Many of the "tricks" this book indicts aren't good hacks and aren't easily formulated as theorems. They are terrible hacks that are ridiculously inefficient, di

Many of the "tricks" this book indicts aren't good hacks and aren't easily formulated as theorems. They are terrible hacks that are ridiculously inefficient, distracting, and only necessary if you fundamentally don't understand what's actually going on. See "Butterfly Method, Jesus Fish" or "Backflip and Cartwheel": http://www.nixthetricks.com/NixTheTricks2.pdf http://www.nixthetricks.com/NixTheTricks2.pdf They're both super inefficient tricks that are totally unnecessary if you know and understand the theorem they embody. > If I can explain and justify the trick - then let me use it. This book is a guide for teachers, not a rule book for students. For the tricks that are arguably good hacks, the authors provide a simple argument: the time investing in teaching the trick is not worth it, and is better spent somewhere else (see the Jim Doherty quote just before the TOC). The argument isn't that students should not be allowed to use certain theorems if they understand those theorems. Rather, the argument is that teachers should invest their finite teaching resources explaining other theorems instead. Often, the authors are arguing that there is an equivalent and equally useful formulation of the same theorem (or a similar one) that's easier to derive and understand. Which is the sort of justification any working mathematician should be on board with (they don't need to agree with the conclusion, but the form of the justification is at least reasonable). > This mode of thinking does not apply to mathematics. But this does apply in education writ large. E.g. sacrificing understanding for good performance on a standardized test. This is not a book telling you how you should do mathematics in your work day. It's a book advocating for certain ways of allocating classroom teaching time.