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The study runs from Plato and the story of the Delian oracle to the second century BC, when Archimedes and Apollonius of Perga flourished; [1] [3] Knorr suggests that the decline in Greek geometry after that time represented a shift in interest to other topics in mathematics rather than a decline in mathematics as a whole. [3] Unlike the ...
Download as PDF; Printable version; ... additional terms may apply. ... Category: Unsolved problems in geometry. 5 languages ...
A bigger motivation for study has been the connection to Moser's worm problem. It was included in a list of 12 problems described by the mathematician Scott W. Williams as "million buck problems" because he believed that the techniques involved in their resolution will be worth at least a million dollars to mathematics. [3]
As this example shows, when like terms exist in an expression, they may be combined by adding or subtracting (whatever the expression indicates) the coefficients, and maintaining the common factor of both terms. Such combination is called combining like terms or collecting like terms, and it is an important tool used for solving equations.
The specific needs of enumerative geometry were not addressed until some further attention was paid to them in the 1960s and 1970s (as pointed out for example by Steven Kleiman). Intersection numbers had been rigorously defined (by André Weil as part of his foundational programme 1942–6, [ 3 ] and again subsequently), but this did not ...
Yamabe problem. Yamabe claimed a solution in 1960, but Trudinger discovered a gap in 1968, and a complete proof was not given until 1984. Mordell conjecture over function fields. Manin published a proof in 1963, but Coleman (1990) found and corrected a gap in the proof. In 1973 Britton published a 282-page attempted solution of Burnside's problem.
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
Moser's worm problem (also known as mother worm's blanket problem) is an unsolved problem in geometry formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem asks for the region of smallest area that can accommodate every plane curve of length 1.