## Remembering John Todd

**December 17, 2007**

John Todd, 1911–2007

**Philip J. Davis**

His long life spanned two computational regimes---pre- and post-electronic digital computers---and, within each, through computation, research, administration, and teaching, he left a significant mark.

Consider the computational milieu in which he worked as a young man for the British Admiralty. At the mathematical laboratory at the University of Edinburgh, established by E.T. Whittaker around 1912, students were advised to provide themselves with a pad of squared paper and Barlow's and Crelle's multiplication tables. Computation was done in such places as the NPL (National Physical Laboratory) and the Admiralty. Apart from specific scientific computations, producing tables of special functions was a major industry. In his war work in the British Mine Design Department, as Jack reported in his *History of Computation* [2], he used the (American) WPA tables of special functions; all scientific computational projects made substantial use of tables, these and others, that had been computed some years before.

Fletcher, Miller, Rosenhead, and Comrie's *An Index of Mathematical Tables* was on all of our desks at that time, and the journal MTAC (*Mathematical Tables and Other Aids to Computation*) was prominent. Table making lasted well into the '60s; the very popular NBS *Handbook of Mathematical Functions* (a.k.a. Abramowitz and Stegun), containing tables, came out in 1964.

Jack grew up in the computational era of slide rules, tables, planimeters, multi-parameter graphs, adding machines, on which, if one were lucky, multiplication might be done without manual shifting of the registers. To compute the eigenvalues of a 3 x 3 matrix was not a job to be taken lightly, and a 6 x 6 was a virtual impossibility or at least a cause of heartburn. This was the era of the famous (1948) paper of von Neumann and Goldstine on the solution of n x n systems of linear equations; the authors were quite pessimistic about the possibility of numerical solution for high values of n.

In 1938, Jack married Olga Taussky, a PhD from the University of Vienna and a refugee from the Nazi regime. I suspect that their interest in the Gershgorin circle theorem of 1931 was motivated by the difficulties of computing eigenvalues.

Around 1948, John Curtiss, a probabilist and a student of J.L. Walsh, was named head of the National Applied Mathematics Laboratories of the National Bureau of Standards (now NIST). Building on a core group from the late-'30s WPA Tables Project who had moved from New York to Washington, Curtiss put together what was certainly the first substantial American group dedicated to the study of numerical methods vis-à-vis the potentialities of the new computers. The National Physical Laboratory in England was another such place.

In 1949, Curtiss hired Jack to head the Computation Laboratory at NBS, and Olga Taussky Todd as a consultant. That is where, a few years later, I met up with the couple. From 1954 to 1957 Jack was chief of the Numerical Analysis Section. Jack, my boss, was open and affable, whereas Olga was shy and a bit remote.

On arriving at NBS in 1952, I found several senior mathematicians: Along with the Todds were Milton Abramowitz, Irene Stegun, Churchill Eisenhart, Ida Rhodes, Ted Motzkin, Ky Fan. Among my contemporaries were Alan Hoffman, Morris Newman, Karl Goldberg, Henry Antosiewicz, Marvin Zelen, and a bit later, Philip Rabinowitz, Walter Gautschi, Peter Henrici, John Rice, Marvin Marcus, Emilie Haynsworth, Joan Rosenblatt.

We had a steady stream of visitors, often from abroad, all mathematicians of the first class who had or developed a deep interest in computation. I can cite Eduard Stiefel, Helmut Wielandt, Alexander Ostrowski, and J.M. Synge. Mina Rees and Marc Kac, members of the advisory committee to our group, played active roles in suggesting future visitors.

In the mid-'50s, computers and computation laboratories were beginning to appear at universities where previously a single, heavy, rusty, dusty adding machine might have been found in the office of the professor of astronomy. Toward the end of his stay at NBS, Jack conceived the idea of running a training program for future directors of academic computing labs. He received NSF support for the program, which was run in 1957 with great success; about ten people spent three months at the NBS campus listening to lectures by NBS staff and doing hands-on stuff. Inheriting the program from Jack, I repeated his formula in 1959 and was equally gratified by the results. This program sounds quaint now and seems not to be mentioned in the various John Todd write-ups I have seen.

Now fast-forward a half century. Table making is dead as a doornail, the activities of, for example, the Tables Committee of the British Association for the Advancement of Science having lasted from 1871 to 1965. MTAC has had a face-lift. Computation has been chipified, is done at nano-speed and faster, and is cheap and universally available. Trips to Mars would have been impossible without computer guidance and control. To the practice of scientific computation, one of Jack's students, Cleve Moler, has contributed with his MATLAB packages to the ease and delight of numerical analysts and scientists. The whole world has become mathematized, computerized, chipified, cyber-gadgetized, for better and, not infrequently, for worse.

In the years following Jack and Olga's departure from Washington, I moved to Providence and a professorship at Brown and saw the couple only sporadically at national meetings. In 1997, two years after Olga's passing, I met Jack and his companion Rosemary Lonergan in Vienna. Together with Christa Binder and Peter Schmitt, both Viennese mathematicians, we heard a talk by Roger Penrose about the brain. The next day we all went to Nussdorf and by tram to a "Heurigen," where we sat outside, drank wine and ate cold cuts. Although I met up with Jack several times later, I end this piece with the pleasant recollection of the five of us sitting in the fresh air and enjoying the fine Viennese food and drink.

**References**

[1] O. Taussky-Todd, *An autobiographical essay: The truth, nothing but the truth, but not all the truth*, in *Mathematical People*, D.J. Albers and G.L Alexanderson, eds., Birkhauser, Boston, 1985.

[2] J. Todd, *The prehistory and early history of computation at the NBS*, in *A History of Scientific Computation*, S.G. Nash, ed., Addison Wesley, Boston, 1990, 251–268.

*Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at **[email protected]**.*