Motive theory. Presumably, the term motive in the realm of art vaguely means something between ''raw material that inspires an art'' and ''a completed work of art''. A single motive may be realized as many forms in art like painting, music and literature. In mathematics, too, a single raw material often be realized as rich theories, like algebra, geometry and analysis. The goal of motive theory in the realm of mathematics is to capture the source of this phenomenon.

Collaboration. I visited Professor Bruno Kahn in Paris to ask a question on the motive theory arising from my older subject (which was different from motive theory). It was the starting point of a long collaboration that lasts more than 10 years. Some papers we wrote created new problems, which promote other collaborations with other researchers. This is how I carried my research. To think, it has been supported by extraordinary luck of meeting new people.

Different people can go with mathematics differently. Some stick to abstract theories, some spend a lot of time with concrete calculation. Some like to work alone, some like to discuss with others. Different views toward mathematics constitute rich world of mathematics. Let's go find out your own mathematic!