On the profession of a mathematician

The significance of mathematical methods in such disciplines as science, mechanics, physics or astronomy is well known. Also known to everyone is that mathematics is necessary in the practical work of engineers and technicians. Elementary knowledge of geometry or the ability to use symbolic formulas are necessary to almost all masters or qualified workers. Less clear for many is the question of what it means to have the speciality of a mathematician and to do mathematics itself as a primary profession.

Very many imagine that in textbooks and mathematical [dictionaries] are already collected enough formulas and rules for the solution of all sorts of mathematical problems that one comes across in practice. Even the very educated often ask [with incomphrension]: is it possible to make something new in mathematics?

That is why a mathematician is sometimes imagined to be a boring person, who has learned a large number of formulas and theorems, and whose task is to transfer the learned, ready knowledge to others.

In all this, the only truth is that mathematical knowledge, taught in high school and on the first steps of studying mathematics in college, were obtained by humans long time ago. But even those simplest of mathematical knowledge can be used thoughtfully and usefully only when they are learned artfully, which means that the learner herself sees how it would be possible to get to them on her own.