The German noun "Ansatz" is widely used (at least) in physics and, less frequently, in math texts in English. I have seen it always in singular though and now I must use its (English) plural. The German plural of this word is "Ansätze".
Which of the following plural forms is the right one for the Germanism "Ansatz"?
The OED entry for ansatz lists it as a regular noun in English. That means it takes -es for the plural here.
On the other hand, its earliest citation almost looks invariant:
The other citations, through 1990, all look completely singular. There are no clear examples of a plural. It just isn’t marked as irregular, and they always do that if it is.
There are extremely few words in the OED of German derivation that retain their German plural in English, perhaps a half-dozen odd ones, and seldom as the dominant form. For example, there is one citation from 1962 of bratwurst > bratwürste:
In contrast, Wandervogel is definitely marked Wandervögel in the plural, and the plural forms Wandervogel and Wandervogeln are marked catachrestic — that is, erroneous. Here are two examples of the word as an irregular plural:
You can tell those uses aren’t assimilated because they’re still written in italic in the original. And they’re still capitalized, unlike most (but not all) citations of ansatz.
One more example with an irregular German plural in English is Land, “a semi-autonomous unit of local government in Germany and Austria”, whose plural is given as any of Länder /ˈlɛndər/, Laender, Lands, and in that order.
The most commonly used plural in English seems to be "ansätze".
Searching in Google books between 1990 and 2010, I find 98 results for "the ansatze" and only 36 for "the ansatzes". (I added "the" to eliminate German results, which dominate if you leave it out, even if you ask for English pages).
Google web search returns 372 results for "the ansatze" and 283 results for "the ansatzes".
Looking at the actual results, the majority of them seem to have umlauts (you often have to click the link and look at the document itself to check for an umlaut) and are lower-case, so despite what the dictionaries say, I would recommend using ansätze as the plural.
"Ansatzes" is most commonly used as a plural in English.
Here is an indirect argument for Ansätze.
The core result of classical algebraic geometry is Hilbert's zeros theorem.
In all languages I am aware of it is usually referred to as Nullstellensatz, with a footnote translating it into the language of the text.
Since there are various more or less general versions of this result one is led to speak of Nullstellensätze or some other plural forms.
Google gives 2590 answers for Nullstellensätze and only 142 for Nullstellensatzs.
Here is the first page of the answers for Nullstellensätze.
On a personal note it has happened a few times that I told mathematicians who had written, say, Nullstellensatzs that the German plural was Nullstellensätze.
What is interesting is that, although I absolutely did not plead for the German plural but just gave them the information , they immediately modified their original text and adopted that German form.
