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I am teaching mathematical statistics and part of this is large sample theory. I would like to discuss some methods that do not focus on asymptotics and refer to J. M. Keynes quote

In the long run, we are all dead.

I am a bit afraid some students might find this quote a bit too strong.
Could this quote be considered a bit too strong to be presented to 3rd year undergraduate students in the UK?

Opinion, of course, but I think it is fine. It is often quoted in fact. While your students probably still think of themselves as immortal, they almost certainly aren't. No one should really take offense at basic biological certainties.

It is, in fact, a corrective on much illogical thinking, which is why it has lasted.

As a British person, I don't understand why you'd even consider that this quote might be inappropriate. If you feel that it's a good way to get your message across, there's no reason not to use it. However, if you're uncomfortable with it, for whatever reason, don't use it.

Writers often talk about the need to "kill your darlings". This refers to the fact that it's often easy to become enamored with one's own clever ideas and turns of phrase, whether or not they actually accomplish what is needed in the larger context.

Following this advice, I would suggest preparing the lecture without the phrase, simply to see how useful it really is. Come back to it a couple of days later, when you've had time enough to detach a bit, and see how well the lecture works. If the phrase is actually helpful and meaningful (as opposed to merely attention-grabbing), you can always add it back in then.

Your students are not children. They are about twenty years old. If they have not yet accepted the idea of death, it's their problem, not yours. You are being paternalistic from trying to shield them from something so mundane.

Not in the UK, but I was in my 3rd year of college when I took an economics course that used that quote and that was the least of my concerns about that particular course. Of course, I feel like you'd be doing your students a bit of disservice if you don't provide a least a little of the context (which since you mention statistic / asymptotics I'm assuming you're aware of). What I remember is that the context was someone pointing out that following Keynesian economics, in the long run, you'll just have inflation and that was Keynes' reply to that critique. (To which I can envision another professor pointing out "and that's why Keynes was so often invited to all the parties")

I have previously taught a similar course in the UK and would use a quote like this without concern. In my experience UG students are totally unconcerned about their eventual demise.

However, the point of including such aphorisms is that they allow you, the lecturer, to convey something with a bit more interest/ passion / excitement, your students probably won’t get much out of them directly. Thus, if you are uncomfortable about this quote then it isn’t going to serve its purpose and you should drop it.