Editorial introduction: Malcolm MacCallum at 60

Studies in History and Philosophy of Science Part A, 1993

'For a fascinating contemporary discussion of the crisis in the Mathematical Tripos and the relationship between the teaching of mathematics to Natural Sciences and Mathematics students see, 'Discussion of the Report of the Special Board of Mathematics on the Mathematical Tripes',

arXiv (Cornell University), 2022

General Relativity and Gravitation, 2006

Philosophia Mathematica, 2005

Springer Proceedings in Mathematics & Statistics, 2014

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

American Institute of …, 2008

2002

150 yearsafter the discovery of quaternions, Hamilton’s conjecture hat quaternions are a fundamental language for physics is reeva luated and shown to be essentially correct, provided one admits complex numb ers in both classical and quantum physics, and accepts carrying along t he in ricacies of the relativistic formalism. Examples are given in classi cal dynamics, electrodynamics, and quantum theory. Lanczos’s, Einstein ’ , a d Petiau’s generalizations of Dirac’s equation are shown to be very nat urally formulated with biquaternions. The discussion of spin, isospin, and ma ss quantization is greatly facilitated. Compared with other formalisms, biqu aternions have the advantage of giving compact but at the same time explicit for mulas which are directly usable for algebraic or numerical calculation s.

Boston Studies in the Philosophy of Science, 2007

arXiv (Cornell University), 2008

General Relativity and Gravitation