Gnomes in the Fog. The Reception of Brouwer's Intuitionism in the 1920s
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Author(s): D. E. Hesseling
Publisher: Birkhäuser
ISBN: 3764365366
Format: hardback
447pp
Price: €108
Review Date: 10 December 2003
Review: This book covers the period of the history in mathematics when mathematics and philosophy seemed to meet. The debate was provoked by the Dutch mathematician, L. E. J. Brouwer, who developed intuitionism. The analysis centres on two questions: the question of mathematical existence and the status of logic. Here the author studies the reactions, mainly by mathematicians and philosophers to Brouwer’s theories, looking at how the debate developed and continued for many years, why the responses were so agitated and emotional, why mathematicians failed to regard questions such as what kind of mathematical objects exist as merely issues of personal preference, and what the foundational crisis meant for the self-understanding of mathematics. Significantly, this plurality of views took well-known mathematicians several years to develop, but they can now be explained to first-year maths students in a few hours.