Hilbert's famous 24th problems handles the problem of the simplest possible proof of a mathematical statement, in a nutshell.
It is said that there are a few problems with this problem. First of all, which problems arise from this problem?
Besides that, I'm wondering, can't we just define the simplest proof of a statement as the least number of times axioms are used + the number of axioms used in the non axiom statements used in a proof?
To prove statement A we need 3axiom 1 + 2statement B
And to proof statement B we need 1axiom 1 + 2axiom 2.
Hence we need 9 axioms to prove statement A? (Assuming this is the minimum. There may also be another proof using axiom 3, but this proof needs 12 axioms, this it's not the minimum).
It seems to be a very reasonable way of defining the simplicity of a proof, and I don't see any way how it could lead to contradictions or interpretations.
Nevertheless I'm always open for corrections, since I'm just an amateur, passionate about math.