## Math paper draft finished

I reached a milestone tonight as I finished a draft of a paper for submission to Mathematics Magazine.    (There is still the submission process to go, and once I know the result, I’ll either link to the paper, or include it here on the blog.)  It took quite a bit of work to get the paper to this stage, I really tried to do a decent job with the math, and I learned a lot about writing about math too.

The road to this paper started with a recreational problem that came up in discussion at my work about 2 months ago.   The problem caught my attention and since I’d been focusing on improving my math thinking the past few months, I challenged myself to see if I could make any headway on the problem.  I sat down at lunch and worked up the basic idea for the solution.  I was 70% of the way there in that first 15 minutes, and then blocked.  I was blocked that night.  I was blocked for the next week.  For the next two weeks I kept the problem around and tried small avenues forward to see if I could finish it.   It was frustrating, but I kept at it slowly, and after a time, had a realization that not only solved the problem directly, but yielded much more than I expected!   It was that slow two week process that was the most interesting to me.  I had to really detach from the outcome and instead attach to the reasoning process.  I was valuing the progress of small provable steps in any direction rather than the final answer.  (Interestingly, even after the answer was at hand, it still took me a while to verify the numbers with Sage, and even longer to clean up all the peripheral cases.)   This study was a great learning experience.

The last month and a half I embarked on the writing process.  I was shocked that this took even longer than solving the problem.  It was, in fact, rather messy.  However I think much of it was a first-time learning experience.  I learned the value of coming back to the paper after a cool-down period.  And of double checking mywork.  And finishing my work.  I read several wonderful articles on writing mathematics including,

All worth reading if you are planning on doing any writing in math.

However the submission process goes from here – I’m very glad of the effort I put in.  I’ve already learned enough to make it worthwhile.