This is a book in the 'compact collection of science/maths essays' category beloved of publishers because they can charge hardback prices for fewer than 80 pages of text - but don't let that put you off, because it's excellent. Terence Tao introduces six areas of mathematics: numbers, algebra, geometry, probability, analysis and dynamics. Each of these is descriptive rather than practical (there are only a couple of school-level equations in sight), done in a way that gets to the heart of 'what's the point of this subject' with precision and a good level of storytelling. It's a shame in a way that analysis and dynamics form the final third of the book (apart from a short epilogue), because they don't work as well as the other sections. For the first four, practically everyone will have a vague idea of what they are and what they do - but Tao is then able to open our eyes to their wonders and power. Because Tao has to stay away from any detail of what...

A quote on the back cover of this book describes it as monumental - it certainly feels big enough to use as part of a structure with 664 pages plus a further 112 pages of end notes. Colin Gillespie's aim is to 'bring together centuries of ancient thought and modern insights to unearth what is real and what is not'. That certainly sounds like it would need a lot of pages, if it is to be achieved at all. A starting point is to establish what 'real' means. Gillespie gives us the guidance that 'to accept something as truly real, it must be an accurately described objective aspect of the universe.' That may seem obvious, but as he points out 'little in philosophy or physics even aims to pass this test.' Gillespie builds a new conception of physics based entirely on space. As he puts it 'space isn't something; it is literally everything.' In this worldview, the universe began with a single 'space quantum' - a Planck-sized six-dimensiona...

Paul Murdin in his own words : The crucial and overriding incident that defined my life irrevocably was catching polio at the age of 7 years.  That made it difficult to walk. It made me sedentary and an avid reader – a swot. I studied because I liked to, and that made it possible for me to go to university via a scholarship to Oxford. I was able to develop this into a job as an astronomer at the Royal Greenwich Observatory (RGO).   In the late 1960s I became interested in identifying the stars newly discovered as responsible for emitting X-rays. The X-rays are a flag that a star is waving at us saying 'Look at me!  I’m interesting!  Working with Louise Webster, I found in 1971 that one such star, Cygnus X-1, was a black hole. I think that qualifies as interesting!  I went on to work at the Anglo-Australian Observatory but soon returned to the RGO to work setting up the UK telescopes on La Palma.  In the later part of my life, I became a scientific administr...

An old advert had the tag line 'it does what it says on the tin'. There's a vagueness about the title of this book that requires Bayes' theorem to work out whether it really does what it says on the cover. If you think this book will tell you how to think like a statistician, it's unlikely that you will be satisfied. But if you think it will tell you how a statistician thinks, it is much closer to being true. Sadly this makes the tag line I've seen 'Why you don’t need to be a statistician to think like one' entirely wrong. In the book, Bradley Efron gives us plenty of detail on how statisticians apply probability to try to understand better what is happening in the world. He makes a great point that his high school mathematical education consisted primarily of algebra, geometry and trigonometry. While these 'proved invaluable to my subsequent scientific studies' they hardly ever crop up in the news, where the one mathematical subject that does oc...

There are broadly three types of popular science books. There's the skim-level book that's descriptive but hasn't much depth, then there's the book that tries to go as deep as you can without getting into the mathematics, and finally there's the textbook lite. I would normally avoid this last category like the plague, but just occasionally one really works: and that's the case with Wonders in Motion . This is not a book that will appeal if you have an aversion to equations. I don't think there's anything that goes beyond the maths you'd get if studying it at school to age 18 - and you aren't expected to have much prior knowledge - but if you are happy with that, David Acheson does a great job of combining history of science stories with a the development of dynamics as an aspect of physics from Newton's second law to viscous flow of fluids. Sometimes reading it does feel a little like being lectured to, featuring rather more hard mental work ...

If there is still such a thing as GOFSF (good old-fashioned science fiction), Entanglement very much fits that category. Our central characters are the classic space travel misfits, on a survey vessel in the Asteroid Belt, hence the series title (this is very much a series book). Our hapless heroes get the opportunity to get the finders' fee on a missing piece of tech in a derelict ship. Briefly they're very happy - until they find out every government and dodgy corporation wants to get their hands on this technology, and will stop at nothing to do so. It all plays out nicely, with two set piece adventures. To be honest, Gerald Kilby's ideas are better than his writing style - but that wasn't a problem for Asimov, so it's not really a criticism. The writing is workmanlike, but rarely page turning, while the characters, if not two-dimensional are on the thin side. At least, unlike Asimov, he has significant female characters. What makes it GOFSF is the solid use of ...

There are a few SF titles that have cut through to be regarded modernish classics in the more general literature sense. One example would be Flowers for Algernon (which I read in English class at school). Another, surely, is the 1959  A Canticle for Leibowicz . There are parallels with Pavane , in presenting a 'modern day' setting with medieval living standards where the Catholic Church remains a major power, yet technology is gradually breaking through. But this is not an alternative history: it's a post-apocalyptic future where civilisation was destroyed by nuclear war, with tiny embers of knowledge kept alive by a monastery dedicated to a twentieth century electrical engineer turned priest called Leibowitz. Divided into three sections, each taking place six centuries apart, we first get a totally medieval view of the discovery of circuitry on a blueprint and more from pre-apocalyptic times. Then we see the gradual re-emergence of electrical technology in the abbey. And ...

As deputy editor of Our World in Data and senior researcher in the Programme for Global Development at the University of Oxford, Hannah Ritchie is ideally placed to get a balanced view of the state of the climate, what we're doing to and how we can try to fix it. And, perhaps surprisingly after reading the doom-laden The Fate of the World by Bill McGuire, it's a reasonably positive read. Ritchie does not set out to sugar coat things, and is no kind of climate change denier. But in answering 50 key questions about our climate and its future she is often able to provide a nuanced response. She assures us that it really isn't too late to take action and that all contributions are helpful (even if, admittedly, we need the big players to do more). So, for instance, in answering 'My country only emits 1% of the world's emissions; surely it's too small to make a difference', she points out that 36% of emissions come from countries whose emissions are 'too smal...

Alex Davies is a technology journalist, author of Driven: The Race to  Create the Autonomous Car, and a former editor at Wired, The Athletic,  and Business Insider. He lives in New York's Hudson Valley. His latest book is How to Keep a Plane in the Sky. Why engineering? I'm not an engineer myself — I'm a journalist who's spent years covering people who are. What draws me to it is that engineering is where abstract values like 'safety' and 'trust' actually get made concrete. Someone has to decide, in specific numbers, how much force a car seat can take before it's a failure, or how many g's a human body can survive. Those decisions are usually invisible to the rest of us, but they're some of the most consequential ones our society makes.  I got hooked on writing about it because it's a way to write about risk, trust, and human judgment while staying grounded in real, physical stakes — a wing that either holds or doesn't, a test that ei...

In the old days books were described as 'X meets Y', while more recently it's the fans who get the mention - in this case 'perfect for fans of Orphan Black, Killing Eve and Keeping it Real ' though we also get in the title tag ' Blade Runner meets Barbie '. There's an element of truth in most of these, but Maud Woolf has nonetheless pulled off an entertaining and different novel. Lulabelle Rock is a film star who over the years has accumulated 12 Portraits - these are not human (so not clones as they are described in the blurb), but are replicas, pretty well only distinguishable by not having palm prints or the usual stuff inside their body. The idea is that the Portraits can be used to do boring tasks that Lulabelle can't be bothered with, from social media to guest appearances. But for whatever reason she has create a thirteenth Portrait, the first person narrator of the book, who is given the task of decommissioning all the rest. (If a human did...