Common Ground

The University of Washington’s Mathematics Department has an annual departmental potluck and musical event – a chance for faculty and grad students to socialize and show off some of their musical and performance talent. Each year I’ve tried to contribute something unique; last year in 2010 I wanted to entertain but also provoke thought. The opportunity to perform in front of a captive audience of my colleagues and mentors is too tempting to resist.

My goal was to capture what it’s like to be a mathematician, in an entertaining yet self-reflective way. My hypothesis is that, across our different fields, the combinatorialist, analyst, and algebraic topologist, etc, share many day-to-day and week-to-week experiences. Of course there is a diversity of experiences, but there are also similarities. It’s rare for the department to come together, and I wanted to use the occasion as an opportunity to express and address these commonalities.

For example, there’s the common, yet somewhat contradictory, philosophical stance of the practicing mathematician – “a formalist during the week and a Platonist on Sunday” (Hersh and Davis). There’s the nonlinear feedback loop and co-evolution of definitions, hypotheses, conjectures, and theorems (as in Lakatos’ Proofs and Refutations). There’s getting into the one-pointed concentration zone, where you feel like a mere conduit for the mathematical flow to express itself. There’s the use of machinery to break problems into smaller, more manageable pieces, slowly extracting small results that bit by bit add together. There’s getting completely stuck. There’s the paperwork and grading, and the extremely difficult casual conversation with the non-mathematician about your work. There are the times that distance and leisure suggest new insights or new perspectives. There’s the creating of new perspectives, and the discovery of what must be so. There’s that moment when the last piece falls into place, and certainty resonates within you (à la Poincaré). There’s the disappointment of finding a counterexample, and having to throw out a week (or month) of work.

My performance tried to express all these, in under ten minutes. It was part theater, part performance art, with a dynamic soundtrack and lots of bizarre props. There’s a video of this performance on my website, (well, any day now).

In a sense, this blog is an attempt at continuing the programme set out in that performance: to express some of the common experiences encountered along the mathematical path.

After the show, the feedback among my classmates and the faculty was better than I hoped. “Luke, you hit the nail on the head!”, “We were all just talking about it together… that’s exactly what it’s like to do math!” “The music you chose was perfect!”

I’ve tried to engage other mathematicians, in more or less formal settings, in this level of meta-mathematics. A continuing issue is that most mathematicians feel that any discussion involving math must proceed with utmost rigor and objectivity. I strongly disagree with this sentiment.  My performance at the math musicale succeeded, I think, because the medium – absurdist performance art – made it clear: we are contemplating mathematics, but in a looser, more subjective way.

So, as you read the blog, please withhold your insistence on rigor. It is necessary to math, but it is not all of math. Try to be mindful of how it feels to surrender rigor – how the subjectivity floods in, and in the flood what are the branches that we can hold on to? These are the threads of intersubjectivity – shared experience.

An everyday metaphor

When you go to the movies to see a romantic drama, the plot usually pulls from a database of common themes.  Likewise when you listen to the lyrics of songs on the radio.  If you’re watching a romance or listening to the radio, you sort of know what to expect.  The themes can be trite and arranged uninterestingly, as in your average romantic comedy.  They can also be presented artfully and uniquely, as in a Leonard Cohen ballad.  These themes are, in part, normative scripts that we are socialized to (e.g. hetero- versus homo-relationship paradigms), but they also express universals that appear across all or most human cultures.

So if this blog were about partnerships rather than mathematics, some flavors might be: the second date, meeting the family, cooking a meal together.  Some seasons might be: getting to know each other, traveling together, long-distance.  Thank Goodness I’m not making a blog about those things.

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