A Brief History of Mathematical Thought

A Brief History of Mathematical Thought - Luke Heaton ***

I had great hopes at the start of this book that we'd get a meaty but approachable history of the development of mathematics. When describing the origins of number, arithmetic and mathematical processes the opening section is pitched well, but things go downhill when we get to detailed mathematical exposition.

The problem may be that Luke Heaton is a plant scientist, which may have prepared him better for using maths than for explaining it. If we take, for instance, his explanation of the demonstration that the square root of two is irrational, I was lost after about two lines. As soon as Heaton gets into mathematical detail, his fluency and readability are lost.

There's a central chunk of the book where the mathematical content seems too heavy for the way the contextual text is written. We then get back onto more effective ground when dealing with logic and Turing's work, before diving back into rather more impenetrable territory.

One slight concern is that, in talking about Turing, Heaton presents the largely discredited idea that Turing committed suicide by eating a poisoned apple, laying the blame for this on his arrest and 'treatment' for homosexuality, a narrative that doesn't stand up (it's a shame the author didn't have a chance to read The Turing Guide). I suspect this is a one-off and much of the mathematical history is fine.

I didn't realise until I'd finished it that it has an interesting publishing history. It was initially part of the same Robinson published series as my A Brief History of Infinity, but this is a US hardback edition, just brought out by OUP. This was, then, a curate's egg book for me. I really enjoyed it when it was dealing with history and philosophy of maths, but found the technical explanations, even of mathematics I understand perfectly well, hard to follow.

Paperback (US hardback):

Kindle:

Using these links earns us commission at no cost to you

Review by Brian Clegg

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