|
Editorial Review Product Description
Filled with compelling insights of special interest to every mathematician, engineer and scientist, this time-honored study by one of the 20th century’s foremost scholars and interpreters of the history and meaning of mathematics, surveys the roled played by mathematics in the evolution of civilization. It describes clearly the main principles, methods and theories of mathematics that have survived from about 4000 BC to 1945. 1945 edition.
... Read more Customer Reviews (7) 
Development of Mathematics
"Once we venture beyond the rudiments," says Bell, "we may agree that those who cultivate mathematics have more interesting things to say about it than those who merely venerate." No more eloquent substantiation of this assertion could be wished for than this book in which it appears. A cultivator himself, Bell requires no introduction to mathematicians. He knows mathematical creation--its trials and its rewards--at first hand. Nor does he need introduction to the wider reading public. It seems, however, that in this work he has risen to a new level of accomplishment, which merits the genuine appreciation of all those who regard mathematics and its related sciences as a vital field of human activity, and find interest in the history of their development. This is an eminently readable book, written in an engaging and graceful style. At the same time it is a scholarly work with a wholly serious purpose, full of information and fact, and covering much material which is otherwise not easily accessible.
As the keynote of the book Bell sounds an old quotation: "There is probably no other science which presents such different appearances to one who cultivates it and to one who does not, as mathematics. To [the noncultivator] it is ancient, venerable, and complete; a body of dry, irrefutable, unambiguous reasoning. To the mathematician, on the other hand, his science is in the purple bloom of vigorous youth, everywhere stretching out after the attainable but unattained, and full of the excitement of nascent thoughts; its logic beset with ambiguities, and its analytic processes, like Bunyan's road, have a quagmire on one side and a deep ditch on the other, and branch off into innumerable by-paths that end in a wilderness."
To the student of mathematics the historical development of his subject appears all too inevitably as a wilderness, and moreover as an almost impenetrable one when the last century or two are approached. With research pressed in this time and at the present on many fronts by a vast number of investigators, with many different groups of these pursuing apparently quite diverse objectives, and with all of them changing their tactics and goals disconcertingly often, the residue of their attainments is a sweltering jungle indeed. Through this the present book lays a very welcome road. The typical and more significant trends and episodes are isolated, the genesis, growth and efflorescence of some of the concepts and methods, whose survival to the present is their guarantee of significance, are traced, and often their decadence in periods of sterile overelaboration is observed.
The book is not of the "popular" kind, as this term is generally understood, since it makes small effort to be intelligible to readers wholly uninitiated mathematically. Indeed, its appeal will probably be found to vary almost directly with the reader's mathematical attainments. The less trained will find much that is entirely narrative and non-technical, and will some-times find quite enlightening the concise but generally clear technical surveys that are given. The advanced student of mathematics and science will find much more to interest him, and will value the orientations which the book supplies. Professional mathematicians, even those who are themselves momentarily engaged in extending mathematical theories and their applications, will find the book a thoroughly worth-while reading of mathematical evolution. This is not to say by any means that they will in all instances read from the noted trends and related episodes precisely the same inferences as does the author. The better, perhaps, that in some cases they should not.
For the purposes of this review it is convenient to regard the book as falling into two parts, consisting respectively of the first six chapters, which treat of mathematics up to the year 1637, and the remaining seventeen chapters which terminate the discussion at the present time. The first part, which begins with a general prospectus, is given over thereafter to a review of mathematics in the ancient Babylonian and Egyptian eras, in the Greek period, in the dark age of Europe, through the Arabian epoch and the Renaissance. While completely nontechnical, even these chapters are not to be regarded as a historical text. There is not the customary cataloguing of names and facts, but rather a sort of running narrative commentary, of which a full appreciation will be somewhat conditioned upon the reader's previous knowledge of the history. Bell acknowledges these pages to hold in the main a collation of material from more or less familiar and classical works. These chapters appear to be by far the weaker part of the book; to be in fact a trifle pedestrian, though not always unprovocative. As is well known, iconoclastic tendencies are not invariably eschewed by Bell. The so-called debunking of tradition is often salutary. An excess of it, however, though it adds a sensational element to the reading, may in the case of immature or otherwise undiscriminating readers leave impressions that are not wholly fortunate or just. Enjoyable or regrettable, as the reader may find them, he will find here, and throughout the book, a sprinkling of the quips and sophistications which those who know Bell would rather expect, and some will perhaps deplore his occasional momentary lapses from a generally prevalent high scholarly objectiveness to the inclusion of less happy and rather discordant contemporary comment.
The peculiar contribution of the book is by all odds to be found in its second part. Here Bell's excellent qualifications for his task, which include a technical equipment beyond the range of the usual historian, and a literary facility far beyond the range of the usual mathematician, really come to bear. The wide gamut of topics discussed is perhaps best suggested by the chapter headings, which are the following: The beginnings of modern mathematics 1637- 1687; Extension of number; Toward mathematical structure; Arithmetic generalized; Emergence of structural analysis; Cardinal and ordinal to 1902; From intuition to absolute rigor, 1700-1900; Rational arithmetic after Fermat; Contributions from geometry; The impulse from science; From mechanics to generalized variables; Differential and difference equations; Invariance; Certain major theories of functions; Through physics to general analysis and abstractness; Uncertainties and probabilities.
It would be entirely impossible to abstract these chapters briefly. They should be read in their completeness. Mathematics and mathematicians live in them, and not infrequently lend themselves to genuine drama. The presentation of the whole is admirable. It is flowing and graceful and often characterized by a genuine and delightful humor. A feature which will be prized is Bell's almost invariable practice of labeling all investigators and notable publications with their nationality and dates.
The publishers of the book are to be thanked for an attractive and legible volume. Bell deserves recognition and high praise for such a significant work. Many the scientist who has come to realize, to his humility, that his vaunted work would in his absence have soon been accomplished by another. One may safely venture that no other would soon have written this book had Bell not done so.
The Mathematicians Bible . . . hardly surpassed;
First, I'd like to point out that Morris Kline's effort, although great, hardly surpasses E.T. Bell's "The Development of Mathematics."I suppose in terms of page length, it does; but, in some of that respect, Morris Kline's effort is a failure; the effort to put more mathematics in it failed because in each mathematical development Mr Kline begins to describe, he leaves out or throws in some part that you don't know where it came from . . . leaving the mathematical presentation wanting.Morris Kline covers the same time period that E.T. Bell does and for the same reasons; to include an account of the mathematics after the early 1900s would more than double the size of the book.With Morris Kline's book out of the way; i'll talk more about E.T. Bell's!
Some, maybe most people would criticize books like this calling them 'popularizers.Well, in terms of some books that like to explain parts of quantum mechanics or general/special relativity; they may be right.But, books like E.T Bell's "The Development of Mathematics" are not about trying to explain this or that esoteric theory without the mathematics; E.T Bell's "The Development of Mathematics" is a bible of mathematics(as is Morris Kline's ); it is the philosophy, history, and reference book to all the relevant knowledge . . . the actual papers.To be a real intellectual is to have perspective; in mathematics, that perspective is really hard; this is what E.T. Bell's effort gives; it gives that perspective of all of mathematics(and its relation to the human condition).
THis is how we should raise mathematicians; read this book as a reference to all the original(as orginal as can be) mathematical papers.
Go, read, and disagree for yourself.
The great mathematician Saunders Mac Lane (1909--2005, with several books available on Amazon) reviewed this book in 1946.His comments are worth reading still:
This magnificent, inclusive, and provocative survey of the origin and adventures of mathematical ideas has now appeared in a second edition. Various material has been added; an extensive survey of recent developments in lattice theory, together with notes on recent advances in such disparate subjects as Diophantine Analysis (Mordell, Segre), Waring's problem (Niven), unified field theory (Einstein), surface area (Youngs), three-valued logic and quantum mechanics (Reichenbach), the inconsistency of Quine's system of logistic (Rosser), the advances in completeness theorems in logic (Kleene), and the use of mathematics during the second world war. Various other statements have been brought up to date by the simple device of replacing 1940 by 1945....
The great virtue of this book is that it does not merely record facts, but it arranges ideas and passes judgment as to their importance. This aim, combined with the tremendous scope of the work, makes it inevitable that there should be errors both of fact and of judgment....
But enough of carping criticism. It's great fun to read this book, just because there are so many chances profitably to disagree with its provocative author. The wealth of possible topics of difference must be read to be appreciated. Is Plato as vicious as Bell's everywhere dense cracks would indicate? Does Bell overemphasize the importance of lattice theory and miss some of the significant developments in modern topology? Has this hard-headed author been duped by the advocates of Brouwerian logic and many-valued logics? Is Frechet's work as significant as Bell claims? Might some mathematical war workers disagree with Bell's dismissal of spherical trigonometry as useless?
The book is of great value for many classes of readers.... The philosopher wiI1 disagree with the jabs at Kant, but will profit from the view of living mathematics. The young mathematician will gain background and will learn of the ebb and flow of fashion in the specialties of research, To all these and others one might say: don't wonder about it, but go, read, and disagree for yourself.
Spellbinding and Provocative
As a retired professional mathematician eager to learn more about the history of my subject, I found this book absolutely fascinating. Bell writes very forcefully, sometimes expressing his personal judgments in a manner that some might find offensive but which I found provocative (he frequently gives references in his notes to other scholars who disagree with his views). He doesn't hesitate to report on the dark side of mathematicians' battles (both philosophical and personal) with one another. I recommend that one read a more conventional history of mathematics (such as Boyer, Kline or Gratton-Guinness) before attempting this controversial one. Be forewarned that Constance Reid, in her biography of Bell, points out errors in this book. I forgive Bell for those because no one person could possibly comprehend in detail all the abstruse mathematics which he covers relatively well. I recommend this book only to readers already somewhat knowledgeable in mathematics.
A good general outline of Mathematics
While the style could be better, this is a general and good outline of the history of mathematics.
I would point out that the little time spent on Al-Magi Al-Khawarizmi (literally "The Magus (Zorastarian, not Muslim) from Khazar (near the Caspian Sea)") is justified.Al-Khawarizmi merely translated the formulaic Algebra (which the Indians developed from the Greeks and systemized it from its rhetorical origin) from a Hindu text (brought to the court of the Caliph by Indian Ambassadors seeking trade, they were soon rewarded with Moghul Jihad) and translated the Hindu word for 'reorganisation' or 'rebalancing' into Arabic (Al-Jabr).From there, Spanish scholars were able to access the work.As a translator, AL-Khawarizmi certainly provided a service, but he was a Zorastarian from the biggest population of Zorastarians outside of Persia, Khazar.No self-respecting Muslim would keep "al-Magus" as part of his name after conversion.
... Read more |
