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Burn Math Class: And Reinvent Mathematics for Yourself

Jason Wilkes

4.09 · Rating details · 126 ratings · 15 reviews

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 su ...more

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Hardcover, 400 pages

Published March 22nd 2016 by Basic Books

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Feb 16, 2019 Ryan Croke rated it it was ok

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 ba 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. ...more

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Mar 22, 2016 Chazzle rated it liked it

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 ridiculous ...more

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Nov 06, 2020 Christian Morse rated it it was amazing

Shelves: mathematics

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.

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Jul 09, 2017 Kristen Heimerl rated it really liked it

Shelves: education, mathematics, study-teaching

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 inve ...more

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May 02, 2016 Trever rated it really liked it

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. ...more

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Jan 30, 2019 Nicolas Bernard rated it it was ok

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 bachelo 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. ...more

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Jul 17, 2018 Andrew Litfin rated it it was amazing

Shelves: to-acquire

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, w ...more

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Aug 14, 2019 Theodore Schwamm rated it it was amazing

Shelves: my-favorite-books

This review has been hidden because it contains spoilers. To view it, click here.

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Jul 18, 2019 David02139 rated it it was amazing

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 ...more

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Nov 09, 2016 C rated it it was amazing

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! ...more

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Oct 28, 2019 Thomas rated it liked it

I enjoyed the meat of this book (up until the last chapter or so) but the text of often too cutesy with silly digressions. The final chapter, about the calculus of variations (or calculus of "cannibal machines") felt rushed and compressed compared with the rest. ...more

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Sep 09, 2018 Raul rated it it was amazing

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. ...more

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Dec 19, 2020 Michael Lortz rated it it was amazing

Enjoyed this book immensely. I wrote a review of it here:

https://medium.com/hybrid-analyst/a-r... ...more

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Nov 01, 2016 Sandy Vanderbleek rated it it was amazing

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. ...more

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Jan 25, 2017 Shriya rated it it was amazing

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. ...more

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