Definite article before a (mathematical) topic's name

Question

I will leap in with two translations by DeepL:

First translation

Input:

Linear regression is a powerful tool.

Output:

Die lineare Regression ist ein leistungsfähiges Instrument.

Second translation

Input:

Modular arithmetic is crucial to cryptography.

Output:

Die modulare Arithmetik ist für die Kryptographie von entscheidender Bedeutung.

Question

In both cases, the definite article was added – die Lineare Regression, rather than merely lineare Regression. How crucial is this definite article? In English one would never use the definite article in this way, but rather only if one were referring to a specific instance and not to the topic itself, for example:

The study was flawed because the linear regression did not control for age.

Even here I would be tempted to write the linear regression model and not just the linear regression.

The two examples are about mathematical topics. I don't know how important that is here.

Answer 1

Note this is not a must.

Lineare Regression ist ein wichtiges Verfahren in der Statistik

is just about as correct and common as

Die lineare Regression ist ein wichtiges Verfahren in der Statistik

This is a bit hard to explain:

Maybe the easiest is

If you can rephrase the sentence to

Die Wissenschaft (or das Verfahren) der ...

you can put a definite article.

(That is, you are referring to the "science" or abstract method).

This is not limited to Mathematics, but can be observed in any science:

Das Galvanisieren ist ein Verfahren zur Oberflächenbeschichtung von Metallen.

Answer 2

I believe what is happening here is that English does not tend to use definite articles before abstract nouns referring to general concepts. This is an unusual feature of English. It is not necessarily true of other languages that have definite articles.

In German, these sentences are fine both with and without a definite article. This is not specific to mathematical or even scientific topics. Another example is the name of ideologies. In English, you can only say someone supports democracy (the definite article would not sound good here), but in German, you can say someone unterstützt die Demokratie and I think this usually sounds better than without the definite article.

Answer 3

You do not need the article because of the adjective:

Regression is female in German, so it's "lineare Regression".

For example:

Schönes Zimmer Schöne Wohnung Schöner Wolkenkratzer

The general topic is the "Nullartikel"

https://www.das-akademie.de/adjektivdeklination-leicht-erklaert/

Adjektivdeklination ohne Artikel (Nullartikel)

Wenn vor dem Nomen kein Artikel steht, nennt man das Nullartikel. Hier muss das Adjektiv den Kasus signalisieren. Die Endung des bestimmten Artikels (der, die, das…) muss also an das Ende des Adjektivs. Die einzige Ausnahme ist der Genitiv maskulin und neutrum. Das -s am Ende des Nomens markiert bereits den Kasus, deshalb bekommt das Adjektiv hier die schwache Endung -en.

Ein altes Auto steht in der großen Garage. Neue Schuhe sind oft teuer. Der alte Mann trinkt gerne kaltes Bier. Der kleine Junge mag schnelle Autos.

Ich bade in kaltem Wasser.

You also do not have to put an article before "Eigennamen", "Lineare Regression" is a "Eigenname".