Re: Chen review

[John Baez <baez@math.ucr.edu>]

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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