Episode 4 of Melancholia begins in the aftermath of Gyu-yeong’s Photoshop fiasco. Yoon-soo’s relationship with her fiancée is somewhat strained and Seong-jae doesn’t enjoy hearing that there’s been gossip about Yoon-soo and Seung-yoo. He tells her she can quit teaching if it becomes too difficult. He also schedules a lunch appointment for the two of them with Vice Minister Shin without consulting her.
Although Gyu-yeong apologizes to Seung-yoo, he’s still jealous of him. He states that he will make the maths prodigy bow to him one day.
Ms. Noh has schemes of her own though. She gives Hye-mi a pre-written speech for Ye-rin. She also warns the mother that they must pretend Ye-rin trained for the Olympiad at school. People could suspect preferential treatment if they learned of her internship.
Min-joon unexpectedly drops in on Yoon-soo and Seong-jae’s lunch with the vice minister. Yoon-soo tells him that she read through his daughter’s speech and got the impression that Ye-rin had expert help.
Min-joon laughs off her implication. He claims that Ye-rin received help from the AI Technology Research Centre, but that she wrote the speech herself.
On their drive back from lunch, Yoon-soo and her fiancée get into another fight. He asks her not to spend too much energy on Seung-yoo. When he implies that he knows the Olympiad is rigged, Yoon-soo becomes angry and gets out of the car.
Seung-yoo finds her sitting on a park bench, where they make plans to go to Jeju island for another art exhibit. Meanwhile, Ye-rin and her mother have plans to go to the AI Centre for Ye-rin to give a presentation.
While Ye-rin is celebrated for her excellent work, Seung-yoo takes pictures of Van Gogh’s paintings and quite a few photos of Yoon-soo.
He tells Yoon-soo that he researched her father, Professor Ji. She explains that her father worked for years on the problem she gave Seung-yoo in episode 2. Professor Ji worked for a decade on that problem, but people discovered a flaw in his theorem. He tried to fix it for years, but never could.
That’s why she asked him not to fall in love with the equation. She says she feels the same about mathematics. She wants him to like it, but not become obsessed with it.
Seung-yoo wonders to himself how it’s possible to have control over the things he falls for. He’s obviously thinking of his teacher, whom he’s developing feelings toward.
At the airport, Yoon-soo falls asleep and Seung-yoo guides her head to his shoulder. Ye-rin sees them and prevents her mom from noticing. But later, it’s revealed that Ye-rin takes a picture of them.
In the meantime, Ms. Noh catches up with her sister after they make connections with the Vice Minister. Ms. Noh threatens Yeon-woo’s assumption that she has no competition for their father’s position as chairman of the Ahseong Academy Foundation. From now on, both sisters are in the running.
Back at school, Yoon-soo gives Ye-rin feedback on her speech. Ye-rin admits that mathematics has never been easy for her. She accuses the teacher of being enchanted with Seung-yoo’s talent, even though people like him don’t have to work as hard. Yoon-soo tells her she hopes she’ll enjoy the Olympiad, not treat it as a competition.
At the speech portion of the Olympiad, Seung-yoo runs into one of his professors from MIT. When the professor mentions what a special child he was, Seung-yoo tenses up. He remembers another person who used to call him special—a fellow student at MIT.
Ye-rin witnesses as he breaks down and runs from the room. He runs crying into a car park on an upper floor. As he walks toward a ledge, he remembers his former classmate again. It’s heavily implied that, as a young child, he discovered that his friend jumped off a ledge to his death.
Over the phone, Seung-yoo tells Yoon-soo that he can’t go through with the speech. Just as he’s ready to give up, he feels light shining on his eyes, reminding him of a picture titled “Melancholia.” He also remembers Yoon-soo’s words when she showed him the picture: “Once you let everything go, you can dream of a new beginning. You can see things you didn’t see before.”
He starts seeing equations all around him. He furiously begins writing. Yoon-soo finds him. As tears streak down his face, he tells her he solved her father’s impossible problem. He decides he’ll go through with his speech.
Ye-rin gives an eloquent speech, and everyone believes she will win. But she feels horrible afterwards, running to the bathroom to throw up.
Seung-yoo’s speech is different from all the rest. Rather than focusing on how AI will change the trajectory of technology, he emphasizes AI’s finite nature. Whereas AI can only perform limited functions, humans are infinite.
The episode closes with his impassioned statement: “Infinity isn’t in the far future, but right now, is in us all.”
This episode is the catalyst for romantic development between Seung-yoo and Yoon-soo. Though Yoon-soo makes no inappropriate overtures to her student, he obviously now has a crush on her.
While I think Melancholia shows Seung-yoo falling too hard and too fast, his infatuation is kind of sweet and relatable. Yet it’s also heartbreaking, considering we know what will come of their attachment—however innocent—due to the flash forward in episode 1.
The show does take a predictable and cheesy turn with Seung-yoo’s speech being a love letter to humanity though.
I definitely don’t see a bunch of bribed judges (or any judges at all) accepting an emotional appeal over logical research. My guess is that Seung-yoo is going to have even more obstacles to overcome in the rest of the Olympiad because of his stint with the speech. Then again, is winning going to be important to him at all?