  Model-independent methods in cosmology has become an essential tool in order
to deal with an increasing number of theoretical alternatives for explaining
the late-time acceleration of the Universe. In principle, this provides a way
of testing the Cosmological Concordance (or $\Lambda$CDM) model under different
assumptions and ruling out whole classes of competing theories. One such
model-independent method is the so-called cosmographic approach, which relies
only on the homogeneity and isotropy of the Universe on large scales. We show
that this method suffers from many shortcomings, providing biased results
depending on the auxiliary variable used in the series expansion and is unable
to rule out models or adequately reconstruct theories with higher-order
derivatives in either the gravitational or matter sector. Consequently, in its
present form, this method seems unable to provide reliable or useful results
for cosmological applications.
