Reading, ‘Riting and ‘Rithmetic

Thoughts of mathematics are never far from my mind — a hazard of the profession as mathematician, perhaps. Often these thoughts are inspired by current events, most recently the extraordinary and extraterrestrial successes of the New Horizons and Kepler missions, much of which was made possible by mathematics. But the truth is that you don’t need to travel to Pluto to see or think about math. You can do it just by going out for breakfast in a bakery in Santa Fe.

The Chocolate Maven in Santa Fe is a bakery well-known for its delicious pastries, cookies, and breads. It’s also a great place for breakfast that has the added attraction of a large glass wall at one end, allowing the diners to watch the baking in action. As I was sitting there slightly bleary-eyed with my wife, I was soon transfixed by the croissant-making going on just on the other side of the wall, enjoying and relaxing to the rhythm of the process and slowly, but inexorably, starting to think about mathematics.

What can I say? I can’t help myself. Part of the danger of the profession I suppose. I like to believe that for most of us the events of the day, even the most quotidian, are filtered through the things that we think about most, so that pretty much every experience becomes some kind of odd Rorschach test. On the other side of the glass an economist might have seen an Adam Smith-like division of labor, a chemist or physicist could have reflected on the baking process, while a businessperson considered the profit margin or workflow. I’m a mathematician and I saw math.

Math? Math in bakery? Sure. Plenty of it.

Directly in front of me a large sheet of pastry dough is laid out, that the baker smooths and trims into a rectangle as the first step to making a tray of croissants. He then runs a knife lengthwise down the middle of the sheet, cutting it into two, he then makes 18 cuts in the opposite direction, creating a grid of 36 smaller rectangles. Finally, he slices each of these rectangles along the diagonal, to make 72 triangles, each of which would soon be rolled up from base to tip (after filling some with either a slab of chocolate or marzipan) before being placed in their trays. The sequence of multiplications that I did (2 times 18 times 2) allows me to count how many croissants were about to be produced with out actually counting them out individually, and I presume the baker did the same as he quickly wrote the number down on the board before rolling up the pastries. There are so many kinds of math, even in this little exercise: the implicit “factoring” of 72 as 2x18x2 that leads one to consider factoring in general and the wide world of number theory. Or the hints of “combinatorics” in the resolution of the question of “how many croissants did we get?”


William H. Neukom ’64 Professor of Computational Science, Director of the Neukom Institute for Computational Science, Professor of Mathematics and Computer Science, at Dartmouth College, Santa Fe Institute External Faculty




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