The universality of applied mathematics
Design and development of novel and advanced mathematical, statistical and computational models and methods for solving problems with high impact on science, society and industry. This is the mission of the Institute for Computing Applications "Mauro Picone" of the Italian National Research Council (IAC-CNR).
In 1927 the mathematician Mauro Picone founded the IAC, CNR’s oldest institute and the first research institute in the world entirely dedicated to - what is nowadays called - applied mathematics. Not by chance, the IAC played a crucial role in the early development of computer science and operation research in Italy.
From the very beginning IAC’s research activities were characterized by a vast spectrum of applications, but in the past decades two major developments have considerably increased the power of mathematics towards applications. Fist of all, the computational power of modern computers has caused an enormous improvement of the efficiency of numerical simulations, a crucial step in the process of mathematical modeling. For example, simulations of both the cardio-vascular and the immune system are carried out at the IAC, with applications to drug development and personalized medical treatments. Secondly, the presence of huge amounts of data creates new challenges to mathematics: interpretation of data, the problem how to select the most relevant data, etc. A typical example is the human genome, and actually data from genetics are elaborated at the IAC in collaboration with biologists (DNA sequencing, etc.), again with numerous applications, such as treatments for diabetes.
From these few examples it becomes clear that biomedical problems represent a particular challenge to mathematics, due to both their extreme complexity and the presence of large amounts of data. Numerous research activities in this field are carried out at the Institute: tissue engineering, tumor growth, Alzheimer’s disease, just to mention a few of them. In addition the IAC has advanced knowhow concerning medical imaging.
The high level of abstraction of mathematics, responsible for its well known reliability, makes it particularly flexible towards applications. Indeed a great variety of applications is treated at the IAC, such as cultural heritage (monitoring of historical buildings), economics and finance (optimal management of the national state debt), environmental issues (forecast of earthquakes, how to slow down a hurricane, elaboration of satellite data, etc.), transport and logistics (optimization of transportation systems, intelligent traffic systems, etc.), social sciences (behavior of crowds in emergencies), etc.
Recently the Institute has created the Mathematical Desk for Italian Industry, financed by the Italian Ministery of Education, University and Research: through a virtual desk, managed by a team of young researchers, private firms (including small and medium enterprises) may apply for a consultancy in mathematics. In addition the team of researchers actively promote scientific interactions between industry and the national mathematics community.