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In Why are special functions special [Physics Today 54, 11 (2007); eprint], Michael Berry makes the following observations:

This continuing and indeed increasing reliance on special functions is a surprising development in the sociology of our profession. One of the principal applications of these functions was in the compact expression of approximations to physical problems for which explicit analytical solutions could not be found. But since the 1960s, when scientific computing became widespread, direct and “exact” numerical solution of the equations of physics has become available in many cases. It was often claimed that this would make the special functions redundant.

Now, this makes a lot of sense, and given that Berry was around as a researcher since 1965, it is reasonable to take this as a primary-source eyewitness account, but I would like to get a bit more flavour for the zeitgeist that Berry depicts in this paragraph (i.e., that the emergence of electronic computers would make special functions obsolete, with direct numerical solution of the problems replacing the special-function corpus). Is there a good primary source from the time showing this view, or (even better) a good review of the development of the viewpoint?

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    $\begingroup$ I don't really see the historical content here. Isn't this better asked at Math.Overflow, there you will probably find plenty who are eye-witnesses? $\endgroup$
    – Mozibur Ullah
    Commented Nov 27, 2020 at 19:03
  • $\begingroup$ On a broader theme, Lufkin in Human v. Machine (1967) noted that machine translation was "more or less dominated by the optimists" and consoled that "no one need fear that machines will replace translators any more than that computers will replace mathematicians". $\endgroup$
    – Conifold
    Commented Nov 28, 2020 at 9:50

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