Mathematics: Queen and Servant of Science

by Eric Temple Bell

An absorbing account of pure and applied mathematics from the geometry of Euclid to that of Riemann, and its application in Einstein’s theory of relativity. The twenty chapters cover such topics algebra, number theory, logic, probability, infinite sets and the foundations of mathematics, rings, matrices, transformations, groups, geometry, and topology. Mathematics was republished in 1987 with corrections and an added foreword by Martin Gardner.

Genres: Mathematics, History

Unknown Binding

First published January 1, 1952

About the author

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.

Reviews

[Nathan Jerpe · Rating 4 out of 5]

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 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...

[Nikunj]

here is the scanned pdf of this book :
https://ia601401.us.archive.org/2/ite...

[Ross · Rating 4 out of 5]

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!

[Erik · Rating 5 out of 5]

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.