A couple o’ days ago, I posted a question about how to come up with a set of parametric equations equivalent to an implicit equation. It seemed to me like the general solution to this broad question would be like differential equations. There would be certain tools you could pull from the toolbox, once you saw what “kind” of equation you were dealing with. There isn’t a one-size-fits-all algorithm for solving differential equations (at least, not that I learned).
I got to thinking… didn’t I learn how to convert between parametric and implicit equations some time years ago? And, in fact, the answer was: yes. I took a class on algebraic geometry. The book we used (one of my favorite math textbooks when I was an undergrad) was:
The way this course was designed (it was officially a “seminar”) was that each day, two students would “teach” a section from the book to the rest of the class. We somehow made it through the whole book. It was a great experience, having to learn a section well enough to teach it the my classmates. The class was — however — a bit of a failure. The desks were in a row, people rarely asked questions, and no one engaged with each other. (Much like most of my college math classes, actually.) For something so student-based, it was strange that I didn’t make a single friend in that class. Plus, there was no “teaching” us how to teach well. Some some of us were great teachers, but most of us sucked. I can’t say what I was, really. I don’t remember. Regardless, I remember thinking: this textbook was incredible because I pretty much had to teach myself the subject. (I have to give major kudos to the instructor because he forced me to learn an entire course by reading a textbook.)
So upon reminiscing about this class and this book, I pulled it down from my bookshelf.
I am so dumb.
I will revise: I am so dumb now.
I look at the pages, and read theorems like Theorem 9 on page 241
“Two affine varieties 
![k[V] \cong k[W]](https://s0.wp.com/latex.php?latex=k%5BV%5D+%5Ccong+k%5BW%5D&bg=ffffff&fg=333333&s=0&c=20201002)
and see words like “Nullstellensatz,” and wonder how I ever got to the point where this stuff made sense, and how I got to the point where I see a bunch of gibberish now. Seriously, it’s disturbing. I mean, I don’t expect to be able to pick up a book I learned from years ago and know everything in it, but I do expect that it is in a language I can read.
I’ve figured it out. I am Charlie in Flowers for Algernon.
I don’t know how to feel about the loss of my mathematical mind, besides sad.
Maybe I’ll try teaching myself some math again, to either prove to myself I still have it somewhere in me, or to know that my brain has truly atrophied to a giant anti-intellectual morass.
Continuous Everywhere but Differentiable Nowhere 
I had a similar realization a few years ago myself and now try to pull out a textbook each summer and “review.” It also reminds me why the parents of students even in Algebra I have no idea what’s going on in there. “If you don’t use it, you lose it” is always appropriate.
You should see what happens to your math brain after teaching fractions for 10 years!
That happened when I first pulled out the calc book last summer. It had been 6-7 years since I took a calc class, and I vaguely remembered all the notation, but I couldn’t spit out any of the theorems or anything. I can only imagine what would happen if I tried to sit down with my Axiomatic Geometry text from college. Oy!
I feel the same way about physics. It should make me feel better that its “not just me” but it doesn’t…
Charlie is the PERFECT analogy.
You are not alone. Grad school keeps reminding me of all I’ve forgotten…
I feel this way sometimes even when reading stuff I wrote myself in college. Paging through my master’s thesis (on educational uses of history of physics), there are sections that seem quite unfamiliar even though it’s not much more than five years since I wrote them. And this will only get worse… sigh.
On another note, one incentive for commenting now was to see what kind of weird avatar would show up. Hoping for one half as cool as the one next to Jessica’s comment. Now what does THIS say about what has happened to my brain? :)
It will all come back and then some! Start where you can understand something and then work the problems! I speak from experience. Eight years ago, after a year of student teaching and four years of college in which I did hardly any math, I worried I’d “lost it” (whatever that “it” was that had made me so triumphant in math as a high schooler including). Now, after two years of studying on my own, taking notes section-by-section on Michael Artin’s Algebra, working every problem, and more recently taking a few grad classes, I’ve never felt more mathematically powerful. In fact I think I might be able to prove the Nullstellenzatz off the top of my head.
Although apparently I can’t spell it.
(Nullstellensatz.)
I’ve returned to grad school after 15 years from an undergraduate degree in math, and it felt very foreign. I remember the first week of class feeling like I was in a Charlie Brown episode. I remembered the words, but could find meaning in them. I had to go back and retake the undergraduate course in hopes of being successful in the graduate course the next time around.
So, you’re telling me that it’s not depression, menopause, early onset Alzheimers, etc., but just a lack of practice? I hope you are right, but I have other confusing symptoms that cause me to constantly say “I feel like Flowers for Algernon. I used to be so smart in math, but my math-brain is broken!”