Although the puzzle we started with might seem silly, the study of these structures — known as Diophantine approximations — is taken seriously and gets complicated fast. For example, it’s possible to construct so-called Liouville numbers that have an infinite irrationality exponent (endless n-good approximations for any n), but it’s a lot harder to prove that there’s any commonly-encountered number with an irrationality exponent greater than two. In the same vein, algebraic irrationals (e.g., √2) all have an irrationality measure of two, but the proof of this is fiendishly difficult and netted its discoverer the Fields Medal back in 1958.
2026-03-03 00:00:00:0本报记者 李维俊3014314110http://paper.people.com.cn/rmrb/pc/content/202603/03/content_30143141.htmlhttp://paper.people.com.cn/rmrb/pad/content/202603/03/content_30143141.html11921 平陆运河，冲刺马年通航加油干（新春走基层）
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Poor software quality already costs the U.S. economy $2.41 trillion per year, according to a 2022 study by the Consortium for Information & Software Quality. That number was calculated before AI began writing a quarter or more of new code at leading companies. Chris Lattner, the creator of LLVM and Clang, put it bluntly: AI amplifies both good and bad structure. Bad code at AI speed becomes “incomprehensible nightmares.” As AI generates an increasing share of the world’s critical infrastructure (financial systems, medical devices, defense, transportation), unverified code becomes a systemic risk, not just a quality problem.
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