CHICAGO — We had just finished the mathematician Eugenia Cheng’s splendid demonstration of nonassociativity where the order of operations counts — as it does in, say, subtraction.

Now she wanted to forge ahead with the next lesson, in knot theory.

I suggested we wait until later. “Why?” she asked.

“Well, we shouldn’t eat two desserts before dinner, should we?” I said, and giggled nervously.

“Why not?” she replied, not giggling. She tightened her apron strings and walked over to her stove.

Of course. What was I thinking? Hadn’t Dr. Cheng already made clear her conviction that in mathematics, rules are like eggs: meant to be broken, stirred, flipped over and taste-tested? And that day, we had broken a lot of eggs.

“You’re absolutely right,” I said, rushing to her side for the grand unveiling of another mathematically themed confection.

Dr. 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. Cheng said. 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. 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?

Another rule, easily broken.

Dr. Cheng, 39, has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board. 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. Cheng said.

At the same time, Dr. 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. 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.

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. The book is being released in paperback this month.

“I spend a lot of time explaining mathematics on blogs, and I try to cut through the technicalities and make things easier to understand,” said John Baez, a professor of math at the University of California, Riverside (and yes, a cousin of Joan). Still, his posts are aimed at scientists and others with some quantitative background.

“Eugenia has gone all the way in,” he said. “She’s trying to explain math to everybody, with or without pre-existing expertise, and I think she’s doing wonderfully.”

So committed is Dr. 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. Cheng adopts a literal approach to making math more appetizing. “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. To demonstrate how math seeks to identify underlying similarities across a broad set of problems, for example, Dr. 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. 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. Dr. 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. 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. In its additive capacity, however, 1 is unstoppable: if you keep adding 1 to itself, Dr. Cheng noted, you can generate all the natural numbers, out to infinity.

Context can prod numbers to defy grade-school verities: 2 plus 2 equals 4, and that’s that. But not if you’re talking about a clock face with only three numbers: 1, 2 and 3. In that case, 2 plus 2 equals 1 – if you start at the 2 and move clockwise by 2, you reach 1.

“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. Refreshing is the word that keeps coming to mind.”

Dr. Cheng insists that the public has it all wrong about math being difficult, something that only the gifted mathletes among us can do. 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.

“The great thing about math is you don’t need much to start exploring it,” Dr. Baez said. “No expensive equipment, just pencil and paper, and you can start fiddling around with patterns and numbers.”

Dr. 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. “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. “That’s what abstraction is,” she said. “You reveal the structure underneath.”