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Amazon is planning to cut as many as 30,000 corporate jobs beginning Tuesday, as the company works to pare expenses and compensate for overhiring during the peak demand of the pandemic, Reuters reported Monday, citing sources familiar with the matter. From the report: The figure represents a small percentage of Amazon's 1.55 million total employees, but nearly 10% of the company's roughly 350,000 corporate employees. This would represent the largest job cut at Amazon since around 27,000 jobs were eliminated starting in late 2022.

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Mathematicians have identified the first shape that cannot pass through itself. Jakob Steininger and Sergey Yurkevich described the Noperthedron in a paper posted online in August. The shape has 90 vertices and 152 faces. The discovery resolves a question that began in the late 1600s when Prince Rupert of the Rhine won a bet by proving one cube could slide through a tunnel bored through another. Mathematician John Wallis confirmed this mathematically in 1693. The property became known as the Rupert property. In 1968, Christoph Scriba proved the tetrahedron and octahedron also possess this quality. Over the past decade, researchers found Rupert tunnels through many symmetric polyhedra, including the dodecahedron and icosahedron. Mathematicians had conjectured every convex polyhedron would have the Rupert property. Steininger and Yurkevich divided the space of possible orientations into approximately 18 million blocks and tested each. None produced a passage. The Noperthedron consists of 150 triangles and two regular 15-sided polygons.

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Apple is moving ahead with plans to bring advertising to its Maps app. Starting next year, businesses will be able to pay for more prominent placement within search results, according to Bloomberg [non-paywalled source]. The approach mirrors Search Ads in the App Store, where developers purchase promoted slots based on user queries. Apple has said the sponsored results will remain relevant to searches.

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Finland's fertility rate has dropped below 1.3 children per woman, the lowest among Nordic countries and far beneath the 2.1 replacement level needed to maintain a steady population. The rate has declined by a third since 2010. Kela, Finland's social insurance agency, started distributing 2025 "baby boxes" -- filled with clothing and other infant supplies -- in August instead of spring because so many 2024 boxes remained unclaimed. More parents now choose cash payments over the traditional boxes filled with infant supplies. The decline puzzles researchers because Finland offers paid parental leave for both mothers and fathers, subsidized childcare and national healthcare. Anneli Miettinen, Kela's research manager, said that good family policies no longer explain birth rates in Nordic countries. Immigration has offset some population loss, but officials worry about workforce shrinkage and pension system strain. Anna Rotkirch, who authored a government-commissioned report, found that many 17-year-olds describe wanting a house, garden, spouse and three children. Her research suggests young people struggle to form relationships, focus on education and careers, and delay childbearing. Some researchers attribute relationship difficulties to technology reducing physical interactions.

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