Computation by Hand in the Computer Era

New calculation by hand after a long time…Already some decades in the computer era, it is not at all surprising that scientific research is mainly done through computers. In fact it has often been their first context of development!

Even in Theoretical and Mathematical Physics, computations are increasingly done through sophisticated softwares, regardless whether they are of numerical or symbolic nature. Numerical computations are the ones made with pure numbers. They are the easiest to implement in a program and so the most widely applicable. However, they can be only instances of general mathematical expressions, which use instead algebra to indicate any number. Moreover, given the infinite character of numbers, numerical computations are typically only approximate.

Softwares can also make symbolic computations, expressed through algebra and exact numbers. Recently, developments in machine learning have also allowed automation of highly abstract tasks like formal rigorous proofs. Still, mathematical teaching in both schools and universities, appears almost slumbering, slow to catch the full power of the technological revolution…For the poor students, math consists mainly of long, tedious and risky computations by hand, which nowadays in the real work are perfectly done on computers. Certainly some innovation in math teaching is highly desirable!

Yet…computers need developers! After all, traditional math teaching could not be completely replaced. Delving in the details of a computation is often the only way to truly understand it and also to imagine modifications of it, thus stimulating creativity and allowing research!