Thanks for your comments, Andres! Let me first state one point of agreement: that mathematics isn’t captured well by the revolutionary/stable distinction. Apart from subjective assessments of what’s important and what’s not, I am also looking for the cultural influences - especially in intellectual culture - of developments in mathematic…
Thanks for your comments, Andres! Let me first state one point of agreement: that mathematics isn’t captured well by the revolutionary/stable distinction. Apart from subjective assessments of what’s important and what’s not, I am also looking for the cultural influences - especially in intellectual culture - of developments in mathematics (or of physics/biology etc) and here, I believe that there’s been a sharp drop off in our lifetimes. That doesn’t mean mathematics isn’t evolving internally or that those internal developments aren’t momentous, but I was specifically looking for mathematical modes of thought that have become widespread in intellectual culture as a whole, just as computational modes of thought have become.
This is the beginning of a long conversation, but my gut instinct is that the real transformation that’s waiting to happen is in the amalgamation of mathematics with other formal disciplines and their practices: programming in particular. This will bring new cognitive styles into mathematics. For example, a great deal of (good) programming is about building systems (let’s say, a newsletter platform like Substack) and that means creating software structures that are modularizable, easy to repair etc. These qualities are complementary to rigor (exemplified in proof) and offer ooportunities for entirely new forms of mathematical system building.
Thanks for your comments, Andres! Let me first state one point of agreement: that mathematics isn’t captured well by the revolutionary/stable distinction. Apart from subjective assessments of what’s important and what’s not, I am also looking for the cultural influences - especially in intellectual culture - of developments in mathematics (or of physics/biology etc) and here, I believe that there’s been a sharp drop off in our lifetimes. That doesn’t mean mathematics isn’t evolving internally or that those internal developments aren’t momentous, but I was specifically looking for mathematical modes of thought that have become widespread in intellectual culture as a whole, just as computational modes of thought have become.
This is the beginning of a long conversation, but my gut instinct is that the real transformation that’s waiting to happen is in the amalgamation of mathematics with other formal disciplines and their practices: programming in particular. This will bring new cognitive styles into mathematics. For example, a great deal of (good) programming is about building systems (let’s say, a newsletter platform like Substack) and that means creating software structures that are modularizable, easy to repair etc. These qualities are complementary to rigor (exemplified in proof) and offer ooportunities for entirely new forms of mathematical system building.