Borovik A. Mathematics Under the Microscope

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Published under Creative Commons (Sep 5, 2007)

Notes on Cognitive Aspects of Mathematical Practice

Part I Simple Things:
How Structures of Human Cognition Reveal Themselves in Mathematics
A Taste of Things to Come
What You See is What You Get
The Wing of the Hummingbird
Simple Things
Infinity and Beyond
Encapsulation of Actual Infinity

Part II Mathematical Reasoning
What Is It That Makes a Mathematician?
Kolmogorov’s Logic and Heuristic Reasoning
Recovery vs. Discovery
The Line of Sight

Part III History and Philosophy
The Ultimate Replicating Machines
The Vivisection of the Cheshire Cat
References
Index

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