Penelope Maddy was recently interviewed by 3am magazine (h/t Brian Leiter). I found the interview interesting.
Maddy is a philosopher of mathematics. In the past I have read some of her work related to set theory. I very much disagreed with her philosophy, but her work was still worth reading. She was very much into questions such as whether axioms are true. That’s sometimes called “mathematical realism” because it is based on the idea that mathematics is saying something about the real world.
For myself, I could never make sense of mathematical realism. As I saw it, axioms were neither true nor false. I saw axioms as just useful assumptions whose consequences interested the mathematician.
It seems that Maddy has now moved away from that realism, so is adopting a view a bit closer to mine. She now also doubts the Quine-Putnam indispensability thesis (that mathematical platonism is indispensable to physics). Again, that is closer to my view.
I’m not at all sure that one’s philosophy of mathematics affects how one does mathematics. But I did find it interesting to read of this evolution in her thinking. And I’ll put this down as recommended reading for those interested in the philosophy of mathematics.