In article <firstname.lastname@example.org>, Bill Dubuque <email@example.com> writes: > >Speaking of simultaneous discoveries in math, does anyone know >any historical works that explicitly study the reasons for such >remarkable confluences? E.g. > > o calculus (Newton and Leibnitz) > o geometric representation of complex numbers > (Argand, Buee, Gauss, Mourey, Warren, Wessel) > o non-Euclidean geometry (Bolyai, Gauss, Lobatchevsky) > o Hilbert's 10th problem (Chudnovsky, Matiyasevich) > o Kolmogorov complexity (Solomonoff, Kolmogorov, Chaitin) > I would say that major advances of this sort don't come out of the blue, they only happen when a sufficient "critical mass" of background material has been generated. Of course it still takes then a gifted individual to see the connections in what's already known and recognize where they lead, but there is certainly a significant probability that more than one such individual will be available.
So the confluence is there because all of them drink from the same river.
>I was going to close by quoting W. Bolyai's remark such that when the >time is ripe for certain ideas they blossom like violets in spring,
Mati Meron | "When you argue with a fool, firstname.lastname@example.org | chances are he is doing just the same"