Yoshihiro Horihata is an associate professor of NIT, Yonago college. His work focuses on the mathematical logic, specifically reverse mathematics. He also interested in study of relations between the liberal arts and "mathematical attitude" which defined by himself.
National Institute of Technology, Yonago CollegePosition –
Associate professorTitle –
One of the reasons for studying mathematics is to acquire the ability to think freely.
In mathematics, one is free to formulate hypotheses as long as they are consistent (called axioms in mathematics). For example, in non-Euclidean geometry, the sum of the interior angles of a triangle can be greater than or less than 180 degrees. At first glance, this may seem counterintuitive, but it is equivalent to Euclidean geometry in terms of consistency. On the contrary, non-Euclidean geometry is an indispensable theory for the theory of relativity.
Hypothesis is not a concept used only in mathematics and science. Many hypotheses are used in our thinking, both explicitly and implicitly. Hypotheses enable us to think, but sometimes they constrain our thinking.
In the former sense, a person's hypothesis is his/her worldview. In response to this positive aspect of hypotheses, we call the attitude of confronting the world with the idea that "everything is a hypothesis" the "mathematical attitude" in this study. The reason for this is that in mathematics, there is freedom in setting up hypotheses, and all proofs of mathematical theorems start from axioms.
The latter can be freed by becoming aware of the implicit hypotheses within oneself and relativizing or abstracting them. This awareness is the essence of thinking freely. Therefore, it is an important part of the liberal arts.
In this presentation, I will discuss the relationship between "mathematical attitude" and liberal arts, and report on the importance of mathematics education.
The development of technology is changing society. The great social changes that have taken place in the past cannot be separated from technological innovations. Therefore, "mathematical attitude" is especially important in engineering education. If time permits, I would like to make a presentation on this topic as well.