Since we're on this kind of thing, can I also ask about the Cantor set?
My feeling, based on no reliable knowledge, is that it is in a footnote in
??, where he refers to it in a rather offhand kind of way, as if it was a
well-known construction.
On the other hand, a variant of it, a non-closed 'end nth' rather than a
closed 'middle third' set, was given in:
HJS Smith, On the integration of discontinuous functions, Proceedings of
the London Math Soc 6 (1875) 140-153.
Smith's examples were spot on; he even went on to give another now-standard
counterexample using the 'thick' Cantor (Smith?!) set. Apparently the
reviewer (who was he?), perhaps not expecting anything of insight on
analysis to come from Britain at that time, misunderstood the implications
of the paper, gave it an indifferent review in the Fortschritte der
Mathematik, and it was forgotten.
Smith was one of the remarkable but unsung men of mathematical insight in
England at that period. He also - again my details are hazy, so I won't try
to be more precise - solved a Paris Academy prize problem on number theory
before it had been proposed, and certainly before Minkowski (? Poincare?)
won the prize for it! He only got credit posthumously.
Again, details are hazy, and I don't have access to reference books before
tomorrow, when I won't have time. Could anyone fill in the details and
corrections?
David Fowler
PS This reminds me of the problem: Name six English pure mathematicians of
the 19th century.