I am very aware about statistical methods originating in mathematics - I did statistics every semester as part of my biology degree. Indeed, half the reason why the mathematics department existed at my university was to support the biological sciences.

You may be interested to know that my point is that you don't need mathematical proofs to have a pragmatic, beneficial effect - and while the OP is sitting there feeling smug, the others at that dinner table are actually out there reducing pain and disorder in the people around them. Some medical tools are completely impossible without maths - MRIs are the poster child for this - but feeling superior because "my field uses proofs and yours doesn't" is just obnoxious. This vid link is about teachers rather than medicos, but it's the same sitation; a response to the smug one denigrating the others at the dinner table, because those others don't match up to a very narrow standard: https://www.youtube.com/watch?v=RxsOVK4syxU

Besides, as the saying goes: "In theory, there is no difference between practice and theory. In practice, there is".

I think he/she is just being playful and humorous. But since I'm studying math along side EE, I feel like I should comment about the role (or lack thereof) of proof in practical applications.

MRIs fall into the field of electrical engineering, and EEs generally don't understand the math they use. e.g. when working with medical imaging the radon transform is used, which would require a post graduate mathematical education to understand.

That's why it annoys me when the math/physics types think that if they don't make it in academia they can "fall back on engineering", even though they're studying something completely different.

By the time you get to 4th year math, you will be able to prove things about the existence and uniqueness of the Fourier transform. That's one way to understand it. On the other hand, you use Fourier transform (more specifically, the frequency domain), from first year EE - you can see the frequency spectrum on an oscilloscope. That's another way of understanding the Fourier transform.

Part of my issue here is that saying I mentioned. I've experienced first-hand a couple of times where a mathematician tells me something is or isn't possible due to theory X or whatever, and then when practically applied, they've been wrong. So when someone is smug due to something in their head that doesn't have a practical demonstration, I'm suspicious from the outset.

Maths itself may be pure and correct, but it isn't the maths being smug at the dinner party :)

The trick is to first raise the topic of "alternative" therapies so that you can all have a go at being smug. It then becomes an amusing dinner-party contest in who can be the smuggest and no-one is offended, or at least, no-one present.