Based upon six units, the Cluster ranges from pure and applied mathematics to mathematically orientated research in economics as well as interdisciplinary research. Identifying and addressing mathematical challenges of the 21st century is one of the key goals of the HCM, along with the promotion of early-career researchers in an independent and international environment. Established in 2006, it has since been successfully renewed twice, in 2012 and most recently in 2018, for an additional seven years.