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I was a bit disappointed that this article did not offer more practical examples of the ties between the development of mathematics and the history of ideas in general.

For instance, the vision of mathematicians like Hilbert and Russell of a cohesive mathematics defined from first principles seems a very Victorian notion that the universe is knowable if you simply search hard enough. It's the same enlightment frame of mind that resulted in intellectual creations like the Oxford English Dictionary.

Similarly the results of Gödel, Church, Turing, and others showing the limits of mathematical consistency seem of a piece with the confounding discoveries of Quantum physics, which replaced the static models of classical physics. They seem to correspond with a darker vision of the limitations of human intellect that emerge in abstract art and poetry like Eliot's 'The Wasteland' around the same time.

If you push this too far you end up sounding like an idiot (perhaps this is already there) but there are clearly discernible connections across science, art, literature, and politics both now and deep into the past. It might be a personal projection but Brahms concertos always strike me as the music of a people who believed in an orderly, Newtonian universe and upheld the static political order of the Ancien Regime.

At the end of the day most intellectuals read the same books and attend the same salons, however defined. There is continuous cross-fertilization between different realms of thought. The resulting connections are there if you just look for them.

Edit: 'Brahms' should be 'J.S. Bach'.

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