Message from Chair of Mathematics Program

Shigeki Akiyama, Chair of Mathematics Program

Students studying mathematics are often puzzled at first by the strictness and the attitude of digging all the way down to the fundamentals.  Indeed, the process of acquiring mathematics is similar to learning a new language, and moreover, one is not allowed any mistakes in "grammar" or "syntax".  In that sense, strict training is necessary. Why is this?

Although it seems contradictory, the essence of mathematics is in its freedom. In mathematics, with no constraint on what to think, logical derivation will produce results from the given definitions.  Since there is no external framework, we must lay out logical structures strictly in order to maintain consistency.  If we do not do so, we will immediately get a contradiction and meaning will be lost. That is why it feels tough. The lack of a fixed exterior framework is one element that distinguishes mathematics from other disciplines.

As a result of this training, you will be given the fundamental skills and ability to build a framework. Strictness is important at the beginning, but more important is in how to handle "freedom" after that. From here on is your free world. Several paths lie before you, and the choice is yours to make. Initially, anyone will start with imitation of existing results. But life is boring by that alone. Please make full use of your freedom. The mathematics major is here in order to send creative and freely thinking talents out to the world. The mathematics faculty exists to help with that. If you talk with multiple mathematicians, you will see that each has a very different worldview.

Creating a new definition is the heart of mathematics.  Such definitions and concepts arise from internal development of mathematics, from other fields, from various experiments, or from pure thought. Even though we say you may think of anything, not all definitions will survive. Definitions are important, but you have to decide which definitions are good. Historically valuable results are backed by past achievements, so what matters is the global view of history and mathematical aesthetic sense.

Please concentrate in mathematics, while enjoying yourself, and let us contest your worldview and aesthetic sense. We the members of the mathematics faculty would like to support you.