TY - JOUR
T1 - Commuting and noncommuting infinitesimals
AU - Katz, Mikhail G.
AU - Leichtnam, Eric
PY - 2013/8
Y1 - 2013/8
N2 - Infinitesimals are natural products of the human imagination. Their history goes back to Greek antiquity. Their role in the calculus and analysis has seen dramatic ups and downs; they have stimulated strong opinions and even vitriol. Edwin Hewitt developed hyperreal fields in the 1940s. Abraham Robinson's infinitesimals date from the 1960s. A noncommutative version of infinitesimals, due to Alain Connes, has been in use since the 1990s. We review some of the hyperreal concepts, and compare them with some of the concepts underlying noncommutative geometry.
AB - Infinitesimals are natural products of the human imagination. Their history goes back to Greek antiquity. Their role in the calculus and analysis has seen dramatic ups and downs; they have stimulated strong opinions and even vitriol. Edwin Hewitt developed hyperreal fields in the 1940s. Abraham Robinson's infinitesimals date from the 1960s. A noncommutative version of infinitesimals, due to Alain Connes, has been in use since the 1990s. We review some of the hyperreal concepts, and compare them with some of the concepts underlying noncommutative geometry.
UR - http://www.scopus.com/inward/record.url?scp=84880294839&partnerID=8YFLogxK
U2 - 10.4169/amer.math.monthly.120.07.631
DO - 10.4169/amer.math.monthly.120.07.631
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AN - SCOPUS:84880294839
SN - 0002-9890
VL - 120
SP - 631
EP - 641
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 7
ER -