Euler's conjecture, a theory proposed by Leonhard Euler in 1769, hung in there for 200 years. Then L.J. Lander and T.R. Parkin came along in 1966, and debunked the conjecture in two swift sentences. Their article -- which is now open access and can be downloaded here -- appeared in the Bulletin of the American Mathematical Society. If you're wondering what the conjecture and its refutation are all about, you might want to ask Cliff Pickover, the author of 45 books on math and science. He brought this curious document to the web last week.
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This article is even shorter: On a conjecture of R. J. Simpson about exact covering congruences
Author: Doron Zeilberger Drexel Univ., Philadelphia, PA
Published in: American Mathematical Monthly archive
Volume 96 Issue 3, March 1989 Page 243
http://www.jstor.org/discover/10.2307/2325213?uid=3739864&uid=2134&uid=2&uid=70&uid=4&uid=3739256&sid=21106466966333
Here is a longer version of the same article:
http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/simpson.pdf
My contribution to this topic:
Short post, short papers, enjoy! LOG#170. The shortest papers ever: the list.
http://www.thespectrumofriemannium.com/2015/04/13/log170-the-shortest-papers-ever-the-list/
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MATHEMATICS AND EDUCATION
ABSTRACT
]. In these approaches one may derive covariant versions of the Fokker-Planck equation of Brownian motion in curved spaces. The mathematical approach to path integrals uses similar techniques [5]. The inherent ambiguities can be removed by demanding a certain form for Schrödinger equation of the system, which in curved space is have the Laplace-Beltrami operator as an operator for the kinetic energy [2], without an additional curvature scalar.
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GAUSS AND EULER
ABSTRACT
Let’s approach Leonhard Euler and his work the same way. It will make things a whole lot easier.
If one is not a mathematician (and except for a few of you out there, who is?), it’s going to be impossible to actually understand why Euler was such a great man. Other people will have to tell us, and we should probably believe them.