Can we predict the future? Can we see the invisible? To some extent, and in a certain sense, yes! With the help of mathematical formulae and computer programmes the principles of change can be statistically captured or simulated, producing virtual models providing insights into processes in distant places. Time and scale barely play a role. Subatomic elementary particles that change ultrafast or the evolution of galaxies from the Big Bang to the far future which can be reconstructed in computer simulations are examples of theoretical models.
In the Leibniz Assoication mathematical models and simulations are largely utilised for highly-complex physical and technological processes which cannot be directly calculated using simple physical formulae. In addition, statistical methods for medical and financial problems are also developed.