Analogy in William Rowan Hamilton's New Algebra

Abstract

This essay offers the first analysis of analogy in research-level mathematics, taking as its case the 1837 treatise of William Rowan Hamilton. Analogy spatialized Hamilton's key concepts—knowledge and time—in culturally familiar ways, creating an effective landscape for thinking about the new algebra. It also structurally aligned his theory with the real number system so his objects and operations would behave customarily, thus encompassing the old algebra while systematically bringing into existence the new.

Keywords:

• algebra
• analogy
• mathematics
• William Rowan Hamilton

Additional information

Notes on contributors

Joseph Little

Joseph Little is an associate professor of English at Niagara University, where he directs the first-year writing program. His research focuses on the function of analogy in technical discourse.

Maritza M. Branker

Maritza M. Branker is an assistant professor of mathematics at Niagara University. Her research interests include complex analysis and the history of complex analysis.