Math study plan (Part 2)

That purpose laid out (though not to my satisfaction), here is my current four-prong method:

I schedule regular reading for the comfort of home or a coffeeplace. During this time I overdose on coffee and shut myself off from the internet, except to read excerpts chosen beforehand on subjects that I lack. I do not perform many exercises during this time, although I don’t deemphasize their importance in general. It is merely an observation that to learn mathematical theories in an intuitive and visual way requires a different state of mind than exercises. I emphasize a commonsense understanding of proofs.

It is also necessary to have a pen and paper on hand to write down the ideas that inevitably occur to me, as these can be highly distracting.

I schedule different times for completing a small number of exercises while engaged in some mindless distraction, like laundry or cleaning. I believe this is important because exercises can be difficult, boring, and time-consuming all at once. (Sometimes they are exhilerating, when I’ve grasped an idea very quickly or jumped some conceptual hurdle and begin to make great progress very quickly. But often, exercises are well-named.) While engaged in coincidental distraction, there is no distracting pressure to perform this creative task quickly. As you may have experienced yourself (or know from the Duncker’s famous candle experiment), this actually increases your quickness. Given unfettered time to properly consider a question, I can usually answer it more quickly and more easily.

Aside from the aspects of pressure and time, I find that this also encourages me to clean, launder, and iron my clothes more often. And boredom rarely results from this combination of tasks. It seems to be very stimulating for me.

I perform far more exercises at my workplace. I will conceal the text and a notepad in one of my favorite hiding places and read a question, consider it in the course of my mundane activities, and return to write down the answer. This method of mental manipulations and intuitive leaps of logic or cleverness, rather than writing each line in tedious step-by-step applications of algebraic rules, has always been my preferred mode of operation. You can imagine the effect this had on my grades upon entering public school. It served me well enough in college, where my classmates learned that I made far more mistakes in the course of simply reproducing a line than by mistakes of calculation. (My inattention and disaffection to the physical world has always caused me to make this sort of mistake.)

Please note also that this prong is facilitated by previous exercises that ensure I have a beginner’s understanding, else I find myself completely baffled and unable to read up on the subject. In such a crisis, I brush up on previously completed exercises.

Last, I try to follow up on the interesting ideas that occurred to me in the course of reading or calculating. This is, unfortunately, the prong of the approach that receives the highest negligence of the four. There is not much more to say, other than to acknowledge that it is a freeform activity, more or less at leisure, improved by drunkenness, and usually not very constructive. I believe I simply don’t have the necessary intelligence, compulsion, or diligence associated with the purebred stock of true geniuses.

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