  Boosting is a highly successful ML-born optimization setting in which one is
required to computationally efficiently learn arbitrarily good models based on
the access to a weak learner oracle, providing classifiers performing at least
slightly differently from random guessing. A key difference with gradient-based
optimization is that boosting's original model does not requires access to
first order information about a loss, yet the decades long history of boosting
has quickly evolved it into a first order optimization setting -- sometimes
even wrongfully \textit{defining} it as such. Owing to recent progress
extending gradient-based optimization to use only a loss' zeroth ($0^{th}$)
order information to learn, this begs the question: what loss functions can be
efficiently optimized with boosting and what is the information really needed
for boosting to meet the \textit{original} boosting blueprint's requirements?
  We provide a constructive formal answer essentially showing that \textit{any}
loss function can be optimized with boosting and thus boosting can achieve a
feat not yet known to be possible in the classical $0^{th}$ order setting,
since loss functions are not required to be be convex, nor differentiable or
Lipschitz -- and in fact not required to be continuous either. Some tools we
use are rooted in quantum calculus, the mathematical field -- not to be
confounded with quantum computation -- that studies calculus without passing to
the limit, and thus without using first order information.
