An Unlikely Marriage of Mathematicians and Computers

By: Keith Devlin @profkeithdevlin

These days, anyone entering the field of mathematics, either as a researcher, practitioner, or educator, expects to make extensive use of digital technology. But it wasn’t always that way, at least for pure mathematics researchers and the majority of math educators. Though mathematicians invented the modern computer as a theoretical entity, and a few of them helped build the first digital computers, pure mathematicians and math educators as a whole lagged far behind scientists, engineers, and other professionals in actually using them. 

The May/June 1988 issue of the AMS Notices introduced a new special section on “Computers and Mathematics

Recognizing that the field was in danger of falling too far behind, in May 1988, the American Mathematical Society launched a new section in its newsletter Notices, sent out to all members (mainly university-based math researchers and educators) ten times a year, titled “Computers and Mathematics”. Its aim was to promote the use of computers by mathematicians and provide them with information about the many new mathematical software systems being developed.

The section was initially edited by the Stanford mathematician Jon Barwise, who ran it until February 1991, after which the AMS asked me to take it over. I held the reins from the March 1991 issue until the AMS and I decided to end the special section in December 1994. That six-and-a-half-year run achieved the intended goal. By the time the special section wound up, the computer had become a staple tool for mathematicians, both in research and teaching.

The AMS special section initially arose in a round-about way. The one use of computers that mathematicians jumped on early was to write (symbol-laden) mathematical papers, books, lecture notes, and exams, and a number of products rapidly became available, with Donald Knuth’s powerful TeX math typesetting program being the tool of choice for hard-core mathematicians.

In 1987, Richard Palais of Brandeis University wrote a series of articles for the AMS Notices, surveying the various mathematical word processing systems that were available at the time. The interest in those articles was sufficiently strong for mathematicians at the AMS to start talking about the Society taking a pro-active role in helping the community take advantage of the new working possibilities that computers were starting to offer, not only in preparing manuscripts but in teaching and research. That led to a decision for the Notices to introduce the regular section “Computers and Mathematics”, that would serve both to provide inspiration for mathematicians to make greater use of computers, and to act as an information exchange for the various possibilities computers offered in their work. The goal was to jump-start “trickle-down computer use” in the mathematics community.

Jon Barwise (1942-2000) was the first editor of the AMS Notices “Computers and Mathematics” section, which he edited from June 1988 to February 1991.

That same year, 1987, was also when I moved from the UK to the United States, to spend a year as a Visiting Professor at Stanford. My host, Jon Barwise, was the mathematician the AMS asked to edit the new Notices section, and the two of us talked about the upcoming new column on a number of occasions. 

As mathematicians, we both had spectators’ interest in the use of computers within traditional mathematics—indeed, Barwise attended the lavish event launching Steve Wolfram’s new mathematical software system Mathematica on June 23, 1988—but our main interests took different forms. Barwise’s interest was primarily that of a logician, and he soon began working on the development of  instructional software to teach formal logic. My focus was more as part of my growing interest in what would become known as mathematical cognition, where the focus was on studying mathematics as a mental tool, looking at how it arose, and how it related to, fitted in with, and complemented other forms of thinking. From that standpoint, the use of computers to assist in doing mathematics was but one component of what I (and others) would end up calling “mathematical thinking”. 

The “Computers and Mathematics” section launched in the May/June 1988 issue of the Notices, with Barwise leading off with an essay in which he declared that the goal was to reflect, both practically and philosophically, on cases where computers were affecting mathematicians and how they might do so in the future; to act as an information exchange into what software products were available; and to publish mathematicians’ reviews of new software.

In May/June 1988, Jon Barwise launched the new AMS Notices “Computers and Mathematics” section

Barwise edited the section through to February 1991, after which the AMS asked me to take it over. I held the reins from the March 1991 issue until the AMS and I decided to end the special section in December 1994. The reason? That six-and-a-half-year run of the special section had achieved the intended goal. The computer had become a staple tool for mathematicians, both in teaching and research.

The general format of each column was to start with some form of editorial comment, then, frequently, a feature article solicited by the editor, and then a number of reviews of new mathematical software. In all, we published 59 feature articles, 19 editorial essays, and 115 reviews of mathematical software packages (31 features, 11 editorials, and 41 reviews under Barwise,  28 features, 8 editorials, and 74 reviews under me).

When he introduced the last section he edited, Barwise wrote:

Whether we like it or not, computers are changing the face of mathematics in radical ways, from research, to teaching, to writing, personal communication, and publication. Computers are even forcing us to expand our idea about what constitutes doing mathematics, by making us take much more seriously the role of experimentation in mathematics. … Whether we applaud or abhor all these changes in mathematics, there is no denying them by turning back the clock, anymore than there is in the rest of life. Computers are here to stay, just as writing is, and they are changing our subject.

When I wrapped up the “Computers and Mathematics” section four years later, I wrote:

With its midwifery role clearly coming to an end, the time was surely drawing near when “Computers and Mathematics” should come to an end.  … The disappearance of this column does not mean that the Notices will stop publishing articles on the use of computers in mathematics. Rather, recognizing that the use of computer technology is now just one more aspect of mathematics, the […] Notices will no longer single out computer use for special attention. I’ll drink to that. The child has come of age.

In all, that particular mathematical revolution (for such is was) took just over six years from start to completion, an illustration in itself of the speed-things-up power of digital technologies.

NOTE: This post is abridged from my article “How mathematicians learned to stop worrying and love the computer”, in David Bailey, Naomi Borwein, Richard Brent, Regina Burachik, Judy-anne Osborn, Bailey Sims, Qiji Zhu (editors), From Analysis to Visualization, A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017, Springer 2020, pp.133-139. An online Keynote collection of historical images associated with that article can be accessed on iCloud here. (You do not need Keynote to view it. However, different browsers on different devices may change some fonts, resulting in less than optimal display. The same image collection is available in PDF format here.)