Mathematics: The Loss of CertaintyThis 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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LibraryThing Review
User Review  encephalical  LibraryThingThe 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, nonlinear 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. Read full review
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Contents
The Thesis  3 
The Genesis of Mathematical Truths  9 
The Flowering of Mathematical Truths  31 
The Mathematization of Science  50 
The Withering of Truth  69 
The Illogical Development of a Logical Subject  100 
The Morass of Analysis  127 
The Predicament circa 1800  153 
Logicism versus Imuitionism  216 
The Formalist and SetTheoretic Foundations  245 
Disasters  258 
The Isolation of Mathematics  278 
Whither Mathematics?  307 
The Authority of Nature  328 
355  
361  
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Common terms and phrases
accepted according algebra analysis applied approach argument arithmetic assertion axioms basis believed body calculus called century certainly Chapter choice clear complex numbers concepts concerned considered consistency construction continued contradictions correct course criticized deductive defined definitions derivative described equal equations established Euclid's Euclidean example existence experience explanation expressed fact false force foundations function geometry given Greek Hence Hilbert human ideas infinite intuition irrational knowledge known later laws least less limit logic mathe mathematicians mathematics matics means method mind motion nature negative Newton noted objects observations obtained philosophy physical positive possible principles problems proof properties propositions proved pure quantities question rational real numbers reason rigor roots Russell sense sound space statement structure symbols theorems theory things thought tion true truths types universe whole numbers