Wonders Beyond Numbers: A Brief History of All Things Mathematical Hardcover – December 5, 2017

Nice review of math subjects. suggesting my grand children read it now!

I’m a mathophobe but still found is book approachable and interesting.

The book’s materials are presented in a light, breezy fashion. That Ball is excited by mathematics and physics is clear as is also the fact that he is a bit shaky in both.To the mathematically inclined there are many interesting things, perhaps not previously known to them, which are fun takeaways. The highly capsulized lives and contributions of mathematicians and physicists are also of some interest. He writes at times as though readers were completely naïve in physics and in maths (as he puts it). However some of the analytical material especially in the geometry examples will tax many who already have a good grasp of geometry and will be considerably beyond a beginner.As a book to learn from there are many pitfalls: some from lack of clarity and some that are just plain wrong. As an example of something wrong enough to make it dangerous, consider his statement (page 375) of Newton’s three laws of mechanics. Ball gives Newton’s first law as: an object at rest will remain at rest unless acted upon by a force. Then he gives the second law as: an object will travel in a straight line unless acted up by a force. The third law that for every action there is an equal and opposite reaction he got right.However, Ball’s “first” and “second” laws together are actually Newton’s first law (commonly called the Law of Inertia and by way of defining what a “force” as an action is). He has therefore omitted entirely Newton’s all important second law which is commonly stated as the force acting on a body is equal to the mass of the body multiplied by its acceleration. The general statement is that force is equal to the rate of change of the momentum (mass multiplied by velocity) of a body but because in many practical applications the mass does not change the simpler form is used. Newton’s second law defines precisely how to measure a force such as in the first law quantitively.As an example of an incomplete “explanation” consider that as Ball (page 366) correctly points out the not always known but puzzling fact that there is an ocean tidal bulge on the side of the earth opposite to the tidal bulge under the moon’s attraction and is not due to the sun’s influence. The actual explanation is a subtle application of Newton’s laws of mechanics. Ball’s explanation begins rightly enough again by noting that the earth and moon form a two body system with the center of gravity of the two bodies located on the line connecting the two centers and positioned inside the earth nearer to the surface because the mass of the earth is so much greater than the moon’s. (If moon and earth were of the same mass, this center would be half way between their centers.) But from there he really makes no use of that essential fact but gives the misleading statement that both ocean bulges are caused by the earth’s gravity “squeezing” them into this shape. That cannot be considered an explanation. Briefly, the cause of the opposite tidal bulge is because earth and moon as a system actually pivot around this center of gravity like a lopsided dumbbell and the centrifugal force caused by this rotation tries to fling the water on the side opposite the moon off the surface of the earth (somewhat like water on a stone swung in a circle on a rope will be flung off) but earth gravity holds it back. The slight sheer forces imparted by the rotation cause the water which has practically zero sheer resistance to “pile up” on the side away from the moon thus assuming its bulging shape. He could have gone on to mention that strictly speaking the moon does not actually revolve around the earth but around their combined mass center. But this center is close enough to the earth’s center compared to the vastly greater distance between earth and moon to make little practical difference in the statement that the moon revolves around the earth (center).Then there is his statement (page 393) that a proton is a positively charged particle (true) which he then says is the same as a hydrogen atom. It is not. A hydrogen atom consists of a nucleus of a single proton and an electron external to the nucleus. To those who do not know this, his statement is misleading. To those who do know it, it hardly needs space. If he meant an ionized hydrogen atom he should have explained what that is and said so.There are any number of other faulty “explanations”, outright errors, typos, etc., too numerous to state here which suggest that the reviewers who gave the book such glowing blurbs on its dust jacket only skimmed and did not read it with the care they should have as reviewers and that his proofreader only looked for spelling, grammar and perhaps sentence construction problems, if that, rather than actual content.Enjoy it but let the reader beware.

It is really a book about the history of mathematics. The earlier part on Greek n Arab mathematicians are interesting. Some proofs are not clearly explained though. The weight of the book seems to be off balance as I get the sense that he was rushing to finish the book. Ball could have edit out the periodic table section. Quite frankly some sections are science related. His reference on Einstein s E=MC2 is totally superficial. All in all it is still interesting to read.

In this book, the author attempts to recount the history of mathematics from ancient times to the present. He does this mainly through mini-biographies of various personalities: thinkers, philosophers, mathematicians and scientists.On the positive side, I found the book to have been written in a prose that is very friendly, lively and highly accessible. I found the historical snippets to be quite enjoyable to read. The author has covered a lot of territory.On the negative side, the book is riddled with technical mistakes and misleading concepts, when discussing scientific/mathematical topics. Many of the explanations given on various mathematical problems are difficult to follow, either because they are incomplete, very poorly done or because of errors. Mathematically solved examples are usually by the “cook book” method, e.g., “multiply this by that and voila”, rather than by clear explanations showing the basis for the method used.I did enjoy the historical excursions in this book, but the mathematical/scientific aspects leave much to be desired. Consequently, in good conscience, I cannot give this book a higher score. A reader wishing to learn some mathematics should look elsewhere.

This book is a jewel. It mainly covers the history of maths and some science in a thorough and interesting way. It is a delight to read and do not waste one’s time on maths that are not relevant anymore. With the chronical development of the theme a lot of interesting mathematical methods, tricks and principles are worked in. I highly recommend this beautiful and wonderful book.

Quite an enjoyable read as far as the progression of mathematics through the ages and good for the rivalries, collaborations and so on, but when it comes to some of the mathematical explanations, it falls short. There's a few clumsy errors, including:There's an explanation and corresponding diagram of achieving mechanical advantage through gearing. The wording does not describe the diagram, and neither is correct.At one point a cube root is described as "the square root of the square root of the square root". It isn't.Often an explanation and diagram appear on opposite sides of the page, resulting in lots of flicking backwards and forwards between the two. With more effort at the editing stage and a better proof-reader, this could have been a great book.

Thouroughly enjoyable read. Johnny Ball is a brilliant educator and very good at making potentially complex subject matter accessible to the general reader. Reading this book is a great way to refresh one's knowledge and rekindle an appetite for mathematics. Highly recommended indeed!

I am still reading this book. It is interesting but at times a little heavy going and fairly repetitive. The jury is still out and I am havering between 4 and 5 at the moment. It is definitely not as entertaining as I thought it might be but still interests me as a maths enthusiast.

He tries to make out he's something he really isn't, but still manages to make a readable blog. A tad on the lengthy side though, but overall worth a purchase.

Fabulous book great mix of maths and historyManaged to meet legendary Jonny Ball promoting the book. Great inspiration