Alec Nevala-Lee

Thoughts on art, creativity, and the writing life.

Posts Tagged ‘Eric Temple Bell

A deeper intuition

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Something of the luxurious freedom and naive license of the heroic past [of mathematics] may have been curtailed by the close analysis of thoughtlessly inherited intuitions of space and number…In bringing these assumptions to the surface, where they could be seen by anybody, the abstractionists and the topologists did not uproot intuition, to let it wither like a noxious weed on the rubbish heap of the past, but nourished and strengthened itβ€””in general.” If curves and surfaces became somewhat more complicated than the geometers and analysts of the nineteenth century had imagined them, the new definitions did not preclude what was consistent in the old; they merely attempted to clarify it and make it explicit…In short, a deeper intuition broadened and deepened a shallower. It justified itself as mathematics which its practitioners and others found even more interesting than some of the classical geometry and analysis of the past.

β€”Eric Temple Bell, The Development of Mathematics

Written by nevalalee

November 25, 2018 at 7:30 am

Quote of the Day

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A circle no doubt has a certain appealing simplicity at the first glance, but one look at a healthy ellipse should have convinced even the most mystical of astronomers that the perfect simplicity of the circle is akin to the vacant smile of complete idiocy. Compared to what an ellipse can tell us, a circle has nothing to say.

β€”Eric Temple Bell, The Handmaiden of the Sciences

Written by nevalalee

November 10, 2017 at 7:30 am

The gateway to an empire

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Eric Temple Bell

In mathematics it is new ways of looking at old things that seem to be the most prolific sources of far-reaching discoveries. A particular fact may have been known for centuries, and it may have been sterile or of only minor interest all that time, when suddenly some original mind glimpses it from a new angle and perceives the gateway to an empire. What the first flash of intuition sees may take years or even centuries to open up and explore completely, but once a start in the right direction is made, discovery and development go forward at an ever-increasing speed…

Regularities and repetitions in patterns suggest at once to a modern mathematician the abstract groups behind the patterns; and the various transformations of one problem, not necessarily mathematical, into another again spell “group” and raise the question what, if anything, in the problems remains the same, or invariant, under all these transformations…When faced with a new problem, mathematicians frequently try to restate it so that it is equivalent to one whose solution is already known.

β€”Eric Temple Bell, Mathematics: Queen and Servant of Science

Written by nevalalee

October 9, 2016 at 7:30 am

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