This is a story of an ill-posed mathematical problem, which seems to have led to serious injustice to an innocent young mathematician. We want to bring it to the attention of the readers of this journal, not only because it may carry a lesson, but also in the hope that international reaction could help the victim.
(Refer to Sir Atiyah and Prof. Lang at Yale)

MyungHo Kim, a young US-educated mathematician (Ph.D. from University of Michigan, 1988) returned to his homeland and assumed the position of Assistant Professor of Mathematics at Sungkyunkwan University in Seoul, South Korea, in 1991. In 1995, Kim participated in an entrance exam grading, an annual event usually taken very seriously in Korea, where the competition for entrance to college is fierce. During the grading, Kim found a serious mathematical error in the wording of one problem, which counted 15 points out of a total 100 points for the entire mathematical portion of the entrance exam. Here is the misstated problem:

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

$|xA + yB + zC|>=|xA| + |yB|$

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

The difficulty pointed out by Kim is that the hypothesis is null: no three non-zero vectors exist satisfying the hypothesis.

For distribution to students after the exam, the proposers had written out as the solution a (valid) proof of the conclusion.

$A\cdot B=B\cdot C=A \cdot C=0$

In response to Prof. Kim's observation, they called this part (i) of the solution, then appended as part (ii) the proof that also either $A$ or $B$ is 0. But this seems still unsatisfactory, because it leaves the graders with no possible way to grade the problem fairly: the student who had given only the originally intended solution, part (i) of the posted solution, might claim full credit. Yet the courageous student who wrote that the vectors cannot be non-zero has given mathematically a much superior answer. Kim therefore persisted in recommending that no weight be given this question in the grading.

This seems to us to be a sensible position, mathematically and pedagogically. Unfortunately, the senior faculty members(주: 채영도, 이우영 교수) in the department who were responsible for the error chose instead to fight Kim.

Since then, the department as well as the University began to take a number of disciplinary measures against Kim. He was first given stern warning and was threatened to be barred from teaching for one academic quarter (three months) without salary. Later Kim was denied promotion to Associate Professor (necessary for continuing his appointment); therefore his employment at the University was effectively terminated. We are told that both the suspension and the refusal of promotion were unprecedented in his department.

After Kim’s firing, a number of younger mathematical faculty in Korean university circles rose to support him, and petition (주: 법원에 제출된 전국 수학교수들의 의견서) were circulated protesting the University’s unjustified action to the Ministry of Education as well as the University. The petitions, however, did not help. Kim appealed to the courts, so far, unsuccessfully.

In his legal plea, Prof. Kim wanted to present to the court an independent authoritative statement that his objection to the contentious examination question was well founded. The Korean Mathematical Society (which naturally has interlocking directorates with Sungkyunkwan University(주: 성대 정봉화 교수가 당시 대한수학회이사) declined to give such a statement. Prof. Kim therefore turned abroad, and we willingly offered such a statement to the court.

What are the lessons of this extraordinary case? As for making a minor blunder in setting problems for an exam, no reproach should be made. Mathematicians make mistakes. But when their mistake is noticed, they should be quick to apologize and retract. To the colleague who pointed out the mistake, the proper professional response is not punishment, but thanks.



LAWRENCE A. SHEPP
AT&T Laboratories
Murray Hill, NJ 07974
email: las@research.att.com
(Current address: Statistics Department
Rutgers University
Piscataway, NJ
email: shepp@stat.rutgers.edu)
Member, National Academy of Science


SEYMOUR SCHUSTER
Department of Mathematics
Carleton College
Northfield, MN 55057
USA
email: sshuster@mathcs.carleton.edu


CORA SADOSKY
Department of Mathematics
Howard University
Washington, DC, 20059
email : cs@scs.howard.edu


RONALD GRAHAM
AT&T Laboratories
Murray Hill NJ 17974
USA
email:rlg@research.att.com

CHANDLER DAVIS
Department of Mathematics
University of Toronto
Toronto, M5S 1A1
Canada
email: davis@math.toronto.edu


ZANG-HEE CHO
Department of Radiological Sciences
University of California
Irvine, CA 92697, USA and
Department of Information and Communication
Korea Institute of Advanced Science and Technology
Seoul, Republic of Korea
email: zcho@uci.edu


For further developments,