Ian Stewart is arguably the UK's best raconteur of mathematics - here he takes on some of the extremes of the mathematical world, and in doing so gives us some real insights into what makes mathematicians tick. There's a good mix here of the flashy fun aspects of maths - think, for instance of the wonders of infinity or the monster group - and the solid everyday that nonetheless can turn up surprises. The book is littered with little insights. For example, if we think it's easy to work out the area of a rectangle by dividing it up into unit squares, what do you do with one that measures square root of two by pi? You'll find yourself jumping around from what lies beneath calculus to game theory (rock, paper, scissors anyone? - I hadn't realised a version of this game dates back around 2,000 years). One minute you'll be considering colouring maps and the next finding the shortest distance between two points on a curved surface. Some of the mathematics here has eve...

Without doubt one of the most original science fiction books I've ever read. With a mix of narrative and reports (featuring occasional redaction-like antimimetic decays) we are introduced to the work of the Organisation, which takes on weird happenings in the world, from conventional monsters and ghosts to those central to this story. A large contingent of Organisation staff deal with mimetics - ways that concepts can spread in a non-natural fashion and have to be controlled. But a smaller group deals with antimimetics - concepts and even living things that are able to remove themselves from human memory. One of our first introductions to antimimetics is when a senior civil servant summons a supposed spy to his office, only to discover that she is in fact the head of the Antimimetics Division: an antimimetic has stopped the civil servant from taking the medication that enables him to remember the Division's existence, so he is totally unaware of it. This kind of convoluted comp...

Going on the cover you might think this was a political polemic - and admittedly there's an element of that - but the reason it's so good is quite different. It shows how behavioural economics and social psychology have led us astray by putting the focus way too much on individuals. A particular target is the concept of nudges which (as described in Brainjacking ) have been hugely over-rated. But overall the key problem ties to another psychological concept: framing. Huge kudos to both Nick Chater and George Loewenstein - a behavioural scientist and an economics and psychology professor - for having the guts to take on the flaws in their own earlier work and that of colleagues, because they make clear just how limited and potentially dangerous is the belief that individuals changing their behaviour can solve large-scale problems. The main thesis of the book is that there are two ways to approach the major problems we face - an 'i-frame' where we focus on the individual ...

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This book is something of a reboot. It was Neil deGrasse Tyson's first title, dating back to 1997, but was reissued 'fully revised and updated for the 21st century' in 2024. It's mostly a cut and paste book from the Q&A section in a magazine, despite which (or perhaps because of which) it's one of Tyson's better books. The idea is that the questions are answered by Merlin who is 'a visitor from the Andromeda galaxy who is as old as Earth and who has observed all major scientific events of Earth history.' Although some of the questions are from children (and the illustrations look like they were drawn by one) it's intended to appeal to all ages. The book is split into 13 sections, mostly with astronomical topics (such as Earth, Moon, Planets, Black Holes and Quasars), though with a couple of more physics-based sections including Gravity and Light and Telescopes. The questions themselves vary from entertaining thought experiments such as 'What ...

The sequel to Artifact Space is another wrist-busting, high class space opera, again featuring a sort of Star Trek future but where the ships are primarily merchant/military instead of exploration/military. I gave the original book 5 stars, but I've marked this one down, partly because I've already read the third in the sequence, Whalesong , and that one is significantly better. There's still a lot to like about Deep Black . Its action sequences are engaging. There's lots of impressive detail about the ships and life on them - and a far more realistic impression of the less exciting rest of life onboard than you get from most space opera. And there is a lot more on the difficulties of communicating with aliens, which is cleverly handled. But like its predecessor it is too long, and there is just far too much of the detail of daily life for central character Marca Nbaro as she goes about her daily routine. Routine gets a little dull. To add to the negatives, the writing...

Antigravity - the ability to overcome the pull of gravity - has been a fantasy for thousands of years and subject to more scientific (if impractical) fictional representation since H. G. Wells came up with cavorite in The First Men in the Moon . But is it plausible scientifically?  Andrew May does a good job of pulling together three ways of looking at our love affair with antigravity (and the related concept of cancelling inertia) - in science fiction, in physics and in pseudoscience and crankery. As May points out, science fiction is an important starting point as the concept was deployed there well before we had a good enough understanding of gravity to make any sensible scientific stabs at the idea (even though, for instance, Michael Faraday did unsuccessfully experiment with a possible interaction between gravity and electromagnetism). We then get onto the science itself, noting the potential impact on any ideas of antigravity that come from the move from a Newtonian view of a...

History professor Peter Dear gives us a detailed and reasoned coverage of the development of science as a concept from its origins as natural philosophy, covering the years from the eighteenth to the twentieth century. inclusive If that sounds a little dry, frankly, it is. But if you don't mind a very academic approach, it is certainly interesting. Obviously a major theme running through is the move from largely gentleman natural philosophers (with both implications of that word 'gentleman') to professional academic scientists. What started with clubs for relatively well off men with an interest, when universities did not stray far beyond what was included in mathematics (astronomy, for instance), would become a very different beast. The main scientific subjects that Dear covers are physics and biology - we get, for instance, a lot on the gradual move away from a purely mechanical views of physics - the reason Newton's 'action at a distance' gravity caused such ...

The science fiction/murder mystery crossover has been well-established in space opera and Earth-based high-tech futures, but The Tainted Cup gives us a very different, if equally impressive approach. Physical technology on the featured planet is pretty much medieval, but biological enhancements are commonplace. This is not due to advanced science, but rather with the approach of a herbalist on a planet where some of the biological specimens are able to cause such dramatic changes. The narrator, Din, is a young assistant investigator recently started in his first position. His enhancements as an engraver are slightly reminiscent of a mentat in Dune, giving him perfect recall and leading to surprising sword fighting abilities. His boss, Ana, is more complex - a combination of Mycroft Holmes from the modern-day set Sherlock TV show and Judge Dee from van Gulik's remarkable books. Except she wears a blindfold most of the time and swears a lot more. (The author likens her to a cross be...

Subtitled 'overlooked and omitted topics in mathematics', the obvious concern is that there is a good reason these topics are overlooked and omitted. Thankfully, this is not the case, but it's fair to say that despite attempts to dress it up that way, this isn't a recreational maths book. There's a fair description in the blurb: 'the topics which every undergraduate mathematics student "should" know, but has probably never encountered... magnificent secrets that are beautiful, useful and accessible.' As someone who many years ago did a degree with a fair amount of mathematics in it, I think it probably would have appealed back then - though to be honest a lot of it has disappeared from my memory, strongly reducing the entertainment value. Here's an example. The first real page contains the sentence:  'If you are handed a real number 𝓍 ∈  ⁠ ⁠,  one way to tell if 𝓍 is rational or irrational is to look at sequences of rational numbers q n ...