Hi - While we're at it, here is my own review of Cheng's book, which should eventually appear in the notices of the London Mathematical Society. Eugenia Cheng has written a delightfully clear and down-to-earth
explanation of the spirit of mathematics, and in particular category theory, based on their similarities to cooking. Sometimes people complain about a math textbook that it's "just a cookbook", offering recipes but no insight. Cheng shows the flip side of this analogy, providing plenty of insight into mathematics by exploring its resemblance to the culinary arts. Her book has recipes, but it's no mere cookbook.
Among all forms of cooking, it seems Cheng's favorite is the baking of desserts---and among all forms of mathematics, category theory. This is no coincidence: like category theory, the art of the pastry chef is one of the most exacting, but also one of the most delightful, thanks to the elegance of its results. Cheng gives an example: "Making puff pastry is a long and precise process, involving repeated steps of chilling, rolling and foldking to create the deliciously delicate and buttery layers that makes puff pastry different from other kinds of pastry."
However, she does not scorn the humbler branches of mathematics and cooking, and there's nothing effete or snobby about this book. No special background is needed to follow it, so if you're a mathematician who wants your relatives and friends to understand what you are doing and why you love it, this is the perfect gift to inflict on them.
On the other hand, experts may be disappointed unless they pay close attention. There is a fashionable sort of book that lauds the achievements of mathematical geniuses, explaining them in just enough detail to give the reader a sense of awe: typical titles are A Beautiful Mind and The Man Who Knew Infinity. Cheng avoids this sort of hagiography, which may intimidate as often as it inspires. Instead, her book uses examples to show that mathematics is close to everyday experience, not to be feared.
While the book is written in bite-sized pieces suitable for the hasty pace of modern life, it has a coherent architecture and tells an overall story. It does this so winningly and divertingly that one might not even notice. The book's first part tackles the question "what is mathematics?" The second asks "what is category theory?" Unlike timid people who raise big questions, play with them a while, and move on, Cheng actually proposes answers! I will not attempt to explain them, but the short version is that mathematics exists to make difficult things easy, and category theory exists to make difficult mathematics easy. Thus, what mathematics does for the rest of life, category theory does for mathematics.
Of course, mathematics only succeeds in making a tiny part of life easy, and Cheng admits this freely, saying quite a bit about the limitations of mathematics, and rationality in general. Similarly, category theory only succeeds in making small portions of mathematics easy---but those portions lie close to the glowing core of the subject, the part that illuminates the rest.
And as Cheng explains, illumination is what we most need today. Mere information, once hard to come by, is now cheap as water, pouring through the pipes of the internet in an unrelenting torrent. Your cell phone is probably better at taking square roots or listing finite simple groups than you will ever be. But there is much more to mathematics than that---just as cooking is much more than a mere cookbook.
I'm not sure "exacting" is the right word to describe category theory, but there's probably *something* difficult about it that it shares with making pastries. Obviously I couldn't say "abstract". Best, jb On Sat, Aug 29, 2015 at 10:36 PM, pjf <pjf@seas.upenn.edu> wrote:
Free Press Journal (India)
August 28, 2015
Cakes, Custard & Category Theory - Culinary approach to maths
LENGTH: 482 words
New Delhi: Cooking can be an answer to simplifying mathematics, says a new book which tries to whet the appetite of maths whizzes and arithmophobes alike with recipes and puzzles.
From simple numeracy to category theory ('the mathematics of mathematics'), maths crusader Eugenia Cheng prescribes easy recipes for understanding complex arithmetic in her book "Cake, Custard and Category Theory".
Calling on a baker's dozen of entertaining, puzzling examples and mathematically illuminating culinary analogies - including chocolate brownies, iterated Battenberg cakes, sandwiches, Yorkshire puddings and Mobius bagels - Cheng tells readers why everyone should love maths.
So what on earth does a recipe have to do with maths? "You might think that rice cookers are for cooking rice. This is true, but this same piece of equipment can be used for other things as well: making clotted cream, cooking vegetables, steaming a chicken. Likewise, maths is about numbers, but it's about many things as well - getting the right answer, putting ideas together and so on," she says in the book, published by Hachette India.
According to Cheng, a senior lecturer in Pure Mathematics at the University of Sheffield, many people are either afraid of maths, or baffled by it, or both.
"Or they were completely turned off it by their lessons at school. I understand this - I was completely turned off sport by my lessons at school, and have never really recovered. I was so bad at sport at school, my teachers were incredulous that anybody so bad at sport could exist. And yet I'm quite fit now, and I have even run the New York marathon," he writes.
She says 'category theory' which can be thought of as the 'mathematics of mathematics' is about relationships, contexts, processes, principles, structures, cakes and custard.
"Yes, even custard. Because mathematics is about drawing analogies including custard, cake, pie, pastry, doughnuts, bagels, mayonnaise, yoghurt, lasagne and sushi."
Maths, according to Cheng, like recipes, has both ingredients and method. "And just as a recipe would be a bit useless if it omitted the method, we can't understand what maths is unless we talk about the way it is done, not just the things it studies," she says.
Citing examples of cottage, shepherd and fishermen pies, she says all these are more or less the same with the only difference being the filling that is sitting underneath the mashed potato topping. In all these cases, the recipe is not a full recipe but a blueprint and one can insert own choice of fruit or meat or fillings.
"This is also how maths works. The idea of maths is to look for similarities between things so that you only need one 'recipe' for many different situations. The key is that when you ignore some details, the situations become easier to understand, and you can fill in the variables later," she writes.
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