## Movie Review: In Our Prime (2022)

By Peace Foo 胡適之

#### Synopsis

Directed by Park Dong-hoon, the movie opens with high school student Han Ji-woo (Kim Dong-hwi) and his struggles with mathematics. He crosses paths with security guard Lee Hak-sung (Choi Min-sik), a North Korean defector and reclusive mathematician whose story is gradually revealed throughout the movie, and ends up asking him for help in preparation for a tough exam. Hak-sung agrees to teach him – to appreciate math, rather than to cram. The movie then tracks their growing relationship (which the actors portray very well), the involvement of Ji-woo’s friend Park Bo-ram (Jo Yun-Seo), the impact of the exam and Hak-sung’s proof of the Riemann hypothesis (in reality still unsolved to this day). On the whole its setup has been compared to the 1997 film *Good Will Hunting*, which also features an anonymous but mathematically gifted university worker, but it has a strong story of its own and avoids rehashing the same plot. Without spoiling the movie, let’s see whether its plot makes sense in reality!

#### Who Was the Old Man in Hak-sung's Flashback?

At the end of Hak-sung’s first lesson he calls Ji-woo an “epsilon”. The memory that explains this is centered on Hak-sung’s childhood meeting with Paul Erdős, one of the most productive and eccentric mathematicians of the 20th century, who also independently proved the prime number theorem [1]. Erdős traveled around the world with only one suitcase of clothes, collaborating with so many different colleagues that mathematicians still use the “Erdős number” to track the network of people he worked with. He was also famous for his odd vocabulary, where he called women “bosses”, men “slaves”, lectures “sermons”, and non-mathematicians “trivial beings” [2]. (Hak-sung also calls Ji-woo a “trivial being” in the same scene.) Children were called “epsilons” because in calculus an epsilon represents a positive but very small number.

Erdős met many “epsilons” throughout his life. According to his biographer, Paul Hoffman, Erdős “made it his mission to seek out child prodigies all over the world” and encourage them with further problems [3]. He met the 10-year-old Terence Tao at the 1985 International Mathematical Olympiad (IMO), very similar to Hak-sung’s memory of Erdős meeting him at the 1982 IMO.

Erdős had already been teaching children gifted in mathematics as early as the 1960s:

*“[László] Lovász only started doing serious mathematics late in life, said Erdős, ‘at the ripe old age of nearly seventeen. When Lovász was still an epsilon, in the first year of high school, he and … a fellow mathematician courted the same boss-child, also a mathematician and not a bad one as bosses go. The two slave children asked her to choose. She chose Lovász,’ and they got married. But the love story could be improved upon, Erdős noted, by having the boss-child answer: ‘I will choose the one who proves the Riemann Hypothesis.’* *[3]”*

#### Did North Korea Actually Participate in the IMO?

In the segment announcing the proposed proof of the Riemann hypothesis, the mathematician Oh Jung-nam tells viewers that he once represented South Korea at the IMO alongside Hak-sung, who represented North Korea.

In reality, North Korea has participated in the IMO, but they did not begin doing so until 1990 and did not participate between 1993 and 2006. They were disqualified for suspected cheating in 1991 and 2010 [4, 5]. South Korea began participating in 1988 and has attended every IMO since then [6]. So neither Jung-nam nor Hak-sung could have gone to the IMO in 1982 as the movie shows. But it is quite likely that both would have done well based on the overall performance of the Koreas at the IMO: South Korea has the fourth most gold medals and North Korea has the 23rd, out of 120 participating countries in IMO history [7], although it is worth mentioning that North Korea has not participated as often as South Korea and the two countries often perform similarly well in individual tournaments.

#### What About the Nobel Prize?

Another newscaster heard that Hak-sung could be awarded a Nobel Prize for his proof of the Riemann hypothesis. This is not accurate. There is no Nobel Prize for mathematics; the most prestigious prize is the Fields Medal, which is only awarded to mathematicians 40 years old or under. The best estimate for Hak-sung’s age is 45–50 years old, so he would not get the prize. However, he would certainly be awarded the Abel Prize, established in 2001 and often described as a mathematics' equivalent to the Nobel Prize, as well as receiving the Clay Institute’s prize of one million US dollars for a successful solution to the Riemann hypothesis, one of their Millennium Problems. (Out of the seven problems, only one has been solved, the Poincaré conjecture, which we wrote about in Issue 019. Remarking that “Everybody understood that if the proof is correct then no other recognition is needed,” Grigory Perelman, another “hermit mathematician” like Hak-sung, refused both the prize money, and the Fields Medal.)

#### Is the “π Song” Real?

A review claims that the highlight of the movie is the scene where Hak-sung plays the “π song” to “convince [Ji-woo] that math is of ethereal beauty” [8]. With the digits of π written out in front of him, Hak-sung says that he will “play π” by assigning the digit 1 to the note C, 2 to D, and so on. He tells Bo-ram to accompany the melody that this produces. This is not a new way to represent the digits of π and many examples can be found on YouTube [9, 10].

The opening of the song in the movie does correspond to the first 14 digits of π:

3.1415 92

65358 97

As the accompaniment begins, aside from repeating this block, Hak-sung also weaves extra notes into his part of the song that do not correspond to digits of π. Then after the first glissando, he plays a simple repeating pattern of the next 14 digits:

9323 846 2643 383

But he does not follow it exactly throughout. In fact his part corresponds to the sequence:

9323 846 2643 383

9323 846 5

The song dresses these 28 digits of π up with a piano accompaniment. It does not necessarily present many digits of π in order, and is more of an interpretative art piece, though a very beautiful one that matches the tone the director wants to communicate in the movie. By itself π would not make much of a song anyway, since there is perhaps nothing mathematically special about its pattern of decimal digits. What has turned this essentially random pattern into a proper piece of music is the application of the human imagination.

Nevertheless, it’s a very fitting song for a movie that celebrates the advancement of mathematics. So much of this subject began as either a useless curiosity, like a dead butterfly pinned on a card, or a narrow solution to a narrow real-world problem; it is our imagination that propels individual parts of mathematics beyond either of these labels, and gives it the power and scope that makes it beautiful.

## What is the Riemann Hypothesis?If you are a serious math lover who wants to know more about the Riemann hypothesis and analytic number theory, please find the additional content here. |

#### References

[1] Stewart, I. (2013). *The Great Mathematical Problems.* Profile Books.

[2] Monroe, H., & Scott, P. (2004). Paul Erdős. *Australian Mathematics Teacher, 60*(2), 14-16.

[3] Hoffman, P. (1998). *The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth.* Fourth Estate.

[4] International Mathematical Olympiad. (n.d.). *Democratic People's Republic of Korea.* http://www.imo-official.org/country_team_r.aspx?code=PRK

[5] Berg, A. (2021). Statistical Analysis of the International Mathematical Olympiad. *Math Intelligencer, 43*, 105-112. https://doi.org/10.1007/s00283-020-10015-z

[6] International Mathematical Olympiad. (n.d.). *Republic of Korea.* http://www.imo-official.org/country_team_r.aspx?code=KOR

[7] International Mathematical Olympiad. (n.d.). *Results: Cumulative results by country.* http://www.imo-official.org/results_country.aspx?column=awards&order=desc

[8] Kim, B. (2022, February 23). (Movie Review) Mathematics no longer difficult in 'In Our Prime'. *Odyssey.* https://m.k-odyssey.com/news/newsview.php?ncode=179561410240172

[9] Blake, M. (2011, February 13). *What Pi sounds like* [Video]. YouTube. https://www.youtube.com/watch?v=WQdLDMLrYIA

[10] aSongScout. (2011, March 27). Song from π! [Video]. YouTube. https://www.youtube.com/watch?v=OMq9he-5HUU