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Mathematics: The Loss of Certainty (1980)

door Morris Kline

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402463,434 (3.92)2
This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century.
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Toon 4 van 4
7/6/22
  laplantelibrary | Jul 6, 2022 |
The chapters on historical development are great. Math is so often presented as a fait accompli, it's nice to be reminded that it has a messy, non-linear history, just like every other human endeavor. The latter chapters on the state of math research as Kline saw it in the late 70s were tedious. ( )
  encephalical | Jan 10, 2020 |
Rather dry. Probably worth a second pass. ( )
  ndpmcIntosh | Mar 21, 2016 |
In spite of a fascinating subject--the way the once-monolithic field of Mathematics has splintered over the past two centuries into competing, contradictory factions--I had to give up on this book because of the poor writing. Any book that begins with the sentence "ANY CIVILIZATION WORTHY OF THE APPELLATION HAS SOUGHT TRUTHS" is already facing an extreme uphill battle with me (the ALL CAPS is there in the text. Really). It keeps going. Chapter 2 opens with " THE MAJESTIC GREEK CIVILIZATION WAS DESTROYED BY SEVERAL FORCES." Clearly Professor Kline would have benefitted from a few courses in Freshman Composition while teaching at NYU... this is the kind of classically bad writing you get from 17 year olds trying to say something important and not yet knowing how.

Kline could have benefited from taking a few Humanities courses, too. The introduction is a hysteria of blather about how nothing is certain any longer--ok, to whom is this news? Have we not been thinking about this problem at least since Galileo published Starry Messenger? Did Morris Kline never read Hamlet?

Ok, I feel slightly bad slamming the book of a deceased scholar who tried valiantly throughout his life to reform mathematics education. Maybe this is a book he knocked off when he was too busy in the real world to worry about his writing. ( )
  poingu | Jan 29, 2015 |
Toon 4 van 4
"[H]is descriptions suffer from his extreme position as applied mathematician. . . . Kline's zeal obscures his perspective."
toegevoegd door cpg | bewerkModern Logic, Thomas Drucker (Feb 1, 1993)
 
"Professor Kline does not deal honestly with his readers. He is a learned man and knows perfectly well that many mathematical ideas created in abstracto have found significant application in the real world. He chooses to ignore this fact, acknowledged by even the most fanatic opponents of mathematics. He does this to support an untenable dogma. One is reminded of the story of the court jester to Louis XIV: the latter had written a poem and asked the jester his opinion. 'Your majesty is capable of anything. Your majesty has set out to write doggerel and your majesty has succeeded.' On balance, such, alas, must be said of this book."
toegevoegd door cpg | bewerkAmerican Mathematical Monthly, Raymond G. Ayoub (Nov 1, 1982)
 
"I think three quarters of it is superb, and the other quarter is outrageous nonsense . . ."
toegevoegd door cpg | bewerkEducational Studies in Mathematics, Ian Stewart (Nov 1, 1982)
 
"[T]he author's grasp of twentieth century logic is not reliable. . . . The philosophical confusions and the foundational inaccuracies are intimately related and are perhaps jointly explainable by reference to the author's misunderstanding of the complex of traditional philosophic distinctions which have been both exploited by and clarified by modern foundational work. . . . One can only regret the philosophical, foundational, and historical inadequacies which vitiate the main argument . . ."
toegevoegd door cpg | bewerkMathematical Reviews, J. Corcoran (betaal website) (Feb 12, 1982)
 
"[T]he book has disappointed me in two respects. (1) as to the contents and views, nothing much is new; (2) as to the style of presentation, it is too loose, too additive, and a little pretentious."
toegevoegd door cpg | bewerkZentralblatt MATH, W. Rehder (Feb 12, 1981)
 

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The gods have not revealed all things from the beginning,
But men seek and so find out better in time.

Let us suppose these things are like the truth.

But surely no man knows or ever will know
The truth about the gods and all I speak of.
For even if he happens to tell the perfect truth,
He does not know it, but appearance is fashioned over everything.

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To my wife Helen Mann Kline
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Preface — This book treats the fundamental changes that man has been forced to make in his understanding of the nature and role of mathematics.
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This work stresses the illogical manner in which mathematics has developed, the question of applied mathematics as against 'pure' mathematics, and the challenges to the consistency of mathematics' logical structure that have occurred in the twentieth century.

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