What Chocolate Cake Has to Do with Theoretical Mathematics

By Noah Kaufman |

© Julie Craig

University of Sheffield lecturer Eugenia Cheng is and always wanted to be a mathematician, but while pursuing such a complicated, competitive field she wanted to play it safe: Her backup plan was to be a concert pianist. And then if that didn’t work out: pastry chef. Not a bad lineup of dream careers, but you may be thinking that they're pretty divergent paths. Not so, believes Cheng, who's about to release a new book called How to Bake π on May 5. For a book on higher-level math, Cheng, who also just finished a stint teaching at the University of Chicago, made it surprisingly accessible by introducing concepts with tangible goods everyone understands, like brownies and cake.

For example, did you know that the mathematical notion of proof by contradiction is tied to flourless chocolate cake? Here’s how.

It would be tricky to conclusively prove that every cake must have flour in it. In order to do so, you would need to find every cake in the world—probably every cake in history—and check to see if they had flour. Instead of proving that is true, you could prove the opposite is false. Make a cake recipe without flour, and if it fails, you’ve proven that cakes must have flour. As Cheng points out, what you actually end up with in this case is a still tasty but different sort of dessert. 

Setting out to prove one thing and accidentally discovering another like this, she says, is how mathematicians make some of their most important discoveries—it's how Euclid discovered parallel lines. 

If you’ve ever been interested in what happened after that algebra two class you hated so much junior year, this book could be a good way in, especially if you like to cook. And because no good book about math and food would be complete without some recipes, Cheng starts every chapter with one. Here’s hers for what she calls Conference Cake, the first thing she ever baked for a math conference.

Conference Chocolate Cake


  • 5oz butter, softened
  • 5oz granulated sugar
  • 2 large eggs
  • 5oz self rising flour
  • About 7 squares of semi-sweet chocolate 
  • Cocoa powder to taste


1. Preheat the oven to 350 degrees.

2. Cream the butter and sugar.

3. Beat in the eggs, then fold in the flour.

4. Beat in the cocoa powder until the batter looks dark brown.

5. Half-fill 14 small muffin cups with the mixture, then put half a square of chocolate in and cover with more batter.

6. Bake for 10 minutes. Eat immediately.

How to Bake π is available for preorder now.

Related: A Look at Some of the World's Most Beautiful and Modern Chocolates 
 Go See the World's First 4-D Dress at New York's Museum of Modern Art 
7 Things You Didn't Know About Chocolate