What is it about?

Mathematics is not a set of formal rules for the manipulation of symbols and the mere calculation of numbers. Mathematics has primarily to do with ideas, intuition, imagination and with the understanding of the more hidden and profound aspects of the world. Moreover, mathematics is a a way of exploring new unknown territories of the world, and a particular way of uncovering new possible worlds. Mathematics is, likewise somehow music or philosophy, an art of human understanding.

Featured Image

Why is it important?

Modern mathematics encompasses many very deep ideas about the universe, the physical reality, the biological world and many other subjects. It can be said that, in some sense, mathematics is an holistic and artistic activity, first because different source inspire the mathematical reflection and work, such as intuition, imagination, reasoning, visualization, classification, and second because is a way of discovering unknown properties of the world, creating new forms and concepts, educating peoples to be curious, modest and humanistic. In mathematics imagination and rigor are both very important. There is non separation between pure mathematics and applied mathematics, for, in fact, every mathematical idea can be extraordinarily imaginative and at the same time it can be very concrete, that is deeply related with our everyday life.

Perspectives

I wrote this article inspired especially by the work of Riemann, Poincaré, Weyl, Thom and Thurston. My goal was to stress the importance of intuition and visualization in mathematical work, in discovering new concepts and facts as well as in demonstrating their well-foundnness and deep interest. I want to underline the fact that mathematics is an important bridge between our conceptual possibilities of thinking about the world and different phenomena and the discovering of new properties and behaviors of spaces and numbers.

Luciano Boi
Ecole des Hautes Etudes en Sciences Sociales

Read the Original

This page is a summary of: The Role of Intuition and Formal Thinking in Kant, Riemann, Husserl, Poincare, Weyl, and in Current Mathematics and Physics, Kairos Journal of Philosophy & Science, December 2019, De Gruyter,
DOI: 10.2478/kjps-2019-0007.
You can read the full text:

Read

Contributors

The following have contributed to this page