Translation:Üç yaşındayken göz ameliyatı oldum.
so is this an idiom: "to undergo a surgery"="ameliyat olmak"?
TLDR; Yes. But it's not an idiom.
Disclaimer: I'm not a native Turkish speaker
Etymologically, ameliyat is more close to the word "operation", as it can mean other things than a "surgical procedure" .
From my experience olmak, and etmek usually turn Arabic loanwords that are in noun form into things that "happen"... In English surgery is not a verb and it doesn't "happen" by writing "I eye surgeried". You have to write "I had" eye surgery to describe that it has happened. "oldum" takes the role of "I had" here.
For that reason, I don't think any of this is idiomatic.
I think you're right that it should not be called an idiom, yet I felt this use of 'olmak' idiomatic because it is supposed to mean 'to be, to become, to happen', so 'göz ameliyatı oldum' to me would literally read as 'I became an eye surgery'.
With my very limited Turkish knowledge I would think I should say 'ameliyatım oldu' or 'ameliyatım vardı', since it is the surgery that happened, and not me, but I think none of these is actually correct.
But now I wonder, are there more phrases like the one above, where something happens to the subject / someone experiences something, and it is expressed with 'olmak' as an auxiliary verb?
Ameliyatim oldu would mean I had my surgery wheras Ameliyatim vardi implies you had a surgery(giving context (you may not have made the surgery or you missed something because of it)
So if I am a surgeon, and I miss a call while at work, I can say something like this :'Üzgünüm, telefona cevap veremedim, çünkü ameliyatım vardı.' ?
Also I wonder, is there any difference in meaning between 'ameliyat oldum' and 'ameliyat geçirdim'?
It's a really late answer but.
1- It's correct. But it would be better like "... çünkü ameliyattaydım." "I was in an operation."
2- No difference in meaning.
To say 'While I was three (years old)' is very odd English! I would only ever say 'when I was three (years old)' ...
I think that this translation is incorrect and it should be ''when I was three (years old) I had an eye surgery'' According to the Duo TIPS AND NOTES (y)ken if added to the noun it should be translated into when!
I fairly sure it should be 'eye surgery' or 'an eye operation'. I don't think you can have 'a surgery' in English.
Isn it suppose to be 'yaptim'? This makes no friggin sense! Totally wrong options.