Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. I happen to be a frog, but many of my best friends are birds. The main theme of my talk tonight is this. Mathematics needs both birds and frogs. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of concepts with depth of structures. It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper. The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it.
When I quit my academic career, one of my beloved teachers said I was a deserter. I knew she was joking, but it really bugged me. In a way, I was a deserter for I didn’t choose to stay. I couldn’t live my life as a frog anymore because I had seen birds flying high in the air.
So I took a job, but the funny thing is, I still have papers to write and problems to solve in an academic way more or less. Only this time, I can choose to solve problems in a bird way or a frog way. So I’m happy and excited. This is like when I found out the beautiful patterns of mathematics in my childhood.
So, I guess I was a deserter, but I made the right choice.
PS: I really like the awesome talk given by Dyson. There’s so much more I want to talk about, but there’s nothing more to add.