  The perceived dichotomy between analytical and ab initio approaches to theory
in attosecond science is often seen as a source of tension and misconceptions.
This Topical Review compiles the discussions held during a round-table panel at
the 'Quantum Battles in Attoscience' CECAM virtual workshop, to explore the
sources of tension and attempt to dispel them. We survey the main theoretical
tools of attoscience -- covering both analytical and numerical methods -- and
we examine common misconceptions, including the relationship between ab initio
approaches and the broader numerical methods, as well as the role of numerical
methods in 'analytical' techniques. We also evaluate the relative advantages
and disadvantages of analytical as well as numerical and ab initio methods,
together with their role in scientific discovery, told through the case studies
of two representative attosecond processes: non-sequential double ionisation
and resonant high-harmonic generation. We present the discussion in the form of
a dialogue between two hypothetical theoreticians, a numericist and an
analytician, who introduce and challenge the broader opinions expressed in the
attoscience community.
