"On pani nie pamięta."

Translation: He does not remember you.

[mgaristova]

I guess the Genitive here is used because of the negation.
The positive would be "On pamięta panią".
Am I right?

[Jellei]

Perfectly right. Or "on panią pamięta".

[Zed895]

Pani means lady so I wrote this: 'he does not remember her' and it is wrong. Why?
Thanks

[Jellei]

In such a phrase, although it is 3rd person singular, it is in fact the formal 'you'. It's not some lady who is not remembered, it's 'you'. The closest translation would be "He doesn't remember you, madame".

"On nie pamięta tej pani" would be in fact "He doesn't remember this lady", but if there isn't any demonstrative pronoun or something similar ("On nie pamięta żadnej pani" = He doesn't remember any lady) that means it is the formal singular 'you'.

[Mim_Fox]

"He doesn't remember you, madame" is not accepted though.

[Jellei]

That's... unexpected. It obviously should have been accepted... Added now.

[Yola448704]

Ma'am, he doesn't remember you/
He doesn't remember you, ma'am

[Jellei]

Added the first option, the second one worked already.

[JacksonSh]

Pani means She, not he.

[Jellei]

"pani" here means "you, ma'am". And I wouldn't ever say that it means "she", because it doesn't.

[JacksonSh]

Dziękuję, rozumiem! Its a kind of vocative.

[Jellei]

Well, technically it's a pronoun here, just like "cię" in simple "On cię nie pamięta" is. But if it helps you understand it, I guess we can call it here 'a kind of Vocative'.

[Yola448704]

PANI is a formal YOU, used to address directly a stranger, an elderly lady or a person in authority; this type of YOU goes with the 3rd person grammar (she).
It would be "a kind of a vocative" when you addressed the woman directly using the title Mrs./Ms. and her last name:

Mrs. Smith, he does not remember YOU -
Pani Smith, on PANI nie pamięta

Ma'am, YOU are very nice/ YOU are very nice, Ma'am -
PANI jest bardzo miła
(not: PANI jesteś bardzo miła)

When you talk to someone else about this woman:
He doesn't remember Mrs. Smith (her) -
On nie pamięta pani Smith (jej)