16 1 A Taste of Things to Come

We will not understand the psychologi-

cal and neurophysiological roots of an

important aspect of mathematical prac-

tice until we figure out why bubble wrap

popping is such an addictive and pleas-

ant activity.

Still, why is Sudoku popular? I be-

lieve the answer is in a rhythm of

repeated cycles of operations each of

which engages our brains just up to

a right and most pleasurable level of

intensity. As a student, I experienced

the soothing, relaxing effect of car-

rying out a recursive algorithm, like

long division, or Euclid’s algorithm.

Later, in my research work, I felt a

similar emotional impact from inductive arguments in finite group

theory: you start with a minimal counterexample to the theorem

and then simplify it step by step, like removing layers from an

onion, until you pinpoint the core contradiction and destroy the

counterexample. My teacher Victor Danilovich Mazurov expressed

the principle of a “minimal counterexample” using a line from a

Russian fairy tale:

The oldest brother hid behind the back of the younger

one, the younger one hid behind the youngest one, and the

youngest brother fell on his knees, raised his hands and

pleaded for mercy.

In mathematical education, especially at its earlier stages, one

of the teacher’s tasks is to give his/her students the opportunity to

feel this soothing, comforting effect of a rhythmic repetitive activity.

And here I come to the crucial point:

why do people love to pop bubble wrap?

I would not write this now if the audience of my talk at the

WFNMC conference had not immediately agreed with, and ap-

proved of, my comparison of the execution of certain types of re-

cursive algorithms with bubble wrap popping. I should perhaps ex-

plain that the audience included some of the best experts on math-

ematical education in the world, especially on advanced and non-

standard aspects of mathematics teaching. They definitely knew

everything about the so-called “recreational mathematics”, puzzles,

brainteasers, and conundrums of every possible kind. Their sup-

port allows me to be quite confident in my comparison of Sudoku

with bubble wrap popping. In any case, the lady on the train was

doing her Sudoku in an immediately recognizable bubble wrap pop-

ping rhythm.

So, with the authority of the conference on my side, I dare to

formulate my thesis:

We shall not understand the psychological and neurophysi-

ological roots of an important aspect of mathematical prac-

tice until we figure out why bubble wrap popping is such