I updated the reading list with a new entry:

Thurston, William P.
On proof and progress in mathematics.
New directions in the philosophy of mathematics (1998): 337-355.

This is a recommendation for both mathematicians and math educators (and anyone else who cares to listen.)

This paper has been around for a long time, and I’m a little late to the party, but that’s how this sort of thing goes.

It’s a great read, and it does a great job of conveying what mathematicians do and what motivates them to do it. The essay is written in response to another article which I haven’t read yet:

Jaffe, Arthur, and Frank Quinn
Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics.
Bulletin of the American Mathematical Society 29.1 (1993): 1-13.

I’ve got an unfinished draft post laying around about my experiences trying to learn from physics books. To summarize, I feel like students of both disciplines frequently have trouble understanding material from the opposite discipline. They often have divergent opinions on their purpose and processes, and this leads to a lot of friction and misunderstanding.

What’s interesting in this case is that you can see from Thurston’s paper that even within mathematics itself there are some different perspectives on the purpose and process of mathematics.

In the spirit of better understanding your STEM siblings and cousins, I highly recommend checking out both these articles. If you are an educator, I think it is also very relevant to develop your impressions about how to present mathematics.