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Joel Moses

Abstract

Joel Moses (1941–2022) arrived in Brooklyn from Israel at thirteen, wrote a doctoral thesis under Marvin Minsky in 1967 on a program that integrated the way a calculus student does, and then spent eleven years directing Macsyma, the MIT system that made symbolic mathematics something a computer could be trusted with. Macsyma was the largest Lisp program of its day and the ancestor of every computer algebra system since; its free descendant, Maxima, is still maintained. Moses then ran MIT: head of electrical engineering and computer science from 1981, dean of engineering from 1991, provost from 1995 to 1998, Institute Professor from 1999. His late work asked why the flexibility that engineers build into systems always comes back as complexity, which is a fair summary of Macsyma too.

Petah Tikva to Brooklyn

Moses was born on November 25, 1941, in Petah Tikva in Mandatory Palestine, to Bernhard and Golda Moses, who had fled Nazi Germany. The family emigrated to Brooklyn in 1954, when he was thirteen. He went to Midwood High School and to Columbia, taking a bachelor’s degree in 1962 and a master’s in 1963, both in mathematics, then to MIT for a doctorate under Marvin Minsky.

The thesis, Symbolic Integration (1967), described a program called SIN. James Slagle’s SAINT of 1961, also from Minsky’s group, had integrated by heuristic search, trying transformations the way a student guesses. SIN was faster and more systematic: it tried cheap methods first, then a table of substitutions, and only then a general algorithm, and it integrated most of what a first-year calculus course contains in seconds rather than minutes. The question Minsky’s students were asking was whether a machine could do mathematics by reasoning; Moses’s answer was that for integration, at least, it could do better by knowing the algorithms. Robert Risch published a complete decision procedure for elementary integration in 1969, and Moses’s later work put the practical parts of it into software.

Macsyma

In July 1968 Carl Engelman, William Martin and Moses started Macsyma, Project MAC’s Symbolic Manipulator, on the AI Laboratory’s PDP-10 with ARPA money. Martin directed it until 1971 and Moses for the next decade. The design goal was a system a physicist or engineer could hand a page of algebra to and get a page back: simplification, factoring, symbolic integration and differentiation, series, solution of equations and differential equations, exact rational arithmetic, all in one interactive program. Written in Maclisp, it grew into what was probably the largest Lisp program in existence, and Moses’s 1971 paper “Algebraic Simplification: A Guide for the Perplexed” set out why the hardest part was the part users thought was trivial, deciding what “simpler” means. Calculations that had taken physicists months by hand took an hour. It ran on a time-shared machine at MIT that outside users reached over the ARPANET, which made it one of the first pieces of software with a national user community; the users’ conferences of the 1970s were where the field of computer algebra organised itself.

Ownership was the problem. MIT licensed Macsyma to Symbolics in 1982, the Lisp-machine company, and the product went down with the company (see The Lisp Machine Era); a 1982 copy distributed through the Department of Energy was kept alive by William Schelter at the University of Texas and released under the GPL in 1998 as Maxima, which is the version still in use. Maple and Mathematica took the market, and both were built by people who had used Macsyma and wanted something that ran on a machine they could afford. The systems and their lineage are covered in Computer Algebra Systems.

Running MIT

Moses became associate director of the Laboratory for Computer Science in 1974, associate head of Electrical Engineering and Computer Science in 1978, and head of the department in 1981, holding the job until 1989. He was dean of engineering from 1991 to 1995 and provost, the university’s chief academic officer, from 1995 to 1998; in 1999 MIT made him an Institute Professor, its highest faculty rank. He had been elected to the National Academy of Engineering in 1986 for symbolic algebraic manipulation and for leadership in engineering education.

The administrative record is specific. He pushed an “engineering with a big E” curriculum, set up the first five-year combined bachelor’s and master’s programmes, founded the Systems Design and Management programme, raised graduate stipends, and was one of the people who got the Stata Center built. He also ran an interdisciplinary Friday lunch series, the Moses Seminar, that Ronald Rivest later described as “exemplifying Joel and MIT at their finest.” In his later years he was acting director of the Engineering Systems Division, and his research in those years was on the structure of large systems: why layered hierarchies are easier to change than trees, and why, as Gerald Sussman put it in summarising him, every gain in flexibility is paid for in complexity.

He had met Peggy Garvey at an MIT party in 1968 and they were married for 52 years. Joel Moses died on May 29, 2022, aged 80, after years of Alzheimer’s and Parkinson’s disease.

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