milewski-ctfp-pdf
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Erronous claims about Dirac in the Preface
Time for a History of Mathematics lesson with one of it's most notorious debunkers, Mikhail G. Katz:
https://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot2010x-katz-cauchydirac.pdf
Quoting a small part from it:
"This remark is a reflection of a pervasive myth, to the effect that the physicists invented the delta function, and the theory of distributions legalized them after the fact many years later."
While this talks about something Bunge remarked, it applies to part of the Preface as well.
Sorry! But: I have a suggestion for coming up with a replacement remark, check here:
http://math.andrej.com/2008/08/13/intuitionistic-mathematics-for-physics/
Bump
It seems like the link to Tall's work doesn't work, but I was able to find his article. I'm not convinced, though. Cauchy might have anticipated the Dirac delta function, but he couldn't have made it rigorous. This had to wait until the work of Schwartz and Sobolev on the theory of distributions.