1.6 Why are certain repetitive activities more pleasurable than others? 15

1.6 Why are certain repetitive activities more

pleasurable than others?

Ivan crossed it all out and decided

to begin right off with something very strong,

in order to attract the reader’s attention at once,

so he wrote that a cat had got on a tram-car, and

then went back to the episode with the severed head.

Michael Bulgakov, The Master and Margarita

Let us turn our attention to the emotional side of mathematics,

more specifically, to the personal psychological experience of people

working with mathematical algorithms and routines.

I wish to formulate here some of my observations and conjec-

tures which may appear to be bizarre and out of tune from the

usual discourse on mathematics. However, I tested some of them in

a warm-up talk that I gave at the forum discussion Where do math-

ematicians come from? [457], part of a very peculiar conference,

that of the World Federation of National Mathematics Competi-

tions (WFNCM). It was held in July 2006 in Cambridge, England.

On my way from Manchester to Cambridge, four hours by train, I

had seen three people solving Sudoku puzzles. In one case, a lady

of middle age shared a table with me and I had a chance to watch,

in all detail and with a growing fascination, how she was solving

an elementary level Sudoku puzzle. Her actions followed a certain

rhythm: first she inspected the puzzle row by row and column by

column until she located a critical cell (whose value had been al-

ready uniquely determined by the already known values in other

cells) and then, with obvious agitation, checked that was indeed

the case, happily wrote the digit in, smiled with a childish satisfac-

tion, relaxed for a few seconds, and, after a short pause, started the

search again.

The next day, in my talk at the conference, I pointed out that,

from a mathematical point of view, solving an elementary level Su-

doku puzzle is nothing more than solving a triangular system of

Boolean equations by back substitution, something very similar to

what we do after a Gauss–Jordan elimination in a system of si-

multaneous linear equations. But has anyone ever seen people on

a train solving systems of linear equations from a

newspaper?9

Why is Sudoku popular, when systems of linear equations are

not? (Actually, I was slightly wrong: at the time of my talk, I was

unaware of Kakuro, which combines linear and Boolean equations.

But one still has to see whether Kakuro beats Sudoku in popular-

ity.)