Charly

Charly Gordon (Cliff Robertson), an intellectually disabled man with a strong desire to make himself smarter, has been attending night school for two years where he has been taught by Alice Kinnian (Claire Bloom) to read and write. However, his spelling remains poor and he is even unable to spell his own name.
Alice takes Charly to the "Nemur-Straus" clinic run by Dr. Richard Nemur and Dr. Anna Straus. Nemur and Straus have been increasing the intelligence of laboratory mice with a new surgical procedure and are looking for a human test subject. As part of a series of tests to ascertain Charly's suitability for the procedure, he is made to race Algernon, one of the laboratory mice. Algernon physically runs through a maze while Charly uses a pencil to trace his way through a diagram of the same maze. Charly is disappointed that he consistently loses the races. Nevertheless, he is given the experimental surgery.
After the surgery, Charly is initially angered that he is not immediately smarter than he was before and still loses in races against Algernon. Eventually, however, he beats Algernon in a race and then his intelligence starts increasing rapidly. Alice continues to teach him, but he soon surpasses her. Charly's co-workers also try to tease him by making him work on a machine that they believe he will not be able to work. When Charly shows he can work the machine, his co-workers are not pleased with the fact that he is now intelligent and cannot be teased anymore. They sign a petition against him and he loses his job at the bakery. Charly also starts staring at Alice's bottom and breasts as well as drawing and painting abstract nude figures of her. He also questions whether Alice loves her fiancÃ©. One night, Charly follows Alice back to her apartment and sexually assaults her, pulling her to the floor and kissing her forcefully until she breaks free by slapping him.
The film then uses a montage sequence to show Charly â having escaped into the counterculture â wearing a mustache and goatee, riding a motorcycle, kissing a series of different women, smoking and dancing. At the end of the sequence, Charly has returned home and Alice comes to visit him, both having learned during their time apart that they want to be together. A further montage sequence shows Charly and Alice running through woods and kissing under trees accompanied by a voice-over of the two of them talking about marriage.
Straus and Nemur present their research to a panel of scientists, including a question-and-answer session with Charly. Charly is aggressive during the session and then reveals that Algernon has just died, causing Charly to believe that his own increased intelligence is only temporary. After suffering visions of his intelligence fading and of his pre-operative self following him, Charly decides to work with Nemur and Straus to see if he can be saved. Charly discovers that there is nothing that can be done to prevent his own intelligence from fading. Alice visits Charly and asks him to marry her, but he refuses and tells her to leave.
In the film's final scene, Alice watches Charly playing with children in a playground, having reverted to his former self.

Question: What do Charly and Alice realize in their time apart?
Answer: That they want to be together