  As suggested by the title, the aim of this paper is to uncover the vast
computational content of classical Nonstandard Analysis. To this end, we
formulate a template $\mathfrak{CI}$ which converts a theorem of 'pure'
Nonstandard Analysis, i.e. formulated solely with the nonstandard definitions
(of continuity, integration, differentiability, convergence, compactness, et
cetera), into the associated effective theorem. The latter constitutes a
theorem of computable mathematics no longer involving Nonstandard Analysis. To
establish the vast scope of $\mathfrak{CI}$, we apply this template to
representative theorems from the Big Five categories from Reverse Mathematics.
The latter foundational program provides a classification of the majority of
theorems from 'ordinary', that is non-set theoretical, mathematics into the
aforementioned five categories. The Reverse Mathematics zoo gathers exceptions
to this classification, and is studied in [70,71] using $\mathfrak{CI}$. Hence,
the template $\mathfrak{CI}$ is seen to apply to essentially all of ordinary
mathematics, thanks to the Big Five classification (and associated zoo) from
Reverse Mathematics. Finally, we establish that certain 'highly constructive'
theorems, called Herbrandisations, imply the original theorem of Nonstandard
Analysis from which they were obtained via $\mathfrak{CI}$.
