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Amateur makes fools of the experts, Marcus Chown September 1995, [https://www.newscientist.com/article/mg14719952-200-amateur-makes-fools-of-the-experts/] . An experiment that for eighty years has been cited by physicists as a confirmation of Einstein’s special theory of relativity is nothing of the sort. This remarkable discovery has been made not ...


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He was concerned with providing an abstract analog to the geometric notion of dimension for algebraic varieties given by polynomial rings. Zero-dimensional ideals are abstract algebraic analogs of discrete collections of points. The idea goes back to Hilbert's conversion of algebraic geometry into the language of rings and ideals, and Dedekind inspired ...


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The abacists of 16th century Italy correctly identified the rule of signs from multiplication. Typical of their arguments (using modern notation) is: $64 = (10 - 2) \times (10 - 2) = \dots =100 + (-40) + (-2\times-2) = 60 + (-2\times-2),$ so that "subtract 2 times subtract 2" must equal four. (There was still no concept of a negative number.) Cardano ...


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My vote goes to three out of {Michał Dziewicki, Stanisław Zaremba, Jan Śleszyński, Witold Wilkosz, Otto Nikodym, Leon Chwistek, Stanisław Bilski}; most probably the three whose names I put in bold. On May 10, 1915, Russell wrote to Ludwig Wittgenstein who was doing military service in Krakow: "If you have time, you should visit in Krakow a lonely old ...


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This is quite common. Some examples of pairs of very strong researchers who published at least $15$ papers together: Guillemin and Sternberg. Harvey and Lawson. Colding and Minicozzi Ozsvath and Szabo Green and Tao. Schoen and Yau. Mrowka and Kronheimer Atiyah and Bott. Atiyah and Singer. There are of course many more examples, as this list mostly ...


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It depends on what counts as working "on it". His prior work under Hilbert was related to this area of geometry. Bolyai (1832) and Gerwein (1833) proved that polygons of equal area are equidecomposable, and Gauss urged a 3D extension in letters to Gerling mentioned by Hilbert. It was in the works in 1890-s. In 1896 Bricard reproved Gerling's 1844 result that ...


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