# Lecture: A compelling Desire to do Mathematics

## Shigefumi Mori

##### Abstract:

Mathematics is admittedly useful in the current digital world, though it is classified as a curiosity-driven science, which I accept. There is thus a question frequently asked by non-mathematicians.

If mathematicians do their research out of curiosity why should they be supported by tax money?

It is not easy to give a direct answer that everyone accepts.

There are various levels of curiosities depending on the scene; it can be as general as one about the principle of universe, as special as one about an actual mathematical problem, or as practical as one about an application, but it has to be enchanting for the mathematician.

How is the outcome evaluated if it is done out of curiosity? There are notions of rigor and beauty that mathematicians generally accept; while the former is objective and sometimes painful, the latter is subjective and often addictive. I believe that each of us evaluate the work by its beauty even before it is completed, and a good sense of beauty will lead him/her to a final solution. I will show examples including some of my own experiences in my career.

Along this line of arguments, I will give my answer to the first question in my talk.