Illustration by Dana Collins
THE GREAT HUNGARIAN NUMBER THEORIST PAUL Erdös famously remarked that a mathematician is merely a machine for turning coffee into theorems. Erdös (pronounced air-dosh) was one of the most prolific mathematicians of all time, with over 1,500 papers to his name when he passed away in 1996. But it would take more than death to stop this relentlessly protean mind; new Erdös papers appear every year as his many collaborators continue to publish the eclectic fruits of their interactions with him. Utterly disinterested in food, and apparently most other quotidian aspects of life, Erdös was said to be fueled almost entirely by caffeine.
Free associating, food is not likely the first word that springs to mind at the mention of mathematics. Drinkis probably a more common response. Nonetheless, as the mathematicians would say, neither are the two concepts "nonintersecting sets." Let us then, in this season of enthusiasm and ingestive excess, depart from Erdösian disdain of the body and pay homage to the gastronomic delights of the numerical sciences — a mathematical feast.
Naturally, for this event we will be seated at neatly columnized tables. Our wine will be served from a Klein bottle, that enigmatic object closely related to the Moebius strip. Indeed a Klein bottle can be understood as a Moebius strip that has been tubified. You can't actually realize this form in regular space, but imagine a bottle whose mouth twists back through its surface and joins up with its bottom. Nothing but the finest vintage will suffice, and so we choose champagne, Heidsieck Monopole, in honor of the "magnetic monopole," a yet-to-be-detected particle whose existence has been theorized in mathematical equations developed by the quantum theorist Paul Dirac. True to their name, monopoles are isolated magnetic poles — a north without a south or a south without a north. No one has ever seen one, but few theoretical physicists doubt that they exist. Ye of little faith might bear in mind another impossible object first glimpsed in Dirac's equations — antimatter, a negative shadow of regular matter that has now become a mundane tool of particle physics.
Our menu itself promises a unique dining experience that is for the most part more homey than haute. We start — how can we not? — with quark soup, an ultra-dense state of matter that according to current theories filled the cosmos in the split second after the Big Bang. Through mathematical equations, theoretical physicists attempt to model the material world, and no gastro-mathic shindig would be complete without this classic of quantum cuisine. The very ingredients are a mathematical puzzle, for, like monopoles, no one has ever seen a singular quark. In the universe today they always come in pairs (making up mesons) or in triplets (making up protons and neutrons), but when the temperature rises to around 10 trillion degrees, a further state is predicted in which masses of quarks are smushed together into a kind of superdense minestrone formally termed the quark-gluon plasma.
Next, I suggest an appetizer of super-egg, an exotic geometric form whipped up by the Danish scientist-poet Piet Hein. As a furniture maker and constructor, Hein helped to spread the pristine aesthetics of Scandinavian design around the world while as a poet he enchanted his countrymen with whimsical doggerel — think Buckminster Fuller meets Lewis Carroll. But like Carroll, Hein was also a gifted mathematician and in addition to discovering the enchantingly titled "Soma cube," he created the super-ellipse, a sort of hybrid between a rectangle and an ellipse. The three-dimensional version of this chimerical object Hein dubbed the super-egg, or super-ellipsoide, which possesses the enviable property of superbalance. Order up a healthy serving to counter the inevitably destabilizing effects of the Monopole.
Following our elliptical appetizer, we might indulge in a round of ham sandwiches, courtesy of my own personal gastro-mathematical favorite, the ham-sandwich theorem of topology, which addresses a problem regarding the slicing of objects in three-dimensional space. Here's the setup: Take two slices of bread and a slice of ham; now, scatter these items about the room. You can put them anywhere — stick them to the ceiling, hang them from a windowsill, float them in the middle of the room. Now that they are dispersed, ask yourself this: Is it possible with a single cutof a large knife to bisect all three objects — the bread and the ham — in one clean sweep? (Mathematicians really do ponder such things.) The answer is yes.
The ham-sandwich theorem is complemented by the insights of the so-called pancake problem. Here the issue can be stated as follows: Imagine a pancake on a griddle — it can be as irregular and raggedy a shape as you like. Now, is it possible with a single cut to slice this pancake into precisely equal halves? Again the answer is yes — there always exists some line that will neatly bisect the pancake into two equal areas no matter how erratic its shape. What if you have two pancakes? The answer is still yes; it can be mathematically proven. Since the normal operators of algebra and topology were hardly designed with butter and flour in mind, the reader may be wondering just how a mathematician specifies her pancake. To quote from one of the more prominent mathematical Web sites: "A pancake is defined to be a simply connected subset of the plane with nonzero finite area."
