@cwebber I have used it a few times for symbolic equation solving. It's roughly in the same ballpark as REDUCE and other early computer algebra systems. Not quite as convenient as more modern systems (Maple, Mathematica), but free.

Maxima is also part of Sage, so I suspect some people have used it without being very much aware of it:

https://doc.sagemath.org/html/en/reference/spkg/maxima.html

@cwebber
Maxima was integral to a main result in my dissertation basically I took a simple partial differential equation, converted it to dimensionless form, told it how various things changed with time and space, expanded the derivatives, produced a page of expressions, did asymptotic analysis on the terms to estimate their size calculated a series of intermediate results, took the most simplified result and solved it symbolically in some special cases, and then showed that all the textbook...
@cwebber
Descriptions of soil liquefaction were based on faulty logic, gave a new understanding of the mechanism actually at work, and then explained why tabletop liquefaction studies were doomed to failure and entirely based on the behavior of the rubber membrane surrounding the soil sample.

All of it virtually impossible without Maxima

@cwebber If you are into FOSS and want to explore more widespread math languages, checkout https://julialang.org/ — the meta programming is pretty lispy. There are CAS built on top of Julia but they are not so powerful (happy to share deeplinks if you like). My favorite lisp-in-math-production is Mathematica, but unfortunately it's nonfree and expensive as hell. Clones and derivatives lack the large library which makes Mathematica the go-to-tool it is.
@cwebber I used to use wxMaxima all the time back in college! Not for, like, sophisticated mathematics, but it was very capable for helping with calculations in my engineering and math classes

The alternatives I had available at the time were my graphing calculator (more limited) or Mathematica (the university had a volume license I think but I didn't really want to get used to a tool I wouldn't always have)

@cwebber I used Maxima for symbolic equation solving and integration; in high school, in college; I very rarely used it since. It was very helpful.

I think all the alternatives I knew about were sufficiently inaccessible in 2009 that I learned a very small bit of Maxima and wouldn't attempt learning any other CAS.

It wasn't easy, but I usually found a function in its documentation doing what I needed.

Just the idea of software having been maintained since 1960s is very cool.

@cwebber electrical engineering PhD, specializing in control theory. even routine calculations on dynamical systems can get ugly pretty fast, so in cases where i have to work out the details of a specific dynamical model i sometimes use maxima to double-check my work. the most recent example was a few weeks ago when I was working out some first-order sensitivity matrices for the circular restricted three-body problem for a satellite control application.