have shown how this robot, equipped with artificial intelligence, has faced some high-level athletes, holding its own in matches played according to the official rules of table tennis. This feat represents a milestone for the world of robotics, a field that has long regarded this sport, among the most technical in the world, as one of the most difficult tests of technological advances.