Mathematical Monsters

In Diego Compagna & Stefanie Steinhart (eds.), Monsters, Monstrosities, and the Monstrous in Culture and Society. Vernon Press. pp. 391-412 (2019)
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Abstract

Monsters lurk within mathematical as well as literary haunts. I propose to trace some pathways between these two monstrous habitats. I start from Jeffrey Jerome Cohen’s influential account of monster culture and explore how well mathematical monsters fit each of his seven theses. The mathematical monsters I discuss are drawn primarily from three distinct but overlapping domains. Firstly, late nineteenth-century mathematicians made numerous unsettling discoveries that threatened their understanding of their own discipline and challenged their intuitions. The great French mathematician Henri Poincaré characterised these anomalies as ‘monsters’, a name that stuck. Secondly, the twentieth-century philosopher Imre Lakatos composed a seminal work on the nature of mathematical proof, in which monsters play a conspicuous role. Lakatos coined such terms as ‘monster-barring’ and ‘monster-adjusting’ to describe strategies for dealing with entities whose properties seem to falsify a conjecture. Thirdly, and most recently, mathematicians dubbed the largest of the sporadic groups ‘the Monster’, because of its vast size and uncanny properties, and because its existence was suspected long before it could be confirmed.

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Andrew Aberdein
Florida Institute of Technology

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References found in this work

The Foundations of Science.Henri Poincaré - 2017 - New York and Garrison, N.Y.,: The Science press. Edited by George Bruce Halsted.
Proofs and refutations: the logic of mathematical discovery.Imre Lakatos (ed.) - 1976 - New York: Cambridge University Press.
A Philosophical Enquiry Into the Origin of Our Ideas: Of the Sublime and the Beautiful.Edmund Burke - 1759 - Oxford, United Kingdom: Oxford University Press UK. Edited by Paul Guyer.

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