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Harold V. McIntosh

16 December 2015

Harold V. McIntosh died November 30, 2015 in Puebla, Mexico. He was an American mathematical physicist who became interested in what is now known as computer algebra to solve problems in physics, leading to his early adoption of the programming language LISP and to programming language design. In addition, his deep understanding of Weyl’s theory for second order differential equations, Schrödinger quantization as an eigenvalue problem and his proposed computational scheme for Weyl’s m-function provided a novel way to investigate metastable states in atomic and molecular physics and reformulate standard scattering theory from a new angle.

McIntosh was born in Colorado in 1929. In 1949 he received a B.Sc. in physics from the Colorado Agricultural and Mechanical College, and in 1952 he received a M.Sc. in mathematics from Cornell University.

Mac (as he preferred to be called) was widely regarded for his research, writing and teaching. Even as a graduate student his gift for inducing people to learn was evident. In a profile of Sheldon Glashow published in The Atlantic Monthly in 1984,1 Glashow asserted that what he learned as an undergraduate at Cornell from Mac about group theory “was as relevant as any course [he] took there.”

Mac did further graduate studies at Brandeis, but stopped before receiving a Ph.D. to take a job at the Aberdeen Proving Ground. Two years later, he moved to RIAS (Research Institute for Advanced Studies), a division of the Glenn L. Martin Company. Around 1962 he accepted a position in the Physics and Astronomy department and the Quantum Theory Project at the University of Florida. After two years at the University of Florida, Mac was invited to work in Mexico, where he was offered “access to all the computer time he could use,” an offer that, he said, was fully honored.

Mac worked from 1964 to 1965 at the Department of Physics of the CIEA del IPN, now Cinvestav (Center for Research and Advanced Studies of the National Polytechnic Institute); the design and implementation of the programming language CONVERT took place during this period. From 1965 to 1966, Mac was director of the programming department at the Electronic Computing Center of the National Autonomous University of Mexico, where he designed and developed the programming language REC.

Over the following nine years, Mac was a professor at the School of Physics and Mathematics (ESFM) of the IPN, where he became coordinator of the Applied Mathematics group. Under his guidance, compilers for REC were built for newer computers arriving at the IPN’s CeNaC (National Computing Center), and he personally developed software packages for use in the various courses he taught. Of fourteen bachelor’s theses he directed at the ESFM, one stands out for having been published as three separate articles in the Journal of Mathematical Physics, one of which2 discusses a problem in a class that is now called “MICZ Kepler systems”, the initials standing for McIntosh, Cisneros and Zwanziger. Also from this period, Mac’s paper Symmetry and Degeneracy3 was cited enthusiastically three times in the second edition of Herbert Goldstein’s renowned classical mechanics book.4 He took a one-year leave from ESFM in 1972 to obtain his Ph.D. in Quantum Chemistry, which was awarded with the highest distinction, at Uppsala University. Mac’s contributions to the Uppsala Resonance Group led to several doctoral dissertations in Sweden.

Between 1970 and 1975 Mac was also a consultant at the National Nuclear Energy Institute (INEN, now ININ), and in 1975 he and his group moved to the Autonomous University of Puebla (UAP), where he founded the Department of Microcomputer Applications in the UAP’s Institute of Sciences, and where he remained until his passing. He taught courses to computer science students from UAP’s School of Physical and Mathematical Sciences and over the last two and a half decades his interests turned to the study of cellular automata, in which he also became a recognized expert.

Mac will be missed by his friends, colleagues and former students, especially for his lifelong dedication to teaching, high standards and uncompromising principles.

1. R.P. Crease and C.C. Mann, “How the Universe works,” The Atlantic Monthly, Aug. 1984, pp. 66–93.

2. H.V. McIntosh and A. Cisneros, “Degeneracy in the Presence of a Magnetic Monopole,” J. Math. Phys. 11, 896–916 (1970).

3. H.V. McIntosh, “Symmetry and Degeneracy,” in Group Theory and its Applications, Vol. 2, Ernest M. Loebl, ed. (New York: Academic Press, 1971, pp. 75–144)

4. Herbert Goldstein, Classical Mechanics, 2nd. ed. (Reading, MA: Addison-Wesley, 1980).

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