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Edward Kmett
Haskell programmer, mathematician, lapsed graphics guru and demo scener, defense contractor and financial toolsmith.
Haskell programmer, mathematician, lapsed graphics guru and demo scener, defense contractor and financial toolsmith.

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Cakes, Custard, Categories and Colbert

Today, my friend Eugenia Cheng will appear on The Late Show with Stephen Colbert!   She'll be one of three guests, including that guy who starred in some recent James Bond movies.

Eugenia recently wrote a book called Cakes, Custard and Category Theory: Easy Recipes for Understanding Complex Maths, which has gotten a lot of publicity.   This must be why she's on the show.

In the US, this book appeared under the title How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics, presumably because Americans are less familiar with category theory and custard (not to mention the peculiar British concept of “pudding”).

Eugenia learned category theory as a grad student at Cambridge, mainly from Peter Johnstone and her advisor Martin Hyland.  But around that time Hyland became interested in some mathematical structures called n-categories, which are even better than categories.  Eugenia wound up doing her thesis on an approach to n-categories that James Dolan and I had dreamt up. 

I visited Cambridge for the first time around then, for purely coincidental reasons - my wife was visiting a research institute there. I started hanging out in the mathematics department, and Eugenia and I wound up becoming friends.  So, it makes me really happy to see she’s bringing math and even category theory to a large audience.

Here’s my review of Eugenia’s book for the London Mathematical Society Newsletter:

    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 pastery different from other kinds of pastery.”

    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 merely following a cookbook.

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"If two statisticians were to lose each other in an infinite forest, the first thing they would do is get drunk. That way, they would walk more or less randomly, which would give them the best chance of finding each other. However, the statisticians should stay sober if they want to pick mushrooms. Stumbling around drunk and without purpose would reduce the area of exploration, and make it more likely that the seekers would return to the same spot, where the mushrooms are already gone."

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My "Review" of Haskell covering why I am still a programmer today.

Note: You do not need to register with Quora to read. You can click the "Close & Read" button outside of the box.

Why Quora?

Mostly to reach out to people who are outside of our little #haskell  channel / reddit bubble.

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“Much as beavers, who as a species hate the sound of running water, plaster a creek with mud and sticks until alas that cursed tinkle stops, so do category theorists derive elaborate and obscure definitions in an attempt to capture a concept that to most of us seemed perfectly clear before they got to it. But at least sometimes this works admirably …”

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+Simon Marlow shows new GHC developers how the scheduler is implemented.
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