Between the following two extremes, where do you stand?

A good mathematician knows much the subject and solve many given problems.

A good mathematician knows little, but can solve the problems when needed.

As Professor Sayan discussed in his lecture, mathematics is a formal science, meaning that it has a theoretical and abstract world of itself. Mathematical expressions, symbols and other elements exist independently of the human mind. Therefore, mathematicians do not create anything new, they just find out the existing entities. In mathematics, discovering relations, patterns, properties and structures is more important than knowing the subject. In line with this, it can be said that if one knows how to formulate a mathematical problem and how to relate the given parameters with the models components, one can solve the problem with little knowledge about the real system that the model represents. Most of the time, basic concepts of mathematics are enough to answer the given problem. For instance, a person who is skilled at constructing equations can solve many problems independent of her subject. To conclude, a good mathematician is the one who knows little about the subject, but use her mind to solve the problem when needed rather than the one who knows much about many subjects.