History of mathematics
Some very preliminary texts on history of mathematics.
A note on the history of Boolean valued models
which tries to describe some early attempt of Church to get an independence
proof of the axiom of choice. It will be interesting to see if Gödel had
similar attempts, and if he was in contact with Church about this problem.
A note describing Abel's general description of solvable
equations of prime degree. There are wonderful papers by Skau and Gårding, and by
Edwards on this topic. As explained in this paper, Abel's approach was rather different
than the one of Galois: no use of group theory (sometimes this can be an advantage, like
for the description of primitive solvable equations), and the goal was not to give a criteria
of solvability, but to list all solvable equations. What is also remarkable in Abel's unpublished
paper on solvability is that he starts by specifying a general methodology for analysing the
solvability problem, which is extremely natural, and that he follows then in a systematic way. A Here is an older version.
Both Abel and Galois saw the beginning of the theory of Abelian functions in one
formula which generalizes Euler addition formula for elliptic functions. This note
tries to describe this addition formula. (It contains an example that was described as
one of the "most remarkable case" in a letter from Abel to Crelle.)
Last modified: Fri Sep 13 22:08:32 MET DST 2002