Photo by Graham Challifour. Reproduced from Critchlow, 1979, p. 132.
“I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered.”Harold Scott Macdonald (H. S. M.) Coxeter
While a layman in my pursuance and understanding of the nature of geometry, it is along the way we meet some educators who fire up our excitement. For me it is about the truth of what lies so close to the soul’s ideal.
As if searching for a foundation principle, and highly subjective one in my case, I have been touched by example, as if to direct my attention to the early geometer.
Georg Friedrich Bernhard Riemann 1826 – 1866
To me this is one of the greatest achievements of mathematical structures that one could encounter, It revolutionize many a view, that been held to classical discriptions of reality.
In the quiet achievement of Riemann’s tutorial teacher Gauss, recognized the great potential in his student. On the curvature parameters, we recognize in Gauss’s work, what would soon became apparent? That we were being lead into another world for consideration?
XXV. Gaussian Co-ordinates-click on Picture |
So here we are, that we might in our considerations go beyond the global perspectives, to another world that Einstein would so methodically reveal in the geometry and physics, that it would include the electromagnetic considerations of Maxwell into a cohesive whole and beyond.
“Let no one destitute of geometry enter my doors.”
The intuitive development that we are lead through geometrically asks us to consider again, how Riemann moved to a positive aspect of the universe?
See:Donald Coxeter: The Man Who Saved Geometry