  Living systems are subject to the arrow of time; from birth, they undergo
complex transformations (self-organization) in a constant battle for survival,
but inevitably ageing and disease trap them to death. Can ageing be understood
and eventually reversed? What tools can be employed to further our
understanding of ageing? The present article is an invitation for biologists
and clinicians to consider key conceptual ideas and computational tools (known
to mathematicians and physicists), which potentially may help dissect some of
the underlying processes of ageing and disease. Specifically, we first discuss
how to classify and analyze complex systems, as well as highlight critical
theoretical difficulties that make complex systems hard to study. Subsequently,
we introduce Topological Data Analysis - a novel Big Data tool - which may help
in the study of complex systems since it extracts knowledge from data in a
holistic approach via topological considerations. These conceptual ideas and
tools are discussed in a rather informal way to pave future discussions and
collaborations between mathematicians and biologists studying ageing.
