Fundamental scientific discoveries have been made with the help of com￾putational methods and, undoubtedly, more are to come. For example,
commonalities (universality) in the behavior of chaotic systems had not
been discovered or understood without computers. Only with numerical
computations is it possible predict the mass of the proton so accurately
that fundamental theories of matter can be put to test. And numerics
is not only used to determine the binding between atoms and molecules,
but has also led to new quantum-mechanical methods that revolutionized
chemistry and materials science. Such examples highlight the enormous
role of numerical calculations for basic science.