"The imprint of the world in our minds is not photographic; all the brain knows of the outside world is a chaotic sequence of electric impulses and out of these it creates a structural entity: our perception of what we see and hear. Most of the time, an adult's brain talks to itself and creates more "
"I have always preferred working in unpopular areas of mathematics. I recognize the benefits of working in popular areas—a community of experts to discuss problems with, a group of friends you see regularly at conferences, a reference group to compare yourself to, a crowd to instantly appreciate your"
"I prefer to avoid mainstream mathematics research and work on my own. One problem with this is that the most productive areas are (almost by definition) part of mainstream research and the remaining areas are usually rather barren. My own research reminds me of someone picking over a large junkyard "
"In a similar way I find equal difficulty when asked, what kind of mathematician are you? I usually evade the question by just saying that I am a geometer in the broad sense, secure in the comfort that "God is a geometer." For me, just as there is only one world, even if parts of it are more familiar"
"I have always felt that mathematics is a language like music. To learn it systematically, it is necessary to master small pieces and gradually add another piece and then another. In a sense, mathematics is like the classical Chinese language—very polished and very elegant. Sitting in a good mathemat"
"Mathematicians lie somewhere between artists and writers on the one hand and physicists, chemists, and biologists on the other. We try to get natural problems from the physical world, but we also try to create problems based on the development of our understanding of nature. It's like an artist who "
"To explain the power and beauty of mathematics to outsiders is difficult. Mathematics takes ideas from the external world and makes them abstract, juggles them around to creat structure, and then spews them back with amazingly braod and useful consequences. The best comparison that most of us have i"
"My mother was a mathematician. She studied Hilbert's sixteenth problem and made an outstanding contribution. This is a problem of studying a dynamical system governed by two polynomials."