There's a simple differential equation often taught in intro calc courses, "Newton's Law of Cooling/Heating," which basically says that the rate of heat loss is proportional to the difference in temperature between a substance and its environment. I'm curious what that'd look like here. It's a very simple model, of course, not taking into account all the variables that Dynomight points out, but if a simple model can be nearly as predictive as more complex models...
I'm also curious to see the details of the models that Dynomight's LLMs produced!
Mmmm it's something I've done for a long time; I've been at the same school for seven years; it's a ton of fun but also gets repetitive... I want more challenges!
* Get less scared about applying to do stuff! I'm leaving my longtime job---I've taught advanced math to super-smart high schoolers; I'm quitting to be a visiting professor at Deep Springs College for a semester and then ???---and in the past, fear of applying to things (jobs, grad schools, writing residencies) has been a major blocker.
* Learn complex analysis!
* Get a better workflow for writing my notes to myself (e.g., Obsidian) and for publishing my blog/website (have a marginally-functional Hugo instance right now). Small thing, but the kind of important-but-not-urgent thing that it's easy to put off!
I've used Sage for years to run the backend (calculations/computations/graphics/prototyping) for a multivariable calculus class I teach. It's not perfect, but as a lightweight, Python-style CAS to do all sorts of "standard" calculations, it's very easy to use!