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.

• How to measure Borel sets

  An attempt to present the early history of measure theory

• 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 What is also remarkable in Abel's unpublished paper on solvability is that he starts by specifying a general methodology for analysing the solvability problem, which is extremely natural, and that he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.)

• A description of Lorenzen's work in logic.

• A description of Herbrand's work in logic.