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Have you looked at Open Board (https://openboard.ch/index.en.html)? I've just started playing with it and I _think_ it has all of those features.

But I agree. I've been looking for a whiteboarding program that I can use on my iPad and display on my desktop/external display (which, since they're more than five years old, are scrap AFA Apple is concerned).

It seems from the website that OpenBoard is software for actual interactive boards, not for a computer. Is that not the case?

Try https://kinopio.club

You should checkout : https://www.mural.co/ In our organization it's used a lot (sometimes overused), and I find it very helpful.

Excalidraw.com

Doesn't have math input yet but there is a draft PR up for that, so might be there soon.