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This question also has an answer here (in German):
Am Samstag, dem/den

It's more logical to me to be "am Montag, dem 10. August" since without specifying Monday, I would say "am 10. August" Instead, it's like the article is taking on adjectival endings.

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    Nobody so far has answered the "why" question. I am not able to give an exhaustive and robust answer, too, but I think a good answer will mention traditions of writing dates in chanceries from, say, the mit 18th century (i.e. when modern bureaucracy was developed).
    – Christian Geiselmann
    Commented Jan 19, 2018 at 16:07

4 Answers 4

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According to the rules (for example Duden or canoo.net) both variants are correct. After a date specification with "am" one can use dative or accusative for the calender day, so one can write

am Montag, den 10. August
am Montag, dem 10. August

So, the "why" has to be answered that it is layed down by definition that both variants are possible.

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    Looks like a partial answer to me as it does not address the "why?".
    – user1583209
    Commented Jan 17, 2018 at 9:22
  • @user1583209 Good point. I tried to add the "why".
    – IQV
    Commented Jan 17, 2018 at 9:36
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The accusative case is used when referring to a day or month without the preposition "an" preceding it. For example:

Jeden Freitag freue ich mich auf die Ankunft von meinem Freund.

Or

Ich habe für meine Chefin eine Verabredung nächsten Montag um 8:00 Uhr gebucht.

However with "an", the dative case is always used:

Am Montag müssen wir einkaufen gehen.

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Heute ist der neunte Mai is perfectly correct, while die Party findet am ersten Mai 2020 statt is correct, denoting event and the dativ preposition an.

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I always understood that the accusative is used in dates I.e den vierten April , because you are really saying 'Heute haben wir den vierten April' not just nominative ! Heute ist der vierte April , is not said.

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    Heute ist der vierte April. is perfectly fine.
    – Olafant
    Commented Nov 21, 2019 at 20:19

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