Of course, the most rewarding part is the “Aha” moment, the excitement of discovery and enjoyment of understanding something new – the feeling of being on top of a hill and having a clear view. But most of the time, doing mathematics for me is like being on a long hike with no trail and no end in sight.
I find discussing mathematics with colleagues of different backgrounds one of the most productive ways of making progress.
Maryam Mirzakhani, who recently won the Fields Medal prize, talking about what she finds the most rewarding or productive. I was struck between the similarity of this and Steven Johnson’s idea of the slow hunch.
There is also this:
The beauty of mathematics only shows itself to more patient followers.