The model used in German language to distinguish between articles, nouns, and adjectives in their various forms is known as declension—an unfamiliar construct in many languages, such as English. Declension permits speakers to differentiate between subjects, direct and indirect objects, and possessives. Rather than demonstrating these implications through word order or prepositions such as in English, Spanish, or French, the form of the word itself changes. This is known as declension. 


The four cases seem to be the core concept of German grammar. Is it really the number one thing, the most important issue, the one and only obstacle to overcome when learning the German language?

Many German language learners struggle with declensions. Taking an unconventional mathematical approach to analyse them, let's see if we can break them down into smaller groups to simplify the problem and make life easier. 


So, let’s do the math...


In German there are three genders (g), a definite and an indefinite article (a), and four cases (c). Mathematically speaking, that would lead to:


3g x 2a x 4c = 24


Meaning 24 possibilities to choose from each time you want to use a noun in German. Now, let’s assume you are reading a rather short novel of 80,000 words, with every 5th or 6th word being a noun. That would mean…and, in addition to that, we have just addressed the nouns ignoring the pronouns and adjectives. Okay, the above equation is really theoretical, let’s look at it from a practical point of view.



The Nominativ case


The Nominativ case is the standard case. You will learn it in your very first German lesson, and you will probably never forget it for the rest of your life. It is like learning scales in music, forehand in tennis, or whatever you learn first in any given discipline. And, of course, the Nominativ is used over and over again in all German sentences that you will come across. That means that there will be enough occasions to practice it.

Now that we’ve taken care of the Nominativ, we can take it out of our equation. However, that leaves us with the following, which is still a lot:


3g x 2a x 3c = 18



The Genitiv case


Genitiv is rarely used in spoken German, and in addition to that, step by step it is disappearing from written German as well. This is really a shame because Genitiv is the easiest of the declensions. So, it is very easy to learn. And, it can always be “translated” into Dativ using the preposition von.

In order to sum it up, we could just say that Genitiv is easy to learn, you don’t have to use it if you don’t chose to, and sooner or later it will die anyway.


Hmm, with Genitiv gone, let’s look at the equation again. Good news! The numbers are shrinking:


3g x 2a x 2c = 12



The Akkusativ case


Akkusativ is almost as easy as Nominativ. In other words: not a big deal. The easy part is that it only affects one of the three genders. So, let’s alter the equation, splitting it up into two parts:



3g x 2a x 1c = 6



3g x 2a x 1c = 6


As stated above, there is only one gender that changes when using the Akkusativ. So, the partial equation then would be:


1g x 2a x 1c = 2


Now, we sum up the two results of the equations:


6 + 2 = 8



The Dativ case


There is good news and bad news. Let’s deal with the bad news first: In Dativ everything changes, meaning that all the articles and all the genders change once the Dativ has to be applied. Now the good news: It is not as bad as you might think.

Masculine and neuter forms are identical. So now, the new equation is:


2g x 2a x 1c = 4


Now, we still have to add the result of the Akkusativ equation, so:


4 + 2 = 6



Plural forms


The plural forms don’t really matter in Nominativ, Genitiv, and Akkusativ because they are identical to the respective feminine singular form.


However, the Dativ case brings in a plural declension which is different from any other declension that we have seen so far.


Okay, that raises the number of possibilities from 6 to 7:


4 + 2 + 1 = 7


But when you think about it, 7 is not a high number if you compare it to 24 that we came up with in the very beginning.



What about the gender?

Yes, what about it? Right, it's all about the gender. Declensions are something you have to deal with whether you use mathematics or not. Gender is an issue you have to address from the very beginning, way before you even think about declensions. So, once you learn that first, you just apply it along the way, as you learn the declensions. Gender is the first step on the ladder of German grammar.


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