Visualization as an Intuitive Process in Mathematical Practice

In the field of the philosophy of mathematics, in recent years, there has been a resurgence of two processes: intuition and visualization. History has shown us that great mathematicians in their inventions have used these processes to arrive at their most brilliant proofs, theories and concepts. In this article, we want to defend that both intuition and visualization can be understood as processes that contribute to the development of mathematical knowledge as evidenced in the history of mathematics. Like intuition, visualization does not have a definition, and its role has become more prominent both in pure mathematics and in educational research. For us, both visualization and intuition are processes that start from the real world of those who “intuit” or “visualize,” require experience and knowledge of concepts and theories (the more expertise in the subject, the more profound the results will be) and must, in the end, be validated by the specialized academic community. In this article, we defend the importance of visualization in mathematical practice and its role in the advances of great scientists (Euclid, Euler, Galileo, Descartes, Newton, Maxwell, Riemann, Einstein, Feynman, among others) as an alternative and valuable way to symbolic thinking, which has “reigned” in the academic and scientific community.