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.

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, 이우영교수)
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: [email protected] (Current address: Statistics Department
Rutgers University
Piscataway, NJ
email: [email protected])
Member, National Academy of Science

SEYMOUR SCHUSTER
Department of Mathematics
Carleton College
Northfield, MN 55057
USA
email: [email protected]

CORA SADOSKY
Department of Mathematics
Howard University
Washington, DC, 20059
email : [email protected]

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: [email protected]