Eugenia cheng makes math a piece of cake – the new york times

Dr. Making homemade pasta sauce Cheng pulled from the oven a perfectly baked specimen of what she calls Bach pie, named for the great composer beloved by mathematicians everywhere: an oblong rectangle of creamy dark chocolate studded with banana slices and topped by an Escher-like braid of four glazed pastry plaits that followed divergent trajectories, never quite crisscrossing where you expected them to.

The filling was a clever concatenation — “BAnana added to CHocolate gives you Bach,” Dr. Homemade italian sauce for pasta Cheng said. Homemade pasta sauce canned tomatoes The braiding illustrated the structure of a Bach prelude and the sorts of patterns that knot theorists study “to see how looped up the braids are,” Dr. Tomato pasta sauce with cream Cheng said, “and whether you can transform one braid into another by wiggling the different strings.”

The pie was a true union of art and math, too beautiful to besmirch, and besides, you’re not supposed to untie knots with your teeth, are you?

Dr. How to make homemade pasta sauce from scratch Cheng, 39, has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board. Homemade easy pasta sauce She is a theoretical mathematician who works in a rarefied field called category theory, which is so abstract that “even some pure mathematicians think it goes too far,” Dr. Homemade pasta sauce crock pot Cheng said.

At the same time, Dr. Homemade pasta sauce recipe Cheng is winning fame as a math popularizer, convinced that the pleasures of math can be conveyed to the legions of numbers-averse humanities majors still recovering from high school algebra.

White sauce recipe for pasta and chicken She has been featured on shows like “ Late Night With Stephen Colbert,” and her online math tutorials have been viewed more than a million times. Tomato sauce recipe for pasta easy Dr. Homemade pasta sauce in crockpot Eugenia Cheng gives Paula Deen a run for her butter. Homemade pasta sauce for lasagna Video by The Late Show with Stephen Colbert

The hardcover edition of her first book, “How to Bake π: An Edible Exploration of the Mathematics of Mathematics,” has sold about 25,000 copies in this country and been translated into six languages, a surprising hit for a text visibly if judiciously seasoned with numbers, graphs and equations. Homemade pasta and sauce The book is being released in paperback this month. Homemade pasta sauce food network Photo

So committed is Dr. Homemade spaghetti sauce from scratch food network Cheng to mass math demystification that she recently left a tenured professorship at the University of Sheffield in Britain to take a position at the School of the Art Institute of Chicago, where she teaches math to art students, lectures widely and continues her research in category theory on the side.

Dr. Homemade tomato sauce for pasta Cheng adopts a literal approach to making math more appetizing. Homemade pasta sauce using fresh tomatoes “Math is about taking ingredients, putting them together, seeing what you can make out of them, and then deciding whether it’s tasty or not,” she said.

Every chapter in “How to Bake π” offers recipes for desserts and other dishes that encapsulate mathematical themes. Tomato pasta sauce jamie oliver To demonstrate how math seeks to identify underlying similarities across a broad set of problems, for example, Dr. Easy homemade sauce for pasta Cheng starts with a recipe that can be readily tweaked to make mayonnaise instead of hollandaise sauce.

“Books might tell you that hollandaise sauce needs to be done differently,” she writes, “but I ignore them to make my life simpler. Best homemade spaghetti sauce using fresh tomatoes Math is also there to make things simpler, by finding things that look the same if you ignore some small detail.”

Her recipe for lasagna illuminates the importance of context to math. Homemade tomato pasta sauce using fresh tomatoes Dr. Homemade meat pasta sauce Cheng lists among the basic ingredients “fresh lasagna noodles,” and then points out that another cookbook might deem the noodles not truly basic and instead describe their preparation from scratch.

So, too, do numbers change their character and degree of basicness depending on context. Make homemade pasta sauce The number 5, for example, when viewed among the natural, or counting, numbers is one of those elemental creatures: a prime number, divisible only by 1 and itself.

But in the context of the so-called rational numbers, which include fractions, 5 loses its prime identity and gains versatility, able to be divided into ever tinier slivers, like a cake at a dieters’ convention.

The number 1 in its multiplicative identity is practically bedridden, leaving other numbers unchanged: 6 times 1 equals 6. Tomato pasta sauce brands In its additive capacity, however, 1 is unstoppable: if you keep adding 1 to itself, Dr. Homemade pasta and sauce recipe Cheng noted, you can generate all the natural numbers, out to infinity.

“I admit I was skeptical at first about her analogies to cooking, but I ended up being completely sold,” said Steven Strogatz, a professor of applied mathematics at Cornell University who also writes popular books.

“She conveys the spirit of inventiveness and creativity in math that all mathematicians feel but do a very poor job communicating when teaching math. Homemade spaghetti sauce recipe no meat Refreshing is the word that keeps coming to mind.”

Dr. Easy homemade tomato pasta sauce recipe Cheng wears glasses, has long black hair and walks with an elegant, upright posture, like a dancer. Easy homemade spaghetti sauce with meat She is alternately outgoing and reserved, passionate and matter-of-fact. Homemade white sauce for pasta She is a classically trained musician and owns a 1910 Steinway grand piano.

She is also an extremely good cook. Homemade pasta sauce slow cooker On a recent afternoon, we are in her well-stocked kitchen, and she is stirring a mix of egg yolks, sugar and cream — my lesson in nonassociativity, otherwise known as custard. Sauce for pasta noodles This is something where the way you combine ingredients counts, she said.

If you’re making a cake, you can throw together the flour, sugar, butter and eggs however you please, and the cake will come out fine — that’s an associative process. Homemade pasta sauce quick Not so for preparing custard. Homemade spaghetti sauce from whole tomatoes You must first combine the sugar and egg yolks and whisk them into a froth before you pour in the cream.

In math, too, you have associative operations like addition and multiplication, where you can change how your numbers are whisked together as you calculate and still emerge with the same answer: (4+5) + 6 is the same as 4+(5+6).

Subtraction, division and exponentiation are nonassociative operations: Who’s clumped with whom matters. Homemade tomato sauce for pasta recipe So, while 10-(6-4) will give you 8, (10-6)-4 leaves you with nothing.

Dr. Tomato pasta sauce recipe nz Cheng continues stirring the custard, peering into the pot to ensure that lumps aren’t forming. Homemade pasta sauce without tomatoes “People ask me, do you eat your custard warm or cold?” she said. Homemade pasta sauce from garden tomatoes “I tell them, I eat it all at once.”

She adjusts the temperature of the burner, up and down, up and down. Homemade pasta sauce recipe with fresh tomatoes Getting the custard to come out just right can be tricky, she said — harder than doing math, and more like living life.

Dr. Homemade pasta sauce with tomato sauce Cheng insists that the public has it all wrong about math being difficult, something that only the gifted mathletes among us can do. Tomato pasta sauce recipe italian To the contrary, she says, math exists to make life smoother, to solve those problems that can be solved by applying math’s most powerful tool: logic.

Science may depend on forming hypotheses, doing experiments and gathering evidence that support or refute your hypothesis, but math is simply a matter of stating the terms of your argument and then defending those statements using logic. Homemade pasta sauce for baby Photo

Dr. Homemade spaghetti sauce recipe with garden tomatoes Cheng recognizes that people can feel uncomfortable with some of the abstractions required by mathematical thinking, by the need to ignore the particulars of, say, this green round pillow and that square purple pillow in favor of an abstract ideal of a pillow that you’re going to call x.

But it’s just a matter of practice, she said, before the idea starts to feel like a real object that you can manipulate with ease. Homemade pasta sauce with tomato paste “You become very good at separating what’s relevant from what isn’t, and that can be very useful in daily life,” she said.

Sometimes, she finds it “oddly satisfying” to mentally shave a bearded man or imagine how a furry dog would look like after a swim in a lake. Quick homemade pasta sauce recipe “That’s what abstraction is,” she said. Homemade spaghetti sauce recipe from scratch “You reveal the structure underneath.” A Number Chef’s Roots

Dr. Homemade pasta sauce nz Cheng’s upbringing in rural Sussex as one of two daughters led her readily to math love. Best homemade spaghetti sauce recipe from scratch Their mother, a statistician who had been considered the most brilliant math student at her Hong Kong high school, would keep her girls entertained at the beach for hours with books of logic puzzles.

And because their mother commuted each day to a London accounting firm while their father had a child psychiatry practice near home, the girls grew accustomed to the idea of a briefcase mother and a father who made dinner.

“I think Eugenia and I both benefited from the atypical setup,” said Alethea Cheng Fitzpatrick, Dr. Easy homemade cheese sauce for pasta Cheng’s older sister and now an architect in New York. Homemade pasta sauce tomato “We didn’t go into adulthood with any preconceptions about gender roles or gender abilities.”

Later, during graduate school at Cambridge University and three postdoctoral fellowships in Europe and the United States, Dr. Recipe for homemade tomato pasta sauce Cheng would often find herself in a tiny minority. Sauce for pasta and salmon “I’ve been to conferences where there were more cubicles in the women’s bathroom than there were women to use them,” she said.

Today, in the United States, less than 30 percent of graduate students and about 12 percent of tenured faculty members in math are women. Sauce recipe for shrimp pasta Dr. White sauce recipe for pasta with cheese Cheng is striving to change attitudes across the board. Easy homemade spaghetti sauce recipe with canned tomatoes “I want to be a role model for men as well as women,” she said.

* Let x be me and y be my father. Homemade pasta sauce recipe without tomatoes Today, y =3x . Homemade meat sauce for pasta In 10 years, my father will be y +10 and twice my age, so y +10=2(x +10). Best homemade pasta sauce recipe Since 3x =y , we can get rid of the y in that equation, as 3x +10=2(x +10). Best homemade pasta sauce And since 2(x +10) is the same as 2x +20, we can now say 3x +10=2x +20. Homemade pasta sauce jamie oliver Finally, subtract 2x from both sides of the equation and you get x +10=20. Easy canning homemade spaghetti sauce recipe Therefore, x =10, and I am 10 years old.