# Unbowed

One of the movies that didn’t make it into Math Goes to the Movies, appearing just too late, is the 2011 Korean drama, Unbowed. The movie is a legal drama about a mathematics professor and contains almost no mathematics. But mathematics underlies the story, which begins with the professor finding an error in his university’s entrance exam, and with his mathematics department’s reaction:

Unbowed is a true story. In 1995, Kim Myung-ho, an Assistant Professor at Sungkyunkwan University, discovered an error in a problem while grading the University’s entrance exam. As indicated by the above clip, Kim’s department handled the error badly, and then things snowballed, to avalanche levels. The people responsible for the exam error and for subsequently mishandling the error were then also responsible for disciplinary action against Kim, and eventually for Kim not receiving tenure. Kim lost an unfair dismissal case and then lost an appeal in the courts in 2005. This all involved plenty of institutional and judicial arrogance, if not outright corruption. Finally, in 2007, a frustrated Kim confronted, and allegedly shot, a judge with a crossbow. This, to say the least, was not a great strategic move and Kim spent four years in jail for assault causing injury.*

Unbowed is the story of Kim’s legal battles and, reasonably, the movie only gives a very vague sense of the underlying mathematics problem and how the error was dealt with. The exact same problem appears a little more clearly, however, in the 2021 Korean TV series, Melancholia. In the first episode, the new mathematics teacher at a prestigious high school assigns the flawed problem, knowingly, in order to test her advanced but somewhat complacent mathematics students. The subsequent events are an interesting and telling variation of the real life story:

For those who didn’t quite catch it from the clip and who want to know the precise problem, we write it out below. But the essence of the problem, and the fundamental problem with the problem, are easy to state.

The premise of the problem is an inequality satisfied by three non-zero vectors in R3. It is then required to show that the three vectors are mutually perpendicular. The problem with the problem is that the premise is impossible: there do not exist three non-zero vectors satisfying the given inequality.

In response to Kim’s discovery, it seems that the mathematics department decided to award full marks both to students who proved the hypothetical vectors must be perpendicular and to students who proved the hypothetical vectors could not exist. Kim, however, disapproved; he argued, correctly, that the non-existence proof was mathematically far superior, and therefore should appropriately trigger greater reward. And thus the avalanche began.

For long-time readers, if this story seems to have a familiar ring that’s because it should. In 2019, the second Specialist Mathematics exam contained the exact same type of impossible-premise error, and then VCAA pretended the error was no big deal in the exact same cowardly, fantasyland manner.

### Unbowed‘s Mathematical Problem

Three non-zero vectors, A, B, and C in three-dimensional space satisfy the following inequality:

for all real numbers x, y and z. Show that the three vectors are perpendicular to each other.

*) Kim’s story is pretty wild and certain aspects are unclear. The story can largely be pieced together from the links included here and here and here, using Google Translate and the Wayback Machine. Kim’s story also received international coverage, and Kim received strong backing from prominent Western mathematicians, as evidenced by this 1997 letter to Mathematical Intelligencer (paywalled). In summary, it seems that Kim was eccentric and uncompromising, and thereby caused difficulty for his department. But, Kim was also a solid mathematician and had standards, and thereby caused difficulty for his department. There seems to be no doubt that Kim’s department behaved cowardly and then vindictively, and that Kim was denied tenure on contrived and very flimsy grounds. There is also very good reason to question the integrity of the various judges who tried Kim’s multiple court cases.