the open field

The phrase "the theory of ambiguity" occurs in the testamentary letter Evariste Galois wrote to a friend, Auguste Chevalier, on the night before Galois was shot in a duel in 1832.  He was twenty years old.

"This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind." Hermann Weyl, Symmetry, Princeton University Press, 1952

There is always some kind of Galois theory that is responsible for our understanding of the situation, or rather: the measurement of our inability to understand the situation

Gunther Cornelissen

 You know, my dear Auguste, that these subjects are not the only ones I have explored. My reflections, for some time, have been directed principally to the application of the theory of ambiguity to transcendental analysis. It is desired see a priori  in a relation among quantities or transcendental functions, what transformations one may make, what quantities one may substitute for the given quantities, without the relation ceasing to be valid. This enables us to recognize at once the impossibility of many expressions which we might seek. But I have no time, and my ideas are not developed in this field, which is immense.

Print this letter in the Revue Encyclopédique.

I have often in my life ventured to advance propositions of which I was uncertain; but all that I have written here has been in my head nearly a year, and it is too much to my interest not to deceive myself that I have been suspected of announcing theorems of which I had not the complete demonstration.

Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of the theorems.

Subsequently there will be, I hope, some people who will find it to their profit to decipher all this mess.

J t'embrasse avec effusion.
                        
                                                     E. Galois.   May 29, 1832.