"Proven" is not incorrect, although sometimes proscribed. https://en.m.wiktionary.org/wiki/proven#Usage_notes

"Proved" means demonstrated with a formal mathematical argument.

"Proven" refers to something confirmed over time, often used more informally.

"Proofed" is an editorial term—preparing text for publication.

To people who accept "proven" as the past participle of "prove", there is no difference. The only reason it would be rejected in English writing about mathematics might be that a good many of mathematicians are also pedants for prescriptive grammar. It is not a mathematical issue whatsoever.

I would like to note, just for fun, that "proofed" also exists and means something else entirely.

Not a native speaker, here. Do you mean "proved" is preferred in a mathematical context?

Not who you were replying to, but yes, it's a special case. For anything not having to do with a formal math-like proof, you want "has proven" instead of "has proved." It's super weird.

We only have a few of these in English, where one of the tenses of the verb changes depending on the subject matter, but they do exist. The only other one I can think of off the top of my head is hang: past and participle "hanged"/"have hanged" (to execute or be executed via hanging from the neck) versus "hung"/"have hung" (any other meaning).

Hope that helps!

Edit: fixed my example to better match the original text.

This doesn't match my experience, and no dictionary I've checked says the past participle depends on the context; only that "proven" and "proved" can both be used (in any context). See e.g. https://en.wiktionary.org/wiki/proven#Verb

I'm not a mathematician though, so maybe this is a genuine semantic convention that neither I nor my dictionary are aware of. Maybe it's just that some mathematical style guides say to prefer "proved", for consistency, not that it really depends on the context?

Also not aware of it, but am mathematically trained and would always say "proved".

It seems to me that in North American English, we use the proven participle as an adjective (almost exclusively?). So that is to say a remedy, having been proved effective, is then considered "proven effective". This usage is drilled into people's heads by advertisements.

It feels sort of like the difference between gilded and golden. Something that has been gilded now has a golden surface. Now golden has that en suffix like some participles, but isn't one. It's a pure adjective.

I would also always use that in a mathematical context but feel it’s weird to hear, say, “proved in a court of law”.

Grammatically, or semantically?

The curious situation is that verbs similar to prove have past participles which are just the same as the past tense. Even approve!

You don't say "your application has been approven".

Or "the problem has been solven".

Or "the quantity halved again, like it had halven before".

Or "that function has misbehaven again".

Or "I have moven the funds to the correct account".

Yet, "proven" is accepted.

But, "I have given", "I have woven", "I have forgiven", and indeed "I have disproven" (also disproved). "-n" for a past participle of a verb like this is neither universal nor unique to prove. I believe you just have to learn English's irregular verbs; there are no useful rules to follow.

Give has an irregular past tense though. I think if the past tense were gived, probably the past participle would be the same.

Same with: write, wrote, written; smite, smote, smitten; bit, bit, bitten; hide, hid, hidden; ride, ride, ridden; drive, drove, driven.

There's a pattern that the verbs with the en participles do not have ed regular past tenses. They have ove, ote, ode, it, id past tenses.

There are exceptions though like swell, swelled, swollen. It's fuzzy enough that any -en past participle will sound fine if you just get used to hearing it.