That’s it. I can’t go any longer without commenting on this. Since it would be utterly futile to even attempt to candy-wrap my opinions on this particular plaguing issue, I will not bother. The appalling way some mathematics courses, at the third-year level and beyond, are delivered has me lying face down on the shores of nausea. I am so utterly sick and tired of having to scribble down notes while an instructor does almost naught more than rote recitation from a textbook, bashing out long, dull strings of lifeless equations, or proving trivial (or at least very easy) theorems which just about anyone could figure out in less time than it takes them to read what you’re writing on the board. Worst comes to worst, I can always check one of the surely countless number of textbooks that contain this exact same computation. I’m begging you: if you ever catch yourself doing this, stop.
I don’t understand why 90% of lecture time is spent doing “follow-your-nose-and-oh-look-what-do-you-know-it-just-falls-out-of-the-definition” proofs while only around 10% is spent actually introducing new concepts or thought-provoking ideas. I don’t understand why students are asked to bash out boring book-keeping results in full detail on assignments. I know how to unwind definitions already. It just feels masturbatory now, to the point where I feel like getting a 0 on your assignment so I can have the time to solve interesting problems for once. What’s that? You want enlightening examples? Let me show you a trivial proof. What’s that? You think we should talk about alternate ways of viewing things, connections to other concepts, lucid reformulations, fruitful techniques that are ubiquitous in the area? Let me show you a robotic derivation that you could do in your sleep. I’m sorry, but if anyone ever told you that this is what mathematics is about, they lied. How can you defile, with such nonchalance, a subject that spawned from the deepest, most beautiful chasms of our imaginations?
Why are students at this level being treated like first-year calculus students who need to be shown formal, pedantic proofs of everything so they can “get used” to mathematical reasoning and have their notion of rigour properly calibrated? Hello, I’ve only taken like 20+ upper-year pure mathematics courses by now, if not more. I think (or at least by now I sincerely hope) we all know what rigour is, and can all feel whether a proof is legitimate or not. Otherwise, we would have received our mark of 50 or 60 in PMATH 351 (real analysis), realized this wasn’t for us, and moved on to major in something else.
Try as anyone might, they will never manage to extinguish my interest in mathematics. On the other hand, they are driving me straight to the insane asylum (or rather making me simply pass out cold on my desk during class) with such tedious, technical circle-jerking. People are paying a pretty penny to learn about advanced math, and they’re being taught… [??????] well, I don’t even know what the hell they are being taught.
Someone needs to just put an end to this once and for all. I’ve been resisting making a post like this for probably over a year and a half. I should just stick to graduate courses from now on… but if it was up to me, there would be some serious changes in the way people teach mathematics.
(I refuse to comment on which course(s) contributed anything to the ultimate authoring of this post. The reason for this is that I do not intend to personally attack or insult any particular instructor. My post is phrased as a general lamentation. However, I am clearly not cowering behind anonymity: I take full responsibility for my opinions, and am very receptive of any criticism or opportunities for further discussion.)