There are 3 types of mathematician: those that can count and those that can’t.
Old joke (places me in the appropriate, unskilled math category)
Do not worry about your difficulties in mathematics. I assure you that mine are greater.
Einstein (hard to believe in my case, Herr Dr.)
The well-educated person is assumed to have some mathematical skills. Since I want to be one of those people, I must continuously work on my math chops. Welcome to my workout studio.
Einstein reminds us that it never gets easier. The more experience one gets, the more insurmountable the difficulties, so eventually all end up with the same insight at some level: this stuff just got too hard.
So why math for me?
- I wanted the appearance of a well-educated person, which demands math skill.
- Math seemed to have more gravitas than other subjects, although I wasn’t sure why.
- It was not my best subject, but had never given me any particular grief.
- I thought science-oriented studies would land me a job I might like, but I didn’t much like other science. Labs were not my thing. Math posed the least potential drudgery of any of technical course of study.
- Betting four years of one’s life seems at minimum to demand a fair game. Unlike the humanities, the math TAs had very few degrees of freedom with which to mess with one’s success.
- The people I spent time with also liked math.
That’s as many synthetic reasons as I can muster at this late date. Who ever really knows why?
My own mathematics background now resembles a permanent hangover, a faint remnant of my college struggles of long ago. My only antidote consists of the hair of the dog that bit me, my mathematics library. All the information I seek is there, waiting, waiting, waiting…
Math was a slog for me because I never could get to the big picture, the answer to why any sane person would care about all this. I was unsophisticated (apparently more so than the usual undergraduate). Details bored me when they remained disconnected from larger purpose and motivation. I could grasp the beauty of abstraction, but without motivation beyond aesthetics, what’s the point? Math never became my passion, so I am destined to remain a math poser.
My professors seemed clueless about a need to convey mathematical motivation. I never heard from them why I should care about a new topic, before plowing into it. Simple analogies and examples are all it would take to align the student’s mind with the new topic, but such was so seldom offered that it seems in retrospect totally missing from my background. Study was mechanical, all about learning technique, an entirely local view that assumed each textbook and its prerequisites represented the entire universe of relevant mathematics. Mathematics was thus conveyed as comprised of separable entities, not an organic whole. Due to the lack of context, I was uninspired to put in the work necessary to become enlightened.
The world-class research university I attended was not oriented in the slightest to hand-holding and shepherding of students who would benefit from more insight. I realized no one was going to bring it to me; I had to go out and get it. But that is harder than it sounds, particularly for a shy personality. As the first person in my family to attend college, I wasn’t mentally tough enough to make such a learning environment work for me.
My advisor was pleasant, but he did not attempt to cultivate a relationship and I never took a class from him, so I never felt free to just drop in and talk about my concerns. I felt like a faceless statistical aberration during the couple of times I may have met with him. His specialty was Complex Analysis, emphasizing visualization techniques in his pedagogy. This subject was a source of some of my math drudgery, providing an additional disincentive to visit. I could have used some of his visualizations, but the one time I recall going there to ask for more resources to get to a larger picture of my study topics, I received a pleasant pep talk about not wanting too much too soon, to keep grasping what details I could and the larger view would eventually come to me. At that point, I sadly lowered my aim, figuring that I should just ensure I did well enough to graduate. It was close, but I got the cigar.
Here we are now, late in life, without a map or a plan or yet a larger view. So I do random exploration, noodling here anything interesting that grabs my attention, and providing notes regarding my on-line math courses. This is math largely at the high school level for clever students. That I can still follow and improvise mathematical trains of thought makes me feel that my math studies were not a total waste.
My scribblings here are ‘organized’ into n sub-menus (a variable is the principal defense for one who cannot count:-).
About Mathematics is a series of articles describing the ‘big picture’ of mathematics, something one might wish to know before commencing formal coursework in mathematics.
Fearless Symmetry dives deeper into Algebraic Number Theory, son Barry’s research field, following, in chapters, the exposition of the book by the same name. It is essentially a long, technical book report.
Explorations demonstrates development of an occasional mathematical train of thought, or some specific problem of interest, motivated by cognizance that mathematics can’t be experienced without getting one’s hands dirty.
Math Publishing describes how I accomplish my scribbling here.