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Burn Math Class: And Reinvent Mathematics for Yourself

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A manifesto for a mathematical revolution

Forget everything you've been taught about math. In Burn Math Class, Jason Wilkes takes the traditional approach to how we learn math -- with its unwelcoming textbooks, unexplained rules, and authoritarian assertions-and sets it on fire.

Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically -- and it becomes fun!

Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various "advanced" topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus.

Like the smartest, craziest teacher you've ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.

400 pages, Hardcover

First published March 22, 2016

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Jason Wilkes

1 book9 followers

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5 stars
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Displaying 1 - 16 of 16 reviews
Profile Image for Ryan Croke.
118 reviews2 followers
February 17, 2019
I was a full professor at a top tier public university in applied mathematics and here is my opinion: Couldn't agree more with the premise, couldn't be more disappointed in the execution.

I have taught calculus to thousands of students and the author's passion for rethinking the presentation is on the money. I have fought this battle for so long and presenting the rigors of mathematics in a more accessible way and using a "ground-up" approach pays dividends. No doubt.

But where is the research backing this? Were the test scores of his students substantially higher? Where is the data that supports this approach? And, irony of all ironies, as the book goes on he uses the same naming conventions and lexicon that one can find in any textbook at any university. For example, the building of differentiation is almost verbatim what you would find in any Calc 1 class: First look at constants, then lines, then quadratics, then general polynomials. I mean quite literally exactly what you find. Even the idea of looking at infinitesimals is the same. I couldn't find anything new about this presentation other than using softer language.

The provocative title may grab you but in reality there is nothing new here; just a reminder that technical people fall in love with formalism and this is a huge barrier to entering the beautiful world of mathematics. Mathematicians tend to brow-beat their audience at times, though hopefully not on purpose, and the thesis of this book is that they shouldn't.

If you aren't familiar with calculus and higher mathematics the first 2 - 3 chapters will be pretty useful and interesting.

If you are interested in mathematical presentation and education, and have some background, I suggest you look to "Journey into mathematics" by Joseph Rotman or similar works.

To the author - taking some concepts from other areas of mathematics and applying your methodology may have served a stronger case: How would you describe neural nets? Fourier Transforms? Galois theory? Chaos theory? Stochastic Process?

The idea that could potentially resonate is how breaking down hard stuff to easy stuff allows one to solve the harder stuff. This is what I try to do every damn day but it's hard, at least for me. I think you may have minimized that part of it; the creative process inherent in going from difficult to easy.

Moreover, easy and simple are not the same thing.
Profile Image for Chazzle.
268 reviews13 followers
March 22, 2016
Maybe 3 and 1/2 stars. Deductions for way too much explanation in the easy parts, and too many dialogues with fictional characters that sometimes got to be "too clever by half". The author is obviously very bright, but still, the book is quite followable. On that note, I remember picking up a title in a bookstore sometime ago by George Soros, and I can't remember its title because I said to a bookseller, "Why doesn't he just call it 'You'll never be as smart as me'?" Because it was so ridiculously fraught with arcane terminology and deep thoughts. THIS book isn't like that. You DO need an interest in math. The only material I hadn't encountered before was variational calculus, the last chapter of the book. I read that chapter once, and followed about 2/3 of it. I'm not fully convinced yet of everything in the chapter, but I'll give it another go in a day or so.
Profile Image for Amelia.
27 reviews
February 2, 2023
DNF. This was not a bad book by any means, but I didn’t like how I had to force myself to read it.
November 7, 2020
This is the best introduction to advanced mathematics I’ve ever read. It begins with basic properties of functions and works all the way up to infinite dimensional calculus.
Profile Image for Kristen Heimerl.
Author 1 book8 followers
July 9, 2017
What a clever book that serves a brilliant purpose: helping adults and students alike get rid of “bad math tapes” and start anew with mathematics. Is it possible to shift a mental mindset around a subject that has terrified millions? I think so. And if anyone can do it, it’s Jason Wilkes.

His premise is simple: the teaching of math in America is abhorrent—dull, long on memorization, and short on meaning and storytelling. Wilkes doesn’t want to teach us math, he wants to teach us to think by inventing mathematics for ourselves and maybe, just maybe, tying back what we’ve created to the mathematics we see in classic textbooks. He abandons words like “functions” and acronyms like “FOIL” and replaces them with words to which we can relate. For example, The Distributive Law is just a law of “tearing things” and The Pythagorean theorem is simply a formula for shortcut distances.

If a math book can be fun, this one wholly is because Wilkes has a sharp mind, irreverent wit, chatty style and clear passion for his craft.

Burn Math Class is a must-have anti-textbook to add to your child’s library as they embark on learning high school math. And it may be a good one for you too if you’re ready to shed the math anxiety that your ninth-grade teacher inadvertently instilled in you so many years ago. Let’s face it, math solves problems. Big ones. If the only thing standing in our way from using math is fear, that’s silly. Buy this book and let Jason Wilkes charm and educate. It’s not a breezy read; it’s work getting through this one. But it’s worth it if the outcome is a new tool to add to one’s problem-solving toolbox.
Profile Image for Theodore Schwamm.
23 reviews1 follower
December 29, 2021
This was an absolutely splendid book. It completely changed the way in which I thought about Math, and I am very glad that I was able to read it.
To Jason Wilkes, though I don't know if you will read this: Thank you. Thank you for being so honest, and not just about math. Books can sometimes feel a little like the polished math which you discussed so much, with all the blind alleys bricked over to make an elegant journey. That is beautiful in its own way, but so is the process which you adopted. In drawing back the curtain by writing about math, you also drew back the inner curtain of writing. This is a book I intend to take with me everywhere in the future.
P.S. Perhaps the book is flawed, but so is every other, and I think that makes it beautiful.
Theodore Schwamm
This entire review has been hidden because of spoilers.
Profile Image for Trever.
588 reviews12 followers
May 10, 2016
I agree with the beginning of this book. I believe the declaration of independence would be a great thing to have in the classroom. I think the explanations are good, but I don't think it helps understanding of math better.

I do believe that math education needs to be changed, but if you change math at the elementary level you will change math from the ground up.
12 reviews3 followers
January 31, 2019
The premise of the book is that there is a more logical way to teach and learn maths, in which more "advanced" notions should be taught first because it allows deriving so called "easier" notions without having to remember the latter by heart, being able to understand their construction. Spoiler: elephant in the room: using derivatives from 1st grade to prove all the maths you subsequently learn only makes sense once you understand maths better, not as an introduction.

As a note, I have a bachelor in maths and a Masters in cryptography, so I understand the maths here and quite beyond. I was interested in a new approach to maths.

The first part of the book is quite interesting, and the approach consisting in creating "machines (functions) and testing what new knowledge we can get about them is indeed refreshing for a new learner, and gives a new perspective on the often perceived dryness of maths. The application of Pythagoras theorem to understand relativity is indeed something I always felt should be taught early on, for the fun of students, and because I think physics course also need a revamp to get students more interested.

However, the second part just loses it. The author decides to switch to a very mildy funny and often annoying dialog directly inspired by Hofstadter's GEB, andits supposed purpose to make things lighter contradict directly the author's goal of having "something interesting and not just making a couple jokes along a classical maths textbook" (I paraphrase, can't find the quote again).
This dialog which is supposed to represent the path one could take to try to prove some given math theorem get irritating quickly, and actually makes the reader lose track of the reasoning behind.
It feels like the author got excited in his one-shot writing frenzy and had way too much coffee and not enough sleep for the whole second half of the book.

If the dialog was the only problem... Actually, the "Burn math class" becomes a math class. Now I'm French, and I know maths education is not the same in American high schools (we do way more in high school, then our uni curriculum is way more relaxed), but we are used to getting some explanations for the maths we learn. We don't do the whole reasoning process, however we're supposed to have a background of why things happen. The author proceeds to demonstrate theorem after theorem, unhappily keeping bad names that, while making sense in the beginning to show that names are a convention, is annoying because we get lost: wish it or not, people do know what sin and cos are, and after 300 pages still calling them H and V (for horizontal and vertical) is not helping, and visually complexifies equations.

Last point, some obvious mistakes like the explanation for Taylor series. We're supposed to make things ourselves, not accept anything, and here, poof, magic! A few other errors that I forgot, the fact that sine and cosine have other definitions that make sense, and the elephant in the room, using derivatives to prove everything else.

The author gets lost in equations, no more fun example past time relativity (that's chapter 2 over 6 or 7), a confusing math book, and the assumption that using derivatives makes sense for everyone to derive maths theorems, no more analogies to explain theorems, the lauded intuition which is just "we try that rule or that rule", methods conveniently called "hammer" because it's humoristic (wel, huum).

The idea was good, and it started well, and the the author got a bit crazy and just copied a math book while inserting an irritating dialog full of references (from which I guess I got only a small part, but which didn't make me enjoy it more).

Read the first 2 chapters then just go for something else. 2.5 stars for the idea, since here I can't put 2.5 I'll put 2 because only the first 2 chapters are worth reading.
Profile Image for Andrew Litfin.
7 reviews2 followers
July 18, 2018
Word of warning: This book is not what you think it is. You might think you have an idea of what this book is, but it's probably not right. So what is this book?

This book starts from "let's assume the only things you know of are addition and multiplication," and goes all the way to "let's develop calculus of variations [which the book calls "cannibal calculus" {the book makes heavy use of eschewing standard terminology, so as to remind the reader that we are developing everything from scratch, without referencing any outside material (the book also makes unhealthy use of commentary within commentary and commentary about commentary)}]," told through a series of dialogues between the reader, the author, mathematics, and other characters.

If you've never seen calculus before, or if you've got a degree in math, this book has something for you. For the former, you get to learn naive infinitesimal calculus from scratch, both single and multivariable, up through calculus of variations! For the latter, a perspective on pedagogy that I've not seen in most pop math books.

And no, the book doesn't actually advocate burning math class, which I know many will find disappointing. In that manner and others, the book is not perfect, but nothing that would make me hesitate recommending it to someone looking for an informal and entirely different approach to mathematics.
260 reviews
July 18, 2019
I am a high school math teacher who has not taught calculus and had taken calc, and related topics about 40 years ago. I really appreciated this book and it's constructive approach to the main theorems and concepts of calculus. Some of the chapters really gave me a better understanding of where e to the x comes from, how to find the value of pi, and where the Taylor Series come from. I understood the whole book with the exception of last part of the last chapter on Functionals.
I highly recommend this book and may start an after school class to introduce it to some of my high school students
327 reviews
November 10, 2016
I am good at math (up to high school calculus), and like to read math, so I love this book. It teaches me to think about math in a completely different way than how I was taught math. I wish I had learned math from this book instead. It gave me so many "wow!" and "aha!" moments and thrilled me with the creativity of mathematicians. I wish I could understand the last chapter on infinite - dimensional calculus. Maybe one day, when I have a big chunk of time to spend on it!
6 reviews
September 9, 2018
This book is strange but inspirational. It is like using a curved mirror to see something I've known for a very long time with fresh eyes. As I work on problems and read other math texts, I am now asking myself what parts of these are just "how math is done by us" and what parts are universal.
Profile Image for Sandy Vanderbleek.
7 reviews14 followers
November 1, 2016
Very good, I have a decent math background but had gotten out of touch with basic calculus. It seems very beginner friendly but I'll have to leave that the beginners to comment on. I wish there were exercises, and less digressions, that still doesn't take a point away from this unique effort to bring math education to everyone.
Profile Image for Shriya.
22 reviews30 followers
February 4, 2017
I would give this a 4 if I was sticking to my personal rating system, but I can't bring myself to give it less than 5 because Wilkes is so unique and brilliant. An ambitious and enlightening book that I'm certain I'll revisit, and definitely won't forget.
Displaying 1 - 16 of 16 reviews

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