Abstract / Synopsis
Young learners of mathematics share a common experience with the greatest creators of mathematics: ``hitting a wall,'' meaning, first frustration, then struggle, and finally, enlightenment and elation. We tell two intertwined stories. One story is about children, first learning to add, then later learning about negative numbers, still later about complex numbers, and finally about quaternions. Intertwined is the history of the development of number systems -- from Galileo and Bombelli through D'Alembert, Euler and Gauss, up to Hamilton and Cayley.
© Reuben Hersh
Hersh, R. "From Counting to Quaternions -- The Agonies and Ecstasies of the Student Repeat Those of D'Alembert and Hamilton," Journal of Humanistic Mathematics, Volume 1 Issue 1 (January 2011), pages 65-93. DOI: 10.5642/jhummath.201101.06 . Available at: http://scholarship.claremont.edu/jhm/vol1/iss1/6
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