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

In order to appreciate how good we as mathematicians and scientists have it today, with extremely fast hardware and lots and lots of memory, as well as with readily available high-level software, both for numeric and symbolic computation, it may be a good idea to go back to the early days of electronic computers and carefully examine, as a case study, a problem that was considered a huge challenge back then, and compare notes. We chose C.L. Pekeris' 1958 seminal work on the ground state energies of two-electron atoms. All computations will be done ab initio with today's software and hardware, with a special emphasis on the symbolic computations which in 1958 had to be made by hand, and which nowadays can be automated and generalized.