In his pages, one can read for the first time a proposition which formally contradicts Euclid's postulate of the parallels.
For we knew from the very outset, with an absolute certainty, that Euclid's postulate is true.
The work of commentary on Euclid's postulate was decried, it was excluded from the sphere of true mathematical research, and it vegetated, marginalized, at the outermost bounds of true mathematical life.
In these circumstances, it really seems very strange that work on the commentary on Euclid's postulate never stopped, despite repeated setbacks.
Like Euclid's postulate, there is no known way (pace the harmonic series and other red herrings) to "prove" the Resolution Axiom, which is to say that there is no known way of deriving it from a simpler principle, which is to say that, if we decide - or are compelled by personal or cultural circumstance - to alter, replace, deny, or affirm the Resolution Axiom, we will not obtain a contradiction, but we will disclose a variety of valid "musical systems" each of which will be distinguished, at least initially, by precisely how we choose to alter, replace, deny, or affirm the Resolution Axiom.