Mathematics, the old and the new
Mathematics is both old and new. Traditionally, research in mathematics is the study of numbers and spaces, numbers such as the natural numbers 1, 2, 3,... that everyone knows, and spaces such as the 3-dimensional space that we see around us. From a modern viewpoint, one can argue that mathematics is still about numbers and spaces, but then one would have to widen the interpretation of "numbers" and "spaces" to include the great variety of forms that numbers and spaces have recently evolved into. This is what mathematical research has become.
Also, in modern times the distinction between things that are like numbers and things that are like spaces is not always clear. Sometimes numbers are considered as spaces. Furthermore, the spaces that mathematicians now study often do not resemble what most think of when they consider "space". As examples of this, consider the following three examples:
- You probably know that the list of prime numbers is infinite, but you might be surprized to find out that it is still not well understood how how individual prime numbers are spaced out on the real axis as the list of them makes its way to infinity. But when considering prime numbers together as one full collection of numbers (i.e. as a space), various things have become clearly understood.
- The "space" of various data about the economy is something that people now do mathematical analysis on, though one would usually think of data as "numbers".
- Some scientists are now conjecturing that the universe is actually a ten dimensional space, instead of three dimensional as we usually think of it.
So, in modern mathematics, numbers and spaces exist in a wide variety of forms, and included in these forms are mysterious properties and intriguing principles that mathematicians, including us, get excited about.
Mathematics is all one thing
Despite the wide variety of numbers and spaces, we in the mathematics department of the Faculty of Science at Kobe University believe that mathematics is fundamentally just one thing. Algebra, geometry and analysis are examples of separate specialities within mathematics, and we of course consider each of them valuable and hence study them. But we take the view that any branch of mathematics can borrow freely from these specialities, delving into them for ideas that might lead to fundamental new discoveries. Then, in turn, these new discoveries should be freely borrowed by any branch of mathematics. Moreover, they should be freely used outside of mathematics and outside the borders of our university. In this sense, no matter which area of mathematics one is in, the goal is just the same as any other area. All mathematicians are searching for the same thing.
Although it is certainly true that mathematics is both a natural science and a tool of technology, we believe it is more than this. We think of mathematics as a rich and highly intertwined structure that both stands on its own and also has deep and fundamental connections to physics, biology, astronomy, chemisty, computer science, engineering, social science, and other fields as well. We at Kobe University are always interested in the development of these connections, so at times we exit the realm of pure mathematics and go to other fields to conduct joint research projects.
Our hopes for students
We in the mathematics department of the Faculty of Science at Kobe University are looking not just for "good" mathematics students. How "good" you are is not our primary concern. We are looking for students who appreciate our viewpoint as described above, who have an interest and desire to deeply understand the meaning of "numbers" and "spaces". We are looking for students who are interested in the major fields of mathematics and particularly in finding bridges between fields. And we are looking for students interested in learning the connections to physics and computational geometry and the like, an interest held amongst our staff, together alongside with learning pure mathematics.
Here in our department, we all have the desire to understand mathematics penetratingly and to do research that gives real insight, and we welcome you.