Mathematical Monsters
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 nineteenthcentury 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 twentiethcentury 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 `monsterbarring' and `monsteradjusting' 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 DOI:
 10.48550/arXiv.1904.09308
 arXiv:
 arXiv:1904.09308
 Bibcode:
 2019arXiv190409308A
 Keywords:

 Mathematics  History and Overview;
 00A30 (Primary) 01A80 (Secondary)
 EPrint:
 19 pages, 2 figures