Jim Propp... Enchanting Us With Math

Math-Frolic Interview #37

 " 'Enchantment': a feeling of great pleasure, delight; the state of being under a spell; magic." -- Internet dictionary


James Propp doesn't post as much as a lot of other math bloggers... but when he does (once-per-month) it's always a delight! ...But then, if you read Jim you already know that; if you don't, check out his MathEnchantments blog as soon as you can.
Jim is a professor at the University of Massachusetts/Lowell, having been previously associated with Harvard, MIT, and U. of Wisconsin/Madison, among others.
His home page, with a lot more about him, is here:  http://faculty.uml.edu/jpropp/
...and his Twitter handle is: @JimPropp 

Lastly, Jim is a Comic Sans font fan, and as such automatically gets high respect from me! ;-)  Read on (and learn a little about some ideas/problems you've likely not heard of before)....

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1)  Tell us whatever you'd like about your path to becoming a mathematician, including when did you know you wanted to pursue mathematics professionally?

I've been quasi-obsessed with math since an early age. During elementary school recess, I was the kid in center field trying (unsuccessfully) to compute twenty-six cubed in my head (because that's the number of three-letter initials a person could have). I developed strong interests in music and theatre, and toyed with the idea of pursuing musical theatre professionally, but in the end I returned to my "first love" and I've never regretted it.

2)  I love the title of your blog "Mathematical Enchantments" because it captures so well what you do on your site. Just curious if that was a name you easily arrived at, or did you consider a lot of other names before settling on it? (I ask in part because when I chose blog names myself long ago the first ones that came to mind were already taken, and I sort of worked my way down a list 'til I found one available.)

I've wanted to run a Martin Gardner-esque column for decades, but research and teaching and family life kept me busy, and I kept putting it off. But it was family life that eventually led me to the name of the blog. Reading to my kids and making up stories for them made me realize the ways in which the world of math --- a world that at first exists just on the page but then becomes immersive when you figure out how to jump into the page --- has become, for me, a replacement for the magic that I hankered after in my own childhood. Once I became aware of this link, the blog named itself. And luckily no one else was using that name! 

3)  You only blog once per month but it is always a fairly substantive, thoughtful, longish post (and quite unpredictable as far as topic)... How do you decide what you will post on each month, and how far ahead do you work on posts?

Sometimes I write pieces to help jump-start other, more formal writing projects. And sometimes I opportunistically exploit tie-ins with current events (my last essay, on Fermat, was catalyzed by Andrew Wiles winning the Abel Prize, and my next essay, on Ramanujan, will hopefully ride the coat-tails of the movie about Ramanujan now showing in theatres). But mostly I just follow my enthusiasms, which shift unpredictably.

I'm hoping to get six months ahead in my writing, but for now at least I pretty much work month-to-month. I have a large file of ideas, and one of the things I do when I write a piece is I scan through my ideas file to see if any of those ideas tie in nicely with the piece I'm working on. Finding these connections is one of the pleasures of the work. It's also one of the reasons why my essays tend to be on the long side. 

4)  You recently considered starting a podcast... can you say anything about how that's going in these early stages?

Right now I'm considering recording some of my Mathematical Enchantments essays in audio format, for the sake of the vision-impaired and people who like me spend a lot of time driving. I'm not sure that qualifies as a podcast. In any case, I don't plan to do it unless more people say they'd actually like to listen to me reading my essays aloud.

I'm a big fan of podcasts and I'd love to get involved with one, but I don't think I'd want to do it on my own; the podcasts that I love the most (like RadioLab and Invisibilia) feature multiple voices and multiple points of view. Also, most of the ideas in my ideas file have a visual component --- I haven't got a supply of story ideas suited to oral presentation. Maybe in a few years I'll start to think more seriously about podcasting.

In the meantime, I'm planning to make some short videos about chip-firing, discrete probability, and generalized radix-systems, since the link between those topics is a really pretty story that hardly anyone knows. It ties in nicely with the "exploding dots" pedagogy that James Tanton has developed (partly inspired by a talk I gave over a decade ago, which in turn was based on Arthur Engel's "probabilistic abacus"); the World Math Project has adopted exploding dots for its inaugural year, so there should be some Jim Propp videos on chip-firing etc. when the World Math Project debuts in October 2017, if not sooner. You'll have a chance to not just hear me but see me talking about mathematical ideas that excite me.

    
    [...sounds fantastic! ]

5)  Any plans in your future to write a popular math volume, based on your blog (or other material)?

My blog posts double as drafts of chapters of books I hope to write someday. I'm too undisciplined (and busy) to write books one at a time the way most authors do, but I think once I've got ten years of essays written, I'll start tying them into thematically coherent bundles and writing some new material to bring specific themes to the fore. 

6)  What are some of your own favorite popular math reads, and/or books you'd recommend to others wishing to be 'enchanted' by math?

As a kid I enjoyed "One, Two, Three, Infinity" by George Gamow and several books by Isaac Asimov; as a teenager I enjoyed Martin Gardner and Carl Sagan; and in my twenties I enjoyed Douglas Hofstadter and Raymond Smullyan and Rudy Rucker. But that's all old stuff. I wish I'd kept up with the last thirty years of popular writing in mathematics, so that I could give a more up-to-date answer! 

7)  Professionally, what math problems/areas are you currently most interested in, or working on?

I spread myself pretty thin (more than I think is wise, professionally), and am usually thinking about a dozen or more problems in rotation. Right now many of these problems are about iterative processes of a combinatorial nature. One example concerns something called Bulgarian Solitaire that I learned about from a Martin Gardner column. Arrange n objects into piles, and create a new pile by taking one object from each old pile. Do this again. And again. Here's the new bit: Each time you do it, write down the number of piles. As time goes to infinity, the average of the numbers you've written down converges to a particular number that (unsurprisingly) depends on n but (surprisingly) does not depend on the original way in which you arranged the objects into piles. (Compare what you get starting from 6+2 with what you get starting from 5+3, for instance; in both cases the average number of piles converges to 3.5 over time.) There are lots of phenomena like this all over combinatorics.

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Wow! sounds like we have a lot to look forward to coming from you Jim. Thanks for taking time to tell us a little about yourself and what may be coming down the pike.
Again folks you don't want to miss out on:
https://mathenchant.wordpress.com/