전 미국 수학회장의 서한
(1997, 1, 6, Scanned Image)

Professor Hyo Chul Myung(주: 명효철 교수 회신 거부)
KIAS, Dongdaimoongu, Cheongryangri-dong 207-43
Seoul, Korea 130-012


Dear Professor Myung:

The difficulties that a young mathematician, MyungHo Kim at SungKyunKwan University, has come to my attention from the American Mathematical Society's Committee on Academic Freedom, Tenure, and Employment Security

The difficulties that Professor Kim has had with the university authorities appears to have come as a result of Kim's discovery of what he regarded as an error in the statement of a problem on the university's entrance examination. His difference with the people who set the examination seems to have resulted, ultimately, in his being fired from his positions.

To be brief, CAFTES sees its role in assisting Kim as confined to obtaining the judgment of several mathematicians on the problem in question. Accordingly, I have been asked by the Chairman of CFTES to express myself on the matter.

The problem reads.

When three non-zero space vectors a, b, and c satisfy

               abs(xa+ya+zc)>=abs(xa)+abs(yb)

for all real numbers x, y and z, show that a, b and c are mutually perpendicular.

I have been told that Kim, while he and others were grading the examination papers, discovered that the hypothesis of the problem can never be satisfied. When he pointed this out to his colleagues, the previously prepared solution was altered to read that the conclusion of the problems is vacuously true because the hypothesis is never satisfied. Kim contended that everyone who took the examination should be answered the same credit (15%) for the problem, for it had caused confusion and many wasted time trying to solve it.

My own view is that Kim was correct in noting that the hypothesize is never satisfied and he was also correct in asserting that, effectively, the problem should have been discarded or, equivalently, that everyone should have been given full credit.

Statements that are vacuously true have a place in mathematics. They are actually logical conveniences that may make for a simple rendition of a theorem by eliminating special cases. But they seem to me to be inappropriate for problems on a university entrance examination. In fact, I have never encountered such a problem on any examination.

I sincerely, hope that the American Mathematical Society has been of some assistance in resolving the differences that may have occurred at SungKyunKwan University.

Sincerely yours,

R.L. Graham
Past President, American Mathematical Society