How to motivate undergrads to take an Intro to Math Stats course How would you motivate an undergraduate student to take an Introduction to Mathematical Statistics course, if they know that much of their time will be spent proving results they've already seen in Introduction to Applied Statistics? That is, much (though certainly not all!) of the course is "just" about proving mathematically that standard methods for p-values and confidence intervals (z and t tests and intervals; F and chi-square tests) work as advertised.
Context: I teach at a US small liberal arts college. Here is the course description for our version of this class:

Topics in Statistical Inference Building on their background in probability theory, students explore inferential methods in statistics and learn how to evaluate different estimation techniques and hypothesis-testing methods. Students learn techniques for modeling the response of a continuous random variable using information from several variables using regression modeling. Topics include maximum likelihood and other methods estimation, sample properties of estimators, including sufficiency, consistency, and relative efficiency, Rao-Blackwell theorem, tests of hypotheses, confidence, and resampling techniques.

We have used textbooks such as Hogg, McKean, & Craig (table of contents) or Wackerly, Mendenhall, & Scheaffer (table of contents).
Our statistics majors are required to take Math Stats, but I try to give better motivation than just "it's required." And occasionally other students ask me why they should consider taking this course too. What are some ways I could convince them to see the value of taking Math Stats?
I'll post my own answer with what I currently tell them, but I expect that the community here has other great suggestions.

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*Do you hope to do research on statistical or machine-learning methods? Even if this class just proves conclusions that you've already seen, the mathematical techniques and frameworks behind these proofs are the same ones used by research statisticians to develop new cutting-edge results. This class is the first step towards making your own contributions to statistical methodology. It will also help you sanity-check a colleague's work when they say they've developed a "better" statistical method for some scenario. (How is it better: more efficient? more robust? etc. Does it actually work the way they think it does?)

*Do you appreciate beauty in math? I find that some of the math techniques or results themselves are beautiful. For instance, you can approach several common situations from totally different angles (MLE, MOM, Bayesian posterior mode, minimizing MSE...) and they all give the same answer (sample mean)! How cool is that?

*Do you only care about applications, not the "pure" math itself? Even so, a Math Stats course will give you a much deeper understanding of what these methods are doing. Personally, I had seen p-values and confidence intervals many times, but they did not really click for me until I took Math Stats. It will also help you learn to watch out for situations when the standard methods won't work and possibly develop your own solutions or workarounds.

*Do you want to work with data-minded colleagues but not analyze data yourself? Even so, you'll be better prepared to follow other people's new developments in statistics, AI, and machine learning, so you can sensibly decide whether they're useful to your work. For instance, differential privacy has been a recent hot topic in my areas of work, but it's not trivial to understand what it's even trying to solve or how it proposes to do so; some Math Stat background definitely helps.

