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I think I am looking more for how to organize my thoughts, and much of this overlaps with "how to study," which, I am still trying to learn how to do.

My method of working is, well, not working:

Look at the problem in a book, write it down clearly (this is the one to hand in).

Another piece of paper - write down the problem.

I'm showing P implies Q...

Write down the bits of information I know that might be relevant - theorems, definitions.

Look at P... what does it imply? Which of the theorems might be relevant to P in particular?

Start stringing things together.

Out of paper

Grab another... start scribbling implications, stringing things together.

Ok, if Q was true, what would that imply?

more scribbling... more paper...

Then the "staring" phase begins.. it looks like I am not working, but of course I am "thinking." Except I am not thinking... "thinking" implies some sort of linear process. I'm perhaps contemplating or waiting for an idea to strike.

I very rarely get struck with ideas like some people do. My experience is more along the lines of "You don't understand things in math, you just get used to them." (Said some mathematician)

Revelations often come to me like when somebody reveals the secret of a magic trick. Not a delighted "OH so THAT'S how it's done!" But more of a "Oh..so THAT'S how it's done?"

I don't get inspirations on walks or during showers while doing the dishes. I don't wake up at 2:00 in the morning with an idea of how to solve something, though I do tend to have math floating through my head all night, which I suppose is my mind processing something.

I very often end up googling problems or parts of problems, and I feel very bad about this. I do not copy verbatim, but try to convey the idea of the proof in language that I understand, even at the risk of it being wrong. (I'd rather hand in something incorrect and original than something correct and unoriginal, even though it has cost me a grade to do so).

I know there is no "algorithm" to writing proofs, but there must be something better than what I am doing...

-Dave K