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Kazuo Kondo (1911-2001) was Chair of the Department of Mathematical Engineering at the University of Tokyo, Japan. Over a period of 50 years, he and a few colleagues wrote and published a voluminous series of papers and monographs on the applications of analytical geometry within a diverse range of subjects in the natural sciences. Inspired by Otto Fischers attempt at a quaternionic unified theory in the late 1950s he adopted the mathematics of the revered Akitsugu Kawaguchi to produce his own speculative unified theory. The theory appears to successfully apply Kawaguchis mathematics to the full range of natural phenomena, from the structure of fundamental particles to the geometry of living beings. The theories are testable and falsifiable. Kondo and his theories are now almost completely unknown and this paper serves as the barest introduction to his work
The aim of this paper is to prove wordlessly the sum formula of $1^{k}+2^{k}+ldots +n^{k}$, $kin{1,2,3}$.
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