Tuesday, January 29, 2019

the most auspicious tetrahedron &/or two pairs of charming mathematicians












- Niels Henrik Abel
(picture taken from the Internet)















- Évariste Galois
(picture taken from the Internet)









What did they do?
Well, conjure the most remarkable consequences of an old ghost (Vieta's logistica speciosa): "solutions" for the general algebraic equations of degree higher than four.
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- Bernhard Riemann
(picture taken from the Internet)













- Kingdon Clifford
(picture taken from the Internet,
processed by A/Z)









What did they do?
Riemann simply solved the following riddle (and by doing so challenged classical and common sense understanding about space, which remains pretty much our understanding till nowadays): what is real space?
Clifford understood that.
"Riemann's allusions were ignored by the majority of contemporary mathematicians and physicists. His investigations were deemed too speculative and theoretical to bear any relevance to physical space, the space of experience. The only one who allied himself firmly to Riemann was the translator fo his works into English, William Kingdon Clifford... already in 1870, Clifford saw in Riemann's conception of space the possibility for a fusion of geometry with physics... Clifford conceived matter and its motion as a manifestation of varying curvature [of space]... For Aristotle, space was an accident of substance; for Clifford... substance is an accident of space... THESE SPECULATIONS AROUSED GREAT OPPOSITION AMONG ACADEMIC PHILOSOPHERS..." (Max Jammer, Concepts of Space, Dover 1993);
"Riemann came to a deep philosophical conviction that a complete mathematical theory must be established, which would take the elementary laws governing points and transform them to the great generality of the plenum (by which he meant continuously-filled space)... the Riemann Integral calculus is defined as an infinite sum of integrals of step functions. Such infinite sums became the starting points for the study of infinite by Georg Cantor" (Amir D. Aczel, The Mystery of the Aleph, WSP 2000);




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