The central idea of the book is to look at ten key mathematical-philosophical ideas in probability and, using the history of the idea, explain what they are about and why they matter.
It’s not that the book doesn’t have some very interesting material, but it fails to hit its target over and over again and, unfortunately, even contains some obvious and – presumably – not so obvious errors.
This review states it so much better than I can, so here is an extract:
The chapters are invariably a mix of 1. a trivial example that does not penetrate enough the intended topic because it contains too much of the familiar and too little of the topic that’s being introduced 2. references to original texts that are impenetrable nineteenth century translations into English from eighteenth century originals written in French or German or Latin 3. statements of complex results that would take fifty pages to arrive at if the proofs were shown 4. cheerleading
So what I re-lived by reading this book is my Freshman Year nightmare math class where three times a week I’d follow the first five minutes of the lecture only to subsequently find myself furiously copying from the board so I can read my lecture notes later at home and try to make sense of them.
Earlier this month I highlighted how a book that claims to be about using Python to build convolutional neural networks and yet, say readers, contains not a single line of Python, was garnering rave reviews on Amazon.
The trend hasn’t stopped and it is pretty clear to me that these are, in fact, spam.
When I started reading this book by Edward Frenkel (Amazon link here) I became so engrossed in it on my morning commute that I missed my Tube stop – and the next one. I got an insight into life in the Soviet Union on the cusp of perestroika from a contemporary (if somewhat higher achieving student), including into how academic (and anti-scientific in the sense that some were desperate to discredit Einstein) anti-Semitism was on the increase from the 1970s onwards, as well as a new take on group theory in geometry and an introduction to braids.
It really was great – the main text skated over the maths while the footnotes explained it in some detail. Not all of it was perfect – the attempt to explain symmetry at the start left me confused about something I thought I understood – but it seemed to all hit the right note.
But it seems my Leicester Square moment was the pinnacle. Even by the time I had retreated back to Holborn I was starting to struggle as the maths just went off the deep end and the explanations offered no quarter.
It’s a pity, because I do think that just some small additional efforts to explain what some of the concepts meant could have gone a long way – for instance we just get Riemann surfaces dumped on us as though they were something different from manifolds (I am sure they are, but a little more effort at explaining why would have helped). While at the end we get a long, and dry, description of branes and A-models and B-models which we are told are potentially important in quantum physics, but we never quite are told why they are important.
My overall impression was the maths has run away with the science a bit – but I am not really in any position to judge.
This could have been a great book, but unless you really are well read on your complex topologies then I’d have to warn you to stay clear.