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In order to appreciate how well off we mathematicians and scientists aretoday, with extremely fast hardware and lots and lots of memory, as well aswith powerful software, both for numeric and symbolic computation, it may be agood idea to go back to the early days of electronic computers and compare howthings went then. We have chosen, as a case study, a problem that wasconsidered a huge challenge at the time. Namely, we looked at C.L. Pekeris'sseminal 1958 work on the ground state energies of two-electron atoms. We wentthrough all the computations ab initio with today's software and hardware, witha special emphasis on the symbolic computations which in 1958 had to be made byhand, and which nowadays can be automated and generalized.

The 1958 Pekeris-Accad-WEIZAC Ground-Breaking Collaboration that Computed Ground States of Two-Electron Atoms (and its 2010 Redux)