In light of reading Hazard's Shortform Feed -- which I really enjoy -- based on Raemon's Shortform feed, I'm making my own. There be thoughts here. Hopefully, this will also get me posting more.

In light of reading Hazard's Shortform Feed -- which I really enjoy -- based on Raemon's Shortform feed, I'm making my own. There be thoughts here. Hopefully, this will also get me posting more.

I've recently been obsessing over the idea of trying to "make math more like programming". I'm not sure if it's just because I feel fluent at programming and still not very fluent at abstract math or also because programming really does have a feedback loop that you don't get in math.

Regardless, based on my reading it seems like there's a general consensus in math that even the most modern theorem provers, like Lean and Coq, are much less efficient than typical "informal" math reasoning. That said, I wonder if this ignores some of the benefits that programmers get from writing in a formal language, i.e. automatic refactoring tools, fast feedback loops, and code analysis/search tools. Also, it seems like a sufficiently user-friendly math theorem proving tool could be useful for education. If kids can learn how to program in Javascript, I have to believe they can learn to prove theorems, even if the learning curve's relatively steep.

Maybe once I play around with Lean more, I'll change my mind, but for now, I'm sticking to my contrarian viewpoint.

It seems like a useful idea on a lot of levels.

There's a difference between solving a problem where you're 1) trying to figure out what to do. 2) Executing an algorithm. 3) Evaluating a closed form solution (Plugging the values into the equation, performing the operations, and seeing what the number is.)***

Names. If you're writing a program, and you decide to give things (including functions/methods) names like the letters of the alphabet it's hard for other people to understand what you're doing. Including future you. As a math en... (read more)