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We review Eulers idea on the Gammafunction. We will explain, how Euler obtained them and how Eulers ideas anticipate more modern approaches and theories. Furthermore, some questions asked by Euler are answered.
We show that an apparently overlooked result of Euler from cite{E421} is essentially equivalent to the general multiplication formula for the $Gamma$-function that was proven by Gauss in cite{Ga28}.
We give another proof for [ sum_{n=1}^{infty}frac{1}{n^2}=frac{pi^2}{6} ] that basically follows from the theory of difference equations.
New understandings of the functioning of human brains engaged in mathematics raise interesting questions for mathematics educators. Novel lines of research are suggested by neuroscientific findings, and new light is shed on some longstanding issues in mathematics education.
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This paper is an exposition and review of the research related to the Riemann Hypothesis starting from the work of Riemann and ending with a description of the work of G. Spencer-Brown.