Word: proof
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Likewise, Caltech’s case falls far short of a “proof.” Caltech’s emphasis on science research means that its faculty members can rely on federal agencies and other grant-givers for funding—a luxury that many Harvard humanities professors don’t enjoy. Whereas Caltech derives more than 40 percent of its revenue from research grants and contracts, Harvard’s Faculty of Arts and Sciences derives just 17 percent of its income from those sources. In other words, Harvard must be more reliant on private...
...with a full-page illustration rendering a bespectacled, white-haired, Asian man tugging at a medal labeled “Fields” that dangles from the neck of a brown-bearded Caucasian. Below, the caption reads: “Grigory Perelman (right) says, ‘If the proof is correct, then no other recognition is need.’ Shing-Tung Yau isn’t so sure...
...Yorker article discusses the century-old Poincaré conjecture, which states that all closed three-dimensional abstract topological spaces with no holes are spheres. This has been proven for two dimensions, and for the fourth, fifth, and higher dimensions. But the proof for the third dimension has continued to elude mathematicians...
Until 2002 that is, when Perelman presented a proof of the conjecture in three installments. It was unusually short, and unorthodox in another way—instead of publishing it in a peer-reviewed academic journal, Perelman posted it to the Internet. But nobody was able to prove it wrong...
...however, is quoted by The New Yorker as saying that Perelman’s proof “was written in such a messy way” that it was incomprehensible. The Harvard professor is promoting another proof written by two of his protégés—a Guangzhou, China-based mathematician and a Lehigh University professor. Yau and his protégés say that their version—while influenced by Perelman—is a “self-contained and complete proof.” Perelman’s backers dispute that...