Talk:Hilbert's seventh problem
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The 7th problem of Hilbert was solved completely and independently by Gelfond and Schneider. They used slitely different methods. While Schneider only used the addition theorem of the exp-function exp(x+y)=exp(x)exp(y), Gelfond used also the differential equation e'=e. Later Schneider used Gelfond's Methode to prove other results, e.g. an analogue to the Gelfond-Schneider Theorem (Hilbert's 7th problem) for elliptic function.
The translation at http://aleph0.clarku.edu/~djoyce/hilbert/problems.html#prob7 gives the statement in the form to which I've corrected it (i.e. b irrational algebraic). So I believe Gel'fond/Schneider solved the problem as stated (end of para 7 of the reference).
Charles Matthews 12:08, 10 Dec 2003 (UTC)
