“Mathematics has been stolen from us, and it is time we take it back.” – You’ll find this on page 2 of Burn Math Class and Reinvent Mathematics for Yourself, an incredible Book by Jason Wilkes. Has mathematics really been stolen from us? I am not sure. But for me, one thing is certain, this enlightening book goes a long way in presenting the beauty of mathematics in a manner that is perhaps accessible to anyone who is willing to read and think. No prior knowledge is needed.
Jason Wilkes, a young thinking scholar has done wonders in developing a non-conventional mathematics book that contains real mathematics. This book is not an exposition of the History of mathematics nor an ambassador of the usefulness of mathematics in science and engineering. It is rather a journey through thought and discovery that begins with elementary concepts and ends with highly complex notions, all presented in a neat and brilliantly accessible manner.
“Declaration of Independence: The purpose of math courses is not to create students who know things about math. The purpose of math courses is to create students who know how to think.” You’ll find this on page 38 and in the following pages you will find a beautiful exposition of algebraic results, derived geometrically from first principles. See for example this beautiful illustration on page 63,
Think a bit about the areas of right triangles and squares, and then see why the famous “Pythagorean theorem” follows.
On page 39 you bump into “The First Commandment of Mathematics Education: A mathematics teacher should not urge students to remember, but to forget.” While forgetting is not a goal, I think that most good math educators would agree that memorising is also not a goal. But the matter of fact is that much of pre-university mathematics education is centred around memorisation. Burn that! Read this book and reinvent mathematics for yourself.
The book turns mathematics on its head. It is a calculus-focused book that does not require command of the so-called middle and high school subjects, “pre-algebra”, “algebra”, “trigonometry” and “pre-calculus”. As the author claims, these subjects are often taught in a dry and non-insightful manner with the so-called reasoning that they are pre-requisites for the calculus that sometimes follows later. Can the underlying concepts of calculus, really be understood from the go? Indeed, this book shows that they can.
After developing concepts associated with area, the author quickly moves onto understanding slopes and derivatives. Only later, are the basic trigonometric functions introduced – but without all of the bells and whistles that often turn students away from trigonometry. Burn math class – discover mathematics!
On page 164, after some fun and engaging reading, we are introduced to the magical constant, #. This constant, as the author labels it, is the ratio between four times the area of a circle and the area of the square that inscribes the circle.
Without indicating that # is approximately 3.14159, the author continues to use this ratio until he manages to represent it using beautiful formulas of infinite series, for example,
This is all done from first principles. You don’t need to rely on 14 years of a complicated math education to find out this incredible formula for pi (oops I mean #). The book does it from scratch!
In summary, I really enjoyed reading many parts of this 389 page long book. I enjoyed Jason Wilkes’ humour and creativity. I enjoyed the pedagogical journey. And most of all I enjoyed the beautiful art of mathematics. I recommend you try it also and I hope that even if you haven't touched mathematics for many years, this book will drive your curiosity.