Translation:I read the article but I did not understand the theory.
That is grammatically true, so I'm not disagreeing with you. However, I also agree with IanBod's point: Turks often say "Anlamadım" when English speakers would say "I do not understand". Or they will ask "Anladın mı?" for "Do you understand?". I guess they have a point, because what I would or would not have understood is in the past, if only by half a second. :-)
In the lessons that included "sevdim / hoşuma gitti / beğendim" we could translate those phrases into present ("I like") because of the way they are used, and I have often heard "anla(ma)dım" used in a similar way.
Perhaps a native speaker could explain if certain situations can only be translated as past tense.
Please, could anybody (Turkish native) answer this. I have been asking me the same a lot of times now.
Lütfen, anadil Türkçe olan insan belirli durumların ancak geçmiş zamana çevrilip çevrilemeyeceğini açıklayabilir. Bu cümlede "anlamadım" 'I did not understand' yerine "I do not understand" terimini kullanabilir miyim?
Yes, this is true. "Anla(ma)dım" can be used for both past and present in Turkish. You can also use "anlıyorum" or "anlarım" for "I understand" but the context of them could be different sometimes.
"Anlıyorum" could sometimes mean "I see your point [in a conversation]" or "I empathize with you" (halden anlamak).
"Anlarım" could mean that I am pretty knowledgeable on certain subjects. For example; "motordan anlarım" → "I know all about engines."
There are many other meanings for "anlamak" but their context is narrow. I suggest you to use online Turkish-English dictionaries. Some of them are very comprehensive such that they even gives Turkish idioms in equivalance to English idioms.