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Topic: Ten all-time most influential math books
Replies: 8   Last Post: Jul 17, 2006 3:33 PM

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Karl M. Bunday

Posts: 127
Registered: 12/6/04
Re: Ten all-time most influential math books
Posted: Jul 16, 2006 9:43 PM
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Dave wrote:

> I came across the following article recently, and
> I thought it would be interesting to ask how others
> think this list of ten most important math books
> has withstood the 83-year passage of time since
> its publication.

> Walter C. Eells, "The ten most important mathematical
> books in the world", American Mathematical Monthly
> 30 #6 (Sept./Oct. 1923), 318-321.

> EUCLID'S "Elements" (Alexandria, c. 325 B.C.),
> which "has been for nearly twenty-two centuries
> the encouragement and guide of scientific thought"
> (Clifford), which has passed through more than two
> thousand editions and has exercised such profound
> influence on the teaching and knowledge of geometry
> for more than two thousand years, and which is
> "still regarded by some as the best introduction
> to the mathematical sciences" (Cajori).

Euclid's Elements definitely still belong on this list. They are the inspiration
for great books like Robin Hartshorne's Geometry: Euclid and Beyond.

(oddly, Amazon says the book was published in 2005, while reminding me that I
bought it in 2001)

And Heath's annotated English translation of the Elements


is a delightful treasure, as much worth reading for its footnotes as for the text.

> APPOLLONIUS'S "Conic Sections" (Alexandria ?
> c. 210 B.C.), the great systematic treatise
> which developed the geometrical "theory of conic
> sections.

This one is a keeper for the list, too.

But shouldn't the next book on the list be Al-Khwarizmi's?

> LEONARDO OF PISA'S "Liber Abaci" (Pisa, 1202),
> which marked the first renaissance of mathematics
> on Christian soil, introduced Arabian algebra,
> and brought into general use in Europe the
> labor-saving Hindu-Arabic numerals.

This unquestionably belongs if the list is ten most influential WESTERN
mathematics books, but otherwise Al-Khwarizmi really ought to get the honor,
since he influenced Leonardo.

> NAPIER'S "Mirifici Logarithmorum Canonis Descriptio"
> (Edinburgh, 1614), which gave the world Napier's
> great invention of logarithms with their miraculous
> power in modern computation.

The advance in calculating power led to many other advances in mathematics, so
this nomination seems warranted.

> DESCARTE'S "Geometrie" (Leyden, 1637), which in spite
> of its obscure style was of epoch-making importance
> in giving to the world the powerful method of analytic
> geometry.

Too bad Fermat didn't write a book tying together all of his contemporary

> NEWTON'S "Principia" (Full Title: 'Philosophiae Naturalis
> Principia Mathematica') (Lodon, 1687), which established
> the mathematical foundation of the universe.

Yep, for sure. And the University of California translation of this work into

makes for very interesting reading, while the original is worth learning Latin for.

I'm surprised that nothing by Euler, e.g. Introduction to Analysis of the
Infinite, appears on the list.

> LAGRANGE'S "Mécanique Analytique" (Paris, 1788), "an
> epoch-making work ... a most consummate example of
> analytic generality".

Maybe LaGrange's one-book generality is what displaced Euler.

> LAPLACE'S "Mécanique Céleste" (Paris, 5 vols., 1799-1825),
> "the translation of the 'Principia' into the language
> of the differential calculus".

The English translator, Nathaniel Bowditch, is famous for noting "I never came
across one of Laplace's 'Thus it plainly appears' without feeling sure that I
have hours of hard work before me to fill up the chasm and find and show how it
plainly appears."

> BOLYAI'S "Science Absolute of Space" (Hungary, 1833),
> which, although only the appendix of a two-volume
> work by his father, is characterized by Halsted as
> "the most extraordinary two dozen pages in the history
> of human thought," and which, together with Lobachevski's
> work, opened up the whole fascinating and broadening
> field of non-Euclidean geometries.

I might give Lobachevski's work priority on this list, although Bolyai was
probably more widely read in WESTERN Europe.

> HAMILTON'S "Lectures on Quaternions" (Dublin, 1852),
> "the great discovery of our nineteenth century.

Interesting choice.

> It is with much regret that the arbitrary limit of
> ten forbids the inclusion of such works as Diophantus's
> "Arithmetic," Alkowarezmi's "Algebra," Cardan's "Ars
> Magna," Euler's "Analysin Infinitorum," Legendre's
> "Fonctions elliptiques" and "Théorie des Nombres,"
> Gauss's "Disquisitiones Arithmeticae," Cantor's
> "Geschichte der Mathematik" and others which
> could easily be mentioned.

Yeah, I'd definitely mention most of those, especially Gauss's book.

How about top ten influential math books of the twentieth century, now that we
are in the twenty-first?

Thanks for opening this interesting thread.

Karl M. Bunday P.O. Box 1456, Minnetonka MN 55345
Learn in Freedom (TM)
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