This rant is inspired by a debate going on at meta.math.SE. The subject of the debate is what steps the moderators should take to prevent the use of math.SE to cheat in ongoing math competitions. If you have an interest in the subject and an account on meta.math.SE, I encourage you to head over and participate including, if you are so inclined, voting on the poll questions I just posted.
The particular point I want to address is posters who write that the fault is with contest organizers, for not designing their contests with internet age security in mind. A typical exemplar of this viewpoint writes
[Cheating] is a problem with folks using antiquated methods for tests, contests, etc. – methods that are a poor fit to the current information age. Any problems they encounter should be fixed at the source – not kludged here.
I strongly disagree.
How many times in your mathematical career have you heard “math contests test nothing but speed and trickery, and have nothing to do with deep mathematical ability?” “Math contests reward those with strong test taking skills, and discourage those who dislike high pressure gimmicky environments.” “Math contests allow no time for contemplation or discussion?”
I believe that these are all true. This isn’t a case of sour grapes — I test very well, think very fast, and enjoyed math competitions greatly. But I have met many colleagues who think more slowly than I do and nonetheless are superb mathematicians. So the problem emerges, how can we design contests which show students that mathematics has room for contemplation, cooperation and insight, not simply rapid tricks?
In answer to this question, contests like the USAMTS and OMO were born. These contests ask challenging and intriguing problems, require detailed written answers and give weeks to solve them. I loved the USAMTS when I was in high school; every question was well written and interesting, and I pushed myself to write the best answers I could. The OMO is after my time, but it looks like it was designed with similar love.
Such contests are impossible to secure. You can’t ask high school students to live under proctored conditions for a week.
Cheating in contests is damaging to everyone who competes. In theory, of course, participants could simply focus on achieving their own personal best, and not think about their own placement. In practice, seeing cheaters prosper produces disillusionment, disgust and a feeling of wasted effort. This true in any field of competition, but it is worse in competitions where there is no absolute gauge of accomplishment, such as these contests. A runner who finishes the SF marathon in 2:44:05 knows she has a superb race no matter what others may have done; a Math Olympian who sees that someone got 74/75 on the USAMTS has no way of knowing whether his own 72/75 was still a superb performance or not.
If we want there to be contests which reward prolonged thought, we run competitions which can be cheated on. If we want competitors to value their achievements in these contests, we who answer questions on math fora need to be vigilant about shutting cheaters down.
PS A much harder question is how to deal with university courses. Many of the same arguments against high pressure timed exams apply, but part of what universities provide to their students, and to society, is certification of mathematical ability. I am still struggling with these issues.