The Little Book of Mathematical Principles

The Little Book of Mathematical Principles – Robert Solomon **

This is a pocket book in the same series as the entertaining Little Book of Unscientific propositions etc – but there is a fundamental difference between the two. The subject matter in that other title was fun and entertaining, making the little articles on different subjects an enjoyable read, but here it’s more a case of plodding through mathematical history picking out the main features. Frankly it is dull, not aided by the relentless chronological order, which puts all the boring basics at the beginning.

Even when the book moves out of straightforward maths into historical context there are some issues because the history of maths parts don’t always seem particularly well researched. So, for example, the book says that the Pythagorean who let slip that the diagonal of square to be irrational is unknown, but that he was taken out and drowned. The usual version is that we have a name for the man (Hipparsus) but that there is only a legend that he was drowned. Similarly, Newton is identified here as the ‘infidel’ in Bishop Berkley’s discourse on the method of fluxions/calculus – where in fact it was Edmund Halley.

There also seems to be paucity of maths to cover, because a fair number of the topics are straightforward science, like the move from an earth-centred to a sun-centred universe and the mechanics of falling bodies. There’s even a section on special relativity, which is rather poorly handled as the text suggests the effects of relativity are subjective, as if (for instance) time dilation just seems to happen. This is misleading as it is a real, measurable effect.

Overall, then, this is a book that isn’t particularly one you can sit and read through for enjoyment, but neither is it detailed enough to be used as a reference book. I’m really not sure what it’s for. We need more good popular maths books, but sadly this doesn’t make a contribution.

Paperback:

Using these links earns us commission at no cost to you

Review by Peter Spitz

Comments

The Infinity Machine - Sebastian Mallaby ****

It's very quickly clear that Sebastian Mallaby is a huge Demis Hassabis fan - writing about the only child prodigy and teen genius ever who was also a nice, rounded personality. After a few chapters, though, things settle down (I'm reminded of Douglas Adams' description of the Hitchhiker's Guide to the Galaxy ) and we get a good, solid trip through the journey that gave us DeepMind, their AlphaGo and AlphaFold programs, the sudden explosion of competition on the AI front and thoughts on artificial general intelligence. Although Mallaby does occasionally still go into fan mode - reading this you would think that AlphaFold had successfully perfectly predicted the structure of every protein, where it is usually not sufficiently accurate for its results to have direct practical application - we get a real feel for the way this relatively unusual company was swiftly and successfully developed away from Silicon Valley. It's readable and gives an important understanding of...

In Seach of Sea Dragons - Matthew Myerscough ****

It's common advice to would-be authors of narrative non-fiction to open with something dramatic - Matthew Myerscough certainly does this with the story of his being trapped under an avalanche on Snowdon (while his girlfriend, also carried away remains on top of the snow unhurt). It certainly is dramatic, but seemed entirely disconnected from the reason I got the book, which was to read about fossil collecting. Luckily, though, in the second chapter we get into a more conventional 'how I got interested in fossils as a boy'. Having recently reviewed Patrick Moore's autobiography and noting that astronomy was one of the few sciences where amateurs can still make a contribution, it came to mind that palaeontology is another - Myerscough is a civil engineer by trade, but just as amateur astronomers can find new details in the skies, so amateur fossil hunters have been searching for these relics for centuries. When I give talks in junior schools, the two topics that guarant...

Robot-Proof - Vivienne Ming ****

As Vivienne Ming makes apparent, there seem largely to be two views of AI's pros and cons, both of which are almost certainly wrong. It's either doom-saying 'It'll destroy life as we know it' or Pollyanna-ish 'It'll do all the boring work and we can all be wonderfully creative and live lives of leisure.' Instead, Ming gives us a clear analysis of the likely trajectory for the workplace, particularly for the IT industry. She describes three 'equally flawed, intellectually lazy strategies' to deal with the impact of AI. The first is substitution and deprofessionalisation, using AI to allow cheaper 'AI-augmented technicians' to replace more expensive professionals, producing more low wage jobs and fewer mid-range. This does save money but leaves a company at risk of being easily outcompeted. The second is what Ming describes as the '"A-Player" Hunger Games', the approach favoured by Silicon Valley. This sees the growing rif...

Search This Blog