Calculations old-style

John Toland, Professor Emeritus, Department of Mathematical Sciences

Texas Instruments TI-92 symbolic calculator, c 1998.
Texas Instruments TI-92 symbolic calculator, c 1998.

Professor Toland remembers the TI-92 Symbolic Calculators of Edward Fraenkel.

Although trained as an aeronautical engineer, Edward Fraenkel [1] showed no interest in numerical and high-performance computing methods that promised to yield accurate approximations to solutions of otherwise impenetrable nonlinear equations. He simply did not trust computer packages because there was no way of knowing how, or how well, they had been programmed and, throughout his long life, preferred manual calculations as an aid to understanding. Thus, when he saw what calculations were needed, no matter how daunting, laborious and apparently tedious they appeared to be, he was in control and committed to devoting the countless hours demanded by the task.

Since some of these calculations were excruciatingly complex, in 1998 he compromised by buying a TI-92 which was the first Texas Instruments symbolic calculator, and one of the first to offer 3D graphing. In fact by 1998 the TI-92 was already obsolete, that year being replaced by the smaller, faster TI-92 Plus. But from 1998 onwards, Edward painstakingly evaluated functions using the TI-92 and plotted their graphs by hand, in a quest for insights that would render such considerations redundant.

Texas Instruments *TI-92* calculator

While reflecting his deep apprehension about trusting mathematics to mere machines, in the Introduction to his important paper [2] on the existence of Stokes wave of extreme form he acknowledged this debt to the TI-92 when he wrote:

"Throughout the paper, results depend on the numerical evaluation and numerical integration of functions defined by explicit formulae. (These calculations were all done with a Texas Instruments TI-92 calculator.) Therefore, purists may believe that the theorems in the paper have not been proved. I have much sympathy with this point of view, but it seems unlikely that, without numerical evaluation of known functions, a construction as direct as that in this paper could be obtained".

When his machine finally failed in 2013, his colleague Geoff Smith sought a reconditioned TI-92 for him on the web. Edward’s only stipulation had been that it should be absolutely identical to the one he had already used and understood. He was delighted with the outcome and used it until his death in 2019. Both his TI-92 machines, from 1998 and 2013 and an instructional manual, are in the Edward Fraenkel Collection.

[1] G. R. Burton; J. F. Toland. LUDWIG EDWARD FRAENKEL 28 May 1927-27 April 2019. Biogr. Mems. Fell. R. Soc. 69 (2020), 175-201.

[2] L. E. Fraenkel. A constructive existence proof for the extreme Stokes wave. Arch. Ration. Mech. Anal. 183 (2) (2007), 187-214.

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Texas Instruments TI-92 symbolic calculator, c 1998.
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