"For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?"
- Richard Courant
About this Quote
This quote by Richard Courant recommends that the best way to understand mathematics is to actively engage with it. He implies that it is insufficient to simply check out mathematics or to think of it philosophically. Instead, it is through direct experience with mathematics that a person can really comprehend it. Courant suggests that this is true for both scholars and laymen, as everyone can take advantage of engaging with mathematics. He implies that it is just through active experience that one can respond to the concern of what mathematics is. This quote encourages people to check out mathematics and to acquire a much deeper understanding of it through direct experience.
"I think philosophers can do things akin to theoretical scientists, in that, having read about empirical data, they too can think of what hypotheses and theories might account for that data. So there's a continuity between philosophy and science in that way"
"What I mean by photographing as a participant rather than observer is that I'm not only involved directly with some of the activities that I photograph, such as mountain climbing, but even when I'm not I have the philosophy that my mind and body are part of the natural world"
