(Originally published as *The* *Magicians*) *Breakthrough* by Marcus Chown is a popular science book that is sure to please technical profiles, engineers and technology lovers. Through a solid narrative of several amazing discoveries in the world of physics, the author raises and discusses a question that intrigues scientists: Why is mathematics able to describe the universe and the world around us so accurately?

## 1. Argument of *Breakthrough*

Throughout the text, Marcus Chown masterfully compiles the events that led to some of the most relevant discoveries in the world of science. The author demonstrates his narrative skills by embellishing the facts with the best known (or sometimes supposed) anecdotes of the protagonists.

On the other hand, the more technical descriptions, which are generally numerous and in-depth, demonstrate the author’s extensive technical knowledge. In this sense, it is important to emphasize that many of the technical discussions in the book might be too thick for non-technical profiles. However, this depth in the explanations will be highly appreciated by any more technical profile, since it allows the understanding of many discoveries to be taken to another dimension, beyond the banal (and sometimes not very accurate) descriptions that are usually employed for the general public.

The following is a very brief list of the discoveries reported in the book (without giving away any secrets for potential future readers): The planet Neptune, Electromagnetic waves, Antimatter, The creation of the elements of the Periodic Table, Neutrinos, Radiation from the Big Bang, Black holes, The Higgs field and Gravitational waves.

All the above-mentioned discoveries have something in common. Namely, their existence was mathematically predicted long before experimental confirmation. In some cases incredible predictions were made that could later be confirmed by experimental physicists or astronomers. In other cases mathematical models were developed to reflect known reality, but resulted in predictions that were too astonishing to be taken seriously, even when they seemed to be confirmed experimentally.

## 2. Mathematics and Physics

It is precisely this ability of mathematics to describe reality that gives the book another dimension. Apart from narrating and explaining the discoveries themselves, it also discusses the unbreakable relationship between mathematics and physics.

Why is it that mathematics is able to describe the universe and the world around us so accurately? Why were those mathematical geniuses, whom the book calls magicians, able to pull such incredible and realistic predictions out of the hat?

In this way, the book reviews the different theories that have been developed to answer the above questions. There are philosophical visions of all kinds, from those that affirm that mathematics only reflects a simple part of reality, to those that understand that mathematics is physics in itself. There are also theories that show how our laws of physics are mere tools, since what actually happens is much simpler.

In my opinion there is a certain amount of overthinking around this question. It is clear that mathematics allows us to describe how the world works. But not all mathematics is useful for this purpose, only a part of it. That is, we humans are the ones who develop or select the mathematics that allow us to reflect reality. When we are not able to explain something with commonly applied mathematics or theories, we simply look for others until we manage to refine or deepen the previous theory. In a sense, it is like saying that mathematics can be made to reflect any world, both one that is not real and ours that is. So the job of a theoretical physicist is to associate the mathematics we need with our reality. I suppose this is too simplistic a view, because it does not seem that this interpretation is even raised.

## 3. Lessons and Curiosities from *Breakthrough*

As in any interesting book, one can learn lessons or curiosities that are very valid for personal and professional life. Below we develop some of them without going into detail so as not to detract from the reading experience of the book.

### 3.1 The Hard Life of a Scientist

It is both incredible and sad to see how difficult it was (and still is) to pursue a career in science. The book mentions several cases in which brilliant scientists, directly involved in these amazing discoveries, suffer hardships in order to access permanent positions that also allow them to fully develop their personal lives.

### 3.2 Failures and Errors

Throughout the book many errors, both technical and social, of prestigious scientists (including Einstein) are evident. At first glance, we could say that if you have made discoveries of Einstein’s stature, you are allowed to make some mistakes. But surely it is more correct and realistic to see it another way: if even Einstein made mistakes, all the more reason for any of us to be wrong. Mistakes are part of life no matter how much we try to avoid them.

### 3.3 Confidence

It is curious to discover that some physical predictions of mathematics were not taken seriously even by their own creators. In some cases these predictions were sufficiently disruptive to be minimally understood. In other cases, on the other hand, the simple rupture of previous assumptions was a burden that delayed the confirmation of great discoveries for years. We can only reflect and be aware of trusting our own forecasts when, even if on a smaller scale, we have carried out our technical work conscientiously and rigorously. Of course without falling into complacency and a reckless attitude.

## 4. Conclusions on *Breakthrough*

In short, *Breakthrough* by Marcus Chown ensures an enjoyable, interesting and educational experience for our technical audience.

The reading of this work allows us to understand some of the most amazing discoveries in the history of physics, both at a technical level and at a human and social level. And the curiosities surrounding the lives of the protagonists can be as useful, albeit in another domain of life, as low-level knowledge and details.

In addition, the book will allow the reader to learn and reflect on the close relationship between mathematics and physics. All this with the intention of answering a question that borders on the philosophical: Why does mathematics accurately describe the physical properties of our world?

Finally, *Breakthrough* can be purchased at the following link:

Other books by the author, shown in the following link, may also be of interest.

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