전 미국 수학회장의 서한
(1997, 1, 6, Scanned Image)
Professor Hyo Chul Myung(주: 명효철 교수 회신 거부)
KIAS, Dongdaimoongu, Cheongryangridong 20743
Seoul, Korea 130012
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
nonzero 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
