Science and science fiction (SF) are not too far apart and the boundary can become fuzzy in some cases. Terms and ideas now generally accepted were used for the first time in fiction novels. The word "robot" is an example of such an SF product and Jules Verne's space gun is a well known prediction of Apollo 11 used to realize the moon landing realized much later. Where science reaches its current boundaries, fiction can extrapolate and take these results to the next level. Exploring these boundaries is the purpose of this book. There is virtually no limit to the fantasy of fiction writers, but somehow the adventures of their heroes and villains take place in worlds that are inspired by our familiar society and by the environment and technology that we know today. Hence the science in SF involves almost anything we know or struggle with today: from quantum mechanics to biology, to artificial intelligence, to cosmology, to relativity theory, and of course, some ethical and philosophical problems can arise when science is pushed a bit further. All this science can be discussed on a very technical level and that can involves deep mathematics and complicated physics. So it is a challenge to discuss advanced science topics and yet avoiding all the difficult technical details.
Bernstein has written some science fiction himself and he is professionally involved in economics, statistics, and mathematics as a managing consultant. So he is well earthed to real science and has the fantasy to fictionalise it beyond its boundaries. Testimony of his scientific knowledge is the astonishing amount of well documented technical knowledge that he summarizes in this book. Most of this science is based on mathematics, but as he writes in the introduction:
Also, don't worry about the math that occurs here and there, because these references are very limited. Never fear math. It is the language of science. In fact, as with spoken languages, it is fraught with tongue twisters the scientists sometimes take too seriously.
Faithful to his promise, there is indeed not much mathematics explicitly present, and neither does he become technical about the physics. Nevertheless he starts with a discussion of the two pillars of twentieth century physics: quantum mechanics and relativity theory. These two chapters are characteristic in approach and format for the other chapters (there are 21 chapters, which is just half of 42; it might be a coincidence but 42 is, according to Douglas Adams, the answer to the ultimate question of life). Most of the chapters are short chunks, hashing up the complex themes in digestible bites. They place the real science results against the fictional extrapolations. For example spacetime has black holes which may be used for time travelling, or they may create wormholes which would allow just travelling from on point in spacetime to another without violating the speed limit of light. While these are theoretical constructs in real science, they are mostly presupposed trivialities in science fiction. Both chapters have so-called bonus material for example discussing the twin or the grandfather paradox of time travelling or using Einstein's formula to compute the amount of energy that is packed in a human body, or to explain what quantum suicide and quantum immortality means in a multiverse context. Other chapters have "parting comments" which are just take-along summaries of what has been discussed in that chapter. The book has also three "interludes" which are chapters that deviate from the standard format. These discuss only science, there is no fiction. They briefly introduce some basics: the first one is about atomic theory, the second about transhumanism, that is when the human body and brain are biologically and technically upgraded until the result can hardly be called human anymore, and the third is about mass, dark matter and dark energy.
The broad spectrum of themes discussed include string theory and extra dimensions, the vastness of our universe, parallel worlds, energy resources, the origin of life, genetic modification and cyborgs, global warming and other catastrophes, colonisation of the galaxy, computers, robots and AI, extraterrestrial life, materials engineering, virtual reality, and possible ends of the universe as we know it. All of these have shown up in science fiction media (comics, stories, books, films) in some form and Bernstein gives several concrete examples. Everything he claims is well documented with references (to both the scientific and the SF literature). These references are collected chapter by chapter at the end of the book. There you can also find a useful glossary explaining many technical terms from "abiogenesis" and "absolute zero" to "wobble method" and "zombies" but also the useful index and extensive lists of SF literature, movies and songs. Extensive as the latter lists may be, it is obviously reflecting a selective choice made by the author, because the amount SF literature, movies, and TV-series is too vast to aspire any degree of completeness.
So there is no explicit mathematics and there are no formula in the book, but many mathematicians work in applied areas of AI, computer science, theoretical physics, materials science, nanotechnology, and many other engineering applications. So I am sure there are enough geeks among them that love science fiction and thus will probably love this book. The author did an amazing lot of fact checking and he has ample illustrations from SF. His style is really crisp, up tempo, and to the point, but most of all I love the humour he uses. An example: where he explains the spaghettification effect when entering a black hole he writes:
Think of an event horizon as a fence with a big Keep Away sign hammered into it. Personally, I would do what it says. [...] If you do decide to ignore the warning and trespass on the event horizon, I hope you like pasta. This is not an adventure I would recommend. However, if you insist, the first thing you do is put on the latest spacesuit ad disembark from your starship. There is no reason to endanger the rest of the crew.
But don't be mistaken, the technical or philosophical material is serious, and he is not joking much when he discusses global warming, a hot topic these days, that unfortunately is no fiction. Even the geeks among the readers may learn a thing or two that is new to them, and it is also an interesting way to detect some new SF literature or movies you didn't know about. For potential authors who want to start writing their SF novel and they want it to be hard SF, they better check out all the facts that are provided here. If you can't get enough of this, I can refer to a similar book by Charles L. Adler Wizards, Aliens, and Starships who also includes the fantasy literature. Also Paul Nahin wrote about the topic in Holy Sci-Fi! but he is more focussing on the religious aspects and less on the science.