Measurement

Mr. Lockhart has previously written (A Mathematician's Lament) about the joyless methods that were used to teach most of us mathematics. Fortunately I was one who found the joy behind both the practical significance of arithmetic (yes the bank needs to know the exact balance of your account even if you don't care to figure it out) and the memorization of tables; now called math facts (yes, even musicians need to practice scales and train their fingers if they wish to make music, not just appreciate it). If you already know how joyful and remarkable mathematics can be, Mr. Lockhart writes in a way that is easy to read and offers many examples of familiar problems and solves them in a way that emphasizes the elegance and beauty of both the problem and its solution. If you wonder WHY some of us KNOW that mathematics is elegant and beautiful and wish to share that joy, give the book a whirl. You don't need to know more about mathematics than basic arithmetic. As long as you know that algebra and geometry exist; expertise is not required, you will do fine. However as easy as it is to read, be warned that sometimes the mathematics and logic will appear so clearly as if by magic and other times your brain will be challenged and you may struggle mentally as mightily as a women struggles physically (and mentally) to give birth. Whether the struggle is worth it is entirely up to you and fortunately for you, unlike the woman who cannot undo her pregnancy if she finds the struggle to give birth too difficult, you can just give up and read on to the next problem and hope it is easier. There are many, many problems to solve in the book.

A wonderful book! It shows clearly the beauty of mathematics at a quite elementary level. The author goes to great lengths to show what is interesting about Mathematics. It is not the complicated formulae, or the algebra, but great, simple, utterly convincing ideas. If the reader is willing to think hard while reading, he/she will be rewarded by many stunning results presented in a completely straightforward manner. The first part, probably the one that best achieves its stated purpose, deals only with geometry. Since the basics objects of geometry (straight lines, circles, angles...) are familiar to anybody, it is really possible to prove beautiful results without using any of the apparatus, such as algebra and calculus, which many people find difficult. The second part is an attempt to introduce algebra and calculus in a very simple and well motivated way. Since I already know the material quite well, I cannot really say whether the attempt actually succeeds, but I certainly found the presentation very striking and quite engrossing.

All numbers _ all shapes and sizes _ time and space _ all are connected. Such relationships are everywhere at all times. Thus, patterns are created; some tangible; some not so much. Deciphering these connections, determining the general pattern, becomes the task of the mathematician. I discovered this concept when, some sixty plus years ago, my 6th grad teacher spent an entire morning detailing how common shapes (squares, rectangles, triangles, trapezoids, etc) were derived from one another by deriving their area formulas from a single equation. They were, in this way, shown to be all one and the same but simply stretched out into this or that shape or, geometrically, as viewed from various perspectives. This revelation came as a major eye-opener for me and changed my entire direction in life's pursuits. (Now that they 'teach to the test,' such revelations are generally and sadly absent from today's classrooms). Measurement as discussed in this wonderful book is not measurement in the classic sense of the word. In other words, one will not find a ruler with the sq rt of 2 on it. In this case, measurement represents a systematic assignment of a value to some subset of a system such that comparisons can be made between the elements of the system and between systems and (consequently) mathematical links between seemingly unrelated areas of the mathematical universe. The book is divided into two main sections. The first concerns what we used to refer to as "Synthetic" geometry. That is: to build up knowledge based on first principles. Numbers as such are conspicuously absent. Only pure reason is utilized much as it was in "ancient" times. In this manner, the author puts us directly into the mind of the mathematician; solving the riddle with nothing more the the one or two elements at hand. The ancient Greeks did this not so much because they lacked the so-called "brilliance" of the modern day Human but by choice, neglecting the more analytical approach. As such synthesis was more in keeping with their predominantly aesthetic view of nature. The second section adds the coordinate system (ala Descartes), thereby providing an Analytical approach and somewhat greater precision to the solutions (and consequently providing some deeper insights into the connections at large!). This is not a How-To book. It is an argument that is detailed and punctuated with an excellent choice of problems to challenge one's perspective. If the reader has no mathematical background, this book will pose a major challenge for sure. Additionally, if the reader lacks a fair background in both Trig. and The Calculus, this too will make forward motion along the line of comprehension rather tedious. That is not to say that one cannot follow the argument but it will be, at minimum, tough going, especially when the author reveals such links as between the Hyperbolic Integral area (dA = dw/w) and the Natural Log (ln). Calculus is, of course, simply a short cut to solving an infinite series of calculations in a few steps. It's use was initially implemented during the so-called "Kerala" Period in Southern India several centuries before Newton or Leibniz, both of whom systemized the science. It's rules are few but rather messy and often difficult (if not impossible) to apply without extensive practice and a good visual sense. Trig is stymied by its extensive use of the ever so transcendental Sin and Cos, etc. and also requires some fairly able visuals. The ability to convert from the geometric to algebraic represents a major breakthrough in extending Mathematics into further realms of exploration and therefore lends a helping hand to those less able to follow the visual signs so to speak. Again, 'measurement' represents only one area of the whole of Mathematics but this book will give anyone who wishes to tread through the mesmerizing tangle of Mathematical mystery an excellent sense of the Mathematical mind.

Math is fun and everyone can do it, it just needs as much practice as any other thing that you want to be good at. These seem to be Lockhart's main messages and the book wraps them into more than 50 comprehensive sections. The sections combine explanations and plenty of illustrations with questions (or homework) for the reader, so the reader should expect some time away from the book thinking about the problems and maybe discover their own questions and answers. There is a lot of fun and entertainment in these some 300 pages, but there are also (maybe naturally) many things that could have been improved. Lockhart is a mathematician and he repeatedly points out that this profession is completely unconnected from the physical world. To make this even clearer, all the sketches in the book are what looks like hand-copied versions of computer printouts - imperfect representations of the ideal object one has in mind. Almost from the very first page, though, any units are removed from the discussion so we deal with numbers only. But instead of simply referring to meters , inches, degrees or whatever unit you want to use, in the following we are constantly reminded of arbitrary "units of length" and others. In the same way, the book moves from measurement to motion by introducing time - which is then again simply replaced by (or reduced to) an arbitrary dimension similar to length. All that would have been a little easier to swallow if the title of the book had been "geometry" instead of "measurement." Maybe the better approach is to not try to force the reader to decouple the sketches (i.e. the real world) from the objects in mind. Also it is not quite clear who this book is aiming at. Although it starts out with very simple ideas, it is probably not intended as a replacement for a basic course in geometry. While the topics pick up speed pretty soon, the style almost moves in the opposite direction. And I would rather let the reader discover the beauty of the subject herself instead of repeatedly interrupting the text with joyous exclamations by the author. To sum it up, this is still a fun book with an almost honorable purpose. While there were things that I really didn't like, they probably won't interrupt other people's enjoyment of the book. So give it a try.

5 stars are not enough. This is an amazing book. Maybe unique even. Let me explain. There are three kind of math books for school level maths. The first kind teaches math skills. Nowadays the best place for this is probably not a book but Khan academy. These skills are important tools for doing math, but they are not mathematics. The second kind of math books are collections of problems. The Art of Problem Solving series is excellent for this. Problem solving is an important part of mathematics. But it is only a part of mathematics. Where do problems come from? Which problems are interesting? How are mathematicians guided by beauty? The third kind of math books tries to answer these questions. It takes the reader on a journey of beauty and discovery. "Measurement" falls into this category. Chapter 2, for example, starts with the philosophical question of "What is measurement?" and finishes with the concrete problem of why a parallelogram with equal diagonals must be a rectangle. It shows how mathematicians find problems in the first place. It is important to notice that the book does not offer answers to the problems. This is an important feature of the book. If you want problems with answers, buy a math book of the second kind. (For example the Geometry book of the Art of Problem Solving would be a good supplement.) This book is an invitation to start with fundamental questions such as what is measurement and to develop mathematics from there. It is an invitation to do living mathematics, not frozen mathematics. Thinking about it, "Measurement" is the only math book of the third kind I know of. If somebody passing by here knows another one, I would be grateful if they left a comment.

If you only ever read one book on mathematics in your life, read this. Paul Lockhart writes so clearly and passionately. (Yes, I used "passion" and "math" together!) He is a brilliant mathematician AND a great writer! This is a very rare combination. He presents math in an intuitive and conceptual way that shows you the beauty of discovery and patterns and symmetry but requires very little calculation or knowledge of the mathematical language. For non-math people this presentation is very accessible and easy to read. He is talking about concepts that are universal. For math-people to presentation style is a reinforcement of why you love math, do math, and a demonstration of how you really think when you are solving a problem. I highly, highly recommend this book!

This book was amazing. A very personal view (which is really, really rare in maths) about some really interesting parts of very basic mathematics. And yet even if the topics covered are so basic (triangles, conics, lines, derivatives...) the book manages to open a completely new view on them!! A must-read for any teacher or student of math. I suggest, before reading this book, to read the short essay written by the same author commonly known as "Lockhart's Lament" which is available online and circulated greatly among mathematicians, or the published book version "A Mathematician's Lament" which added some material, and is a personal criticism of the mathematical education system. It acts as a good introduction to the feeling and the tone of this more extensive and fascinating book.

I only read the first couple chapters. This book is for when you have time/mental space to devote to study, as a student of the subject. You can do it in small amounts, recreationally, but for the average layperson like myself, this book involves intense mathematical reasoning. I mean, it welcomes everyone! With the same elegance, simplicity and conversational writing that we loved in A Mathematician's Lament. From the first page, you are captivated and wanting more. This is a must-buy for the bookshelf, to have on hand when the mood strikes.

It's impossible not to warm to Lockhart's enthusiasm, and after a year away from maths after finishing a degree, this book kick-started my interest in mathematics and problem solving. It gives a brilliant description of the mathematical process as well as some of the most important ideas from the subject, often in a breathtakingly simple way that even after years of study improved my understanding. I would say the sections on geometry can be understood by most people, as can the description of what calculus is, but it does get a bit more involved from that point on.

Tolles Mathematikbuch.

Una gran obra de Lockhart. Un gran libro para releer una y otra vez. Si te gustan las matemáticas y quieres ver la perspectiva de como un profesor ve la enseñanza actual que se da de ellas, este libro cumple a la perfección.

Great maths book Recommended

It feels like author is sitting next to you, and reading the book. He will not give away solutions just like that, might also throw you into trap, knowingly, but you will only learn from the mistakes. And the feeling you get after finding something is really great. That's what motivated me to write this review, only one suggestion, it is to give some time for the first breakthrough, later that will serve as your motivation!