“There are two ways of doing calculations … One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither.” – Freeman Dyson, “A Meeting with Enrico Fermi”

The first principle is that you must not fool yourself–and you are the easiest person to fool. So you have to be very careful about that. After you’ve not fooled yourself, it’s easy not to fool other scientists. You just have to be honest in a conventional way after that. – Richard Feynman

my primary aim is … to teach how one might go about developing such a theory. Therefore, … I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself (using no outside resources except a vague memory of a lunchtime conversation I had had with John Conway almost a year earlier). – Donald Knuth, “Surreal Numbers: how two ex-students turned on to pure mathematics and found total happiness”

In mathematical sciences, a good notation has the same philosophical importance as a good classification in natural sciences. – Henri Poincaré

It was a period of patient work in the laboratory, of crucial experiments and daring action, of many false starts and many untenable conjectures. It was a time of earnest correspondence and hurried conferences, of debate, criticism, and brilliant mathematical improvisation. For those who participated, it was a time of creation; there was terror as well as exaltation in their new insight. It will probably not be recorded very completely as history. – J. Robert Oppenheimer, “Science And The Common Understanding”