It has been a while; a philosophical question:

The start of the semester has gotten in the way of my blogging. :-) But I am in between watching football and grading exams.

For the first part of the semester, I had a "refereeing" job to do for a math journal. Basically, when someone writes an article for a math journal, the journal sends the paper to a mathematician to be checked for accuracy and to be checked for quality (i. e., is what is being offered really a good contribution to the literature?).

In this referee job, the authors submitted a result that was worth publishing, and their proof was, on technical grounds, basically correct. But their proof was quite dreary; there were far more elegant and elementary ways to reach their conclusions and any specialist who read their article would note that immediately.

So, what was my duty in this case? What I ended up doing is telling the editor what I just said and made the necessary suggestions.

Now, as far as grading exams: I am teaching a "calculus with precalculus" class. Basically, we go through the first semester of a standard engineering/science/math calculus class at half speed; the two semesters of this class put together counts as one semester of calculus.

On this exam, several (20-25% of the class) presented the following answer: "9 < x < 3".

Ok, perhaps a few made a blunder during the pressure of an exam; we've all done that. But, there are students in this class who simply don't see why this statement is complete nonsense. And frankly, they won't be able to unless it is explained to them "very slowly".

Folks, these students simply don't have a chance of success in any major that requires mathematical ability. I actually have stronger thought than this (in that there are majors that these students could succeed in) but I probably better keep these thoughts to myself.

Sigh....I suppose we sometimes have to find things out the hard way.