Book contents
- Frontmatter
- Introduction
- Contents
- Analysis
- Geometry, Topology and Foundations
- Algebra and Number Theory
- Foreword
- Hamilton's Discovery of Quaternions
- Hamilton, Rodrigues, and the Quaternion Scandal
- Building an International Reputation: The Case of J. J. Sylvester (1814–1897)
- The Foundation Period in the History of Group Theory
- The Evolution of Group Theory: A Brief Survey
- The Search for Finite Simple Groups
- Genius and Biographers: The Fictionalization of Evariste Galois
- Hermann Grassmann and the Creation of Linear Algebra
- The Roots of Commutative Algebra in Algebraic Number Theory
- Eisenstein's Misunderstood Geometric Proof of the Quadratic Reciprocity Theorem
- Waring's Problem
- A History of the Prime Number Theorem
- A Hundred Years of Prime Numbers
- The Indian Mathematician Ramanujan
- Emmy Noether
- “ Marvelous Proof,”
- Afterword
- Surveys
- Index
- About the Editors
Hamilton, Rodrigues, and the Quaternion Scandal
from Algebra and Number Theory
- Frontmatter
- Introduction
- Contents
- Analysis
- Geometry, Topology and Foundations
- Algebra and Number Theory
- Foreword
- Hamilton's Discovery of Quaternions
- Hamilton, Rodrigues, and the Quaternion Scandal
- Building an International Reputation: The Case of J. J. Sylvester (1814–1897)
- The Foundation Period in the History of Group Theory
- The Evolution of Group Theory: A Brief Survey
- The Search for Finite Simple Groups
- Genius and Biographers: The Fictionalization of Evariste Galois
- Hermann Grassmann and the Creation of Linear Algebra
- The Roots of Commutative Algebra in Algebraic Number Theory
- Eisenstein's Misunderstood Geometric Proof of the Quadratic Reciprocity Theorem
- Waring's Problem
- A History of the Prime Number Theorem
- A Hundred Years of Prime Numbers
- The Indian Mathematician Ramanujan
- Emmy Noether
- “ Marvelous Proof,”
- Afterword
- Surveys
- Index
- About the Editors
Summary
Some of the best minds of the nineteenth century—and this was the century that saw the birth of modern mathematical physics—hailed the discovery of quaternions as just about the best thing since the invention of sliced bread. Thus James Clerk Maxwell, the discoverer of electromagnetic theory, wrote ([31], p. 226):
The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared, for its importance, with the invention of triple coordinates by Descartes. The ideas of this calculus, as distinguished from its operations and symbols, are fitted to be of the greatest use in all parts of science.
Not everybody, alas, was of the same mind, and some of the things said were pretty nasty (Lord Kelvin, letter to Hayward, 1892; see [38], Vol. II, p. 1070):
Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell.
Such robust language as Lord Kelvin's may now be largely forgotten, but the fact remains that the man in the street is strangely averse to using quaternions. Side by side withmatrices and vectors, nowthe lingua franca of all physical scientists, quaternions appear to exude an air of nineteenth-century decay, as a rather unsuccessful species in the struggle-for-life of mathematical ideas. Mathematicians, admittedly, still keep a warm place in their hearts for the remarkable algebraic properties of quaternions, but such enthusiasm means little to the harder-headed physical scientist.
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- Who Gave You the Epsilon?And Other Tales of Mathematical History, pp. 206 - 219Publisher: Mathematical Association of AmericaPrint publication year: 2009