I’ve heard things like “the linear algebra taught in undergrad was completed 100 years ago” and similarly for intro calculus and statistics and physics.
What makes parts of a mathematical subject “completed”? Can someone give an example of a system of theorems that constitute a completed subset of a mathematical subject?
On
The best example of a "mature" field I read recently from a physicist is when basically all textbooks cover roughly the same material in roughly the same order/way. Thus, when I say I learned undergraduate linear algebra, you know what I'm referring to. Less mature fields/areas have ambiguity in what is meant.
This is really just a matter of pedagogy/terminology though, not really of import
Those subjects were completed a century ago in the sense that no theorem less than a century old is taught in those courses. And the same thing applies to concepts. It does not mean that that subject is complete, in the sense that nothing new can be added to it. For instance, it is not known whether or not the Euler–Mascheroni constant is rational or not. However, the assertion$$\lim_{n\to\infty}\left(\left(\sum_{k=1}^n\frac1k\right)-\log(n)\right)\in\Bbb Q$$fits perfectly on a Calculus course.