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 analyse 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 relatively informal way to pave future discussions and collaborations between mathematicians and biologists studying ageing.

生命系统受制于时间之箭；从出生开始，他们就在不断的生存斗争中经历复杂的转变（自组织），但不可避免地衰老和疾病使他们陷入死亡。衰老可以被理解并最终逆转吗？可以使用哪些工具来进一步了解衰老？本文邀请生物学家和临床医生考虑关键的概念思想和计算工具（数学家和物理学家都知道），它们可能有助于剖析衰老和疾病的一些潜在过程。具体来说，我们首先讨论如何对复杂系统进行分类和分析，并强调使复杂系统难以研究的关键理论难题。随后，我们介绍了拓扑数据分析——一种新颖的大数据工具——它可能有助于研究复杂系统，因为它通过拓扑考虑以整体方法从数据中提取知识。这些概念性思想和工具以一种相对非正式的方式进行讨论，为研究衰老的数学家和生物学家之间的未来讨论和合作铺平了道路。