The professor seemed more interested in companionship than in physical gratification. I also have to wonder whether at his age the equipment is still functional. On the other hand, he knew what she was when he called for her, and one has to wonder what his plan was for the rest of the evening after the soup and wine.
shareI'm going to answer my own question. No, they didn't have sex.
The old man tries too hard to persuade her to come to the other room after she slips into his bed. He doesn't seem at all responsive to her flirtatious suggestions. At no points does he seem even remotely aroused. The night scene ends with Akiko sound asleep, and the old man disconnecting the phone and turning off the light. The fact that he goes to such great lengths to ensure she sleeps well and isn't woken up suggests he wouldn't stir her to satisfy any hypothetical carnal desires he may have. He seems like a selfless and empathetic being.
I've also come to suspect that his relationship with his wife had become largely nonsexual, which I believe is the norm at that age, and that he was merely looking for another outlet for his affection after she passed away. Perhaps his wife was a needy, helpless being, who required him to look after her and drive her places, like Akiko. This would explain why he wouldn't be interested in his neighbour, who despite being interested in him romantically, seemed quite independent and was herself a caretaker to her dependent brother.
I've also come to suspect that his relationship with his wife had become largely nonsexual, which I believe is the norm at that age
I think, based off him falling asleep at the wheel after dropping off Akiko, that he probably didn't even sleep that night. If anything, after making sure there would be nothing to interrupt Akiko's sleep, he just worked through the night. But, being that he was sleep deprived, that is why he made a mistake translating a book.
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Writer at http://amari-sali.blogspot.com/ featuring Overview/ Reviews (with Spoilers)
I think, based off him falling asleep at the wheel after dropping off Akiko, that he probably didn't even sleep that night. If anything, after making sure there would be nothing to interrupt Akiko's sleep, he just worked through the night. But, being that he was sleep deprived, that is why he made a mistake translating a book.
According to the Making Of, the plan in the original script was for them to have sex, but once he cast the role of Akiko and they ran through the first scene in the apartment a couple of times with that actress, Kiarostami realised that the audience would not accept them having sex. So it was removed.
"Please don't eat me! I have a wife and kids. Eat them!"
I don't believe they did. If you see later on he folds the blanket from the couch, which means he slept on the couch.
shareI have seen the making of the film and Abbas says he leaves a lot open to the viewer. Although it is viewed that it is not what he wants to do and is expressed as not the case by the female actress who plays the prostitute as well.
So in 90% of situations the answer is no. Most of the directorial staff and production staff said the same as well, that no, there was no sex involved.
Abbas implied that he was making a film about a man who fell for somebody because she reminded him of somebody so with that in mind, it's likely he didn't.