The Idea as an Organizing Principle

What is the core ingredient of mathematics? Is it logic or precision? Is it ʺnumberʺ or ʺfunctionʺ? Is it ʺstructure,ʺ or ʺpattern,ʺ or the subtlety of mathematical concepts? Perhaps it is abstraction? In our search for the inner nature of mathematics we might do well to listen to the words of mathe...

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Bibliographic Details
Published inHow Mathematicians Think pp. 193 - 252
Main Author Byers, William
Format Book Chapter
LanguageEnglish
Published Princeton Princeton University Press 12.04.2010
Subjects
Ambiguity
Continuous functions
Epistemology
Euclidean geometry
Exponential functions
Geometric lines
Geometric shapes
Geometry
Mathematical expressions
Mathematical functions
Mathematical intervals
Mathematical objects
Mathematical theorems
Mathematics
Philosophy
Polygons
Polytopes
Pure mathematics
Transcendental functions
Triangles
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ISBN9780691145990
0691145997
DOI10.1515/9781400833955.193

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Summary:What is the core ingredient of mathematics? Is it logic or precision? Is it ʺnumberʺ or ʺfunctionʺ? Is it ʺstructure,ʺ or ʺpattern,ʺ or the subtlety of mathematical concepts? Perhaps it is abstraction? In our search for the inner nature of mathematics we might do well to listen to the words of mathematicians. Not just the words they use when we ask them to explain the nature of their subject. The language they use in such an artificial situation is alien to the language that they use when they are discussing mathematics among themselves. When discussing a particular piece of mathematics,
ISBN:9780691145990
0691145997
DOI:10.1515/9781400833955.193