"If he strived to learn, he would be a mathematics professor."
Translation:Öğrenmek için uğraşsa matematik profesörü olur.
These sentences are getting more and more difficult with frequent new vocabulary. The whole 'if' topic should done in at least three stages instead of introducing all types of 'If' sentences at the same time. Probable, possible, impossible and special cases are the normal stages in language courses.
In another sentence - I think it's something like 'If I strive to be healthy I would have a very happy life' - the suggested translation was 'sağlikli olmaya uğraşsam....', but when I use 'Öğrenmeye uğraşsa...' here it is marked wrong. Is it a possible answer, or is the suggested translation in the other sentence wrong?
do you mean like the tips that are already at the beginning of the lesson? https://www.duolingo.com/skill/tr/If_Conditional_Subjunctive/tips-and-notes
There's no accusative in this sentence.
But there's a possessive ending on profesörü which serves to tie matematik profesörü together into a noun–noun compound -- similar to things such as sırt çantası "backpack" (literally, "back its-bag") or havalimanı "airport" (literally, "air its-port").