Essay writing shows that you actually know the domain material, that you are capable of holding onto a thought for more than 3 seconds and that you can communicate thoughts clearly to other people.
I never wrote a single essay for a math class, so I think there are alternatives.
But I think you're missing my point. If a student can go through their education never writing an essay the way everything thinks they're meant to do it and end up doing just fine in life, maybe the merits of essay writing aren't all what they're cracked up to be? Save the skill for specializations where the students are more motivated to learn it, like metalworking or pottery.
If argue that if you were ever asked to show your work, you were writing the equivalent of a mathematical essay. Maybe you never had to learn proofs, but I did.
“I didn’t have to do that and I turned out fine” isn’t a very rigorous pedagogy.
Sure, but now we're stretching the definition of "essay" past what's useful for the topic at hand. This is a thread about AI checkers for essays, not math proofs.
And no, it isn't rigorous, but it's a pretty good hint that you've got correlation and not causation. Perhaps it's worth entertaining the possibility there's a better way.
What’s an alternative way to show those things?