Mathematics Queen And Servant Of Science Pdf

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· 28 ratings · 3 reviews

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Aug 21, 2016 Nathan Jerpe rated it really liked it

Disjointed and uneven, but then we get such sweeping observations as how all of mathematics can be divided into four fields: arithmetic (ancient), geometry (ancient), algebra (Middle Ages), and analysis (17th century). How cool is that? Which leads to things like:

probability = an outgrowth of arithmetic -> 17th c probability (gamblers, Pascal, Fermat) -> apply some 19th c analysis to this 17th probability -> 20th c probability, etc...?

I don't know if any popular math writer would stake his claim

probability = an outgrowth of arithmetic -> 17th c probability (gamblers, Pascal, Fermat) -> apply some 19th c analysis to this 17th probability -> 20th c probability, etc...?

I don't know if any popular math writer would stake his claim on such broad generalities nowadays. Perhaps it isn't even... true? although I'm inclined to believe it's true enough.

The chapter on groups was heavy going early on, it almost put me off the rest of the book. Turns out you can skip it. Each chapter takes on its own subject and can be read independently. My favorites were the bits on number theory, topology, and Cantor's "storming of heaven" as he discovered radical (heretical?) new theories concerning how some infinities are bigger than others. The chapters on calculus and analysis seemed a bit spoonfed to me. Maybe we emphasize integrals and derivatives more in school these days than we did when this was written three generations ago.

ETB's insights into the poetry and romance of mathematical discovery are what make him worth reading. I'm not sure there's anybody who can write like he can, about this, anymore. Also I feel inclined somehow to mention Lewis Carroll here. Remember that poem in Alice in Wonderland that's printed like a curl... a visual pun maybe on the shape of the mouse's tail? It's here in a discussion on the formations of damped sine waves. Of course the shape of the mouse's tail is damped too, no doubt because he was swimming in a pool of Alice's tears, just before...

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Apr 29, 2008 Ross rated it really liked it

A bit dated, but still very clear and interesting. I love how the history and the mathematics are both given the same importance. I enjoy his style, which changes from informal in places, to extremely technical in other, to even grandiose. A highly enjoyable book!

Mar 23, 2016 Erik rated it it was amazing

Lovely and simply explained, but Bell becomes more and more cranky, belligerent and curmudgeonly as the thing rolls on as if he thinks no one really understands.

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Eric Temple Bell (February 7, 1883 – December 21, 1960) was a mathematician and science fiction author born in Scotland who lived in the U.S. for most of his life. He published his non-fiction under his given name and his fiction as John Taine.

The last five years of world history have been nothing if not...eventful. When living in interesting times, there's nothing better for...

"These estimates may well be enhanced by one from F. Klein (1849-1925), the leading German mathematician of the last quarter of the nineteenth century. 'Mathematics in general is fundamentally the science of self-evident things.' ... If mathematics is indeed the science of self-evident things, mathematicians are a phenomenally stupid lot to waste the tons of good paper they do in proving the fact. Mathematics is abstract and it is hard, and any assertion that it is simple is true only in a severely technical sense—that of the modern postulational method which, as a matter of fact, was exploited by Euclid. The assumptions from which mathematics starts are simple; the rest is not." — 1 likes

"In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century (Hermite, 1822-1901) could say without exaggeration, 'Abel has left mathematicians enough to keep them busy for five hundred years.' Asked how he had done all this in the six or seven years of his working life, Abel replied, 'By studying the masters, not the pupils." — 1 likes

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