The Universe Speaks in Numbers - Graham Farmelo ****

Theoretical physics has taken something of a hammering lately with books such as Sabine Hossenfelder's Lost in Math. The suggestion from these earlier titles is that theoretical physics is so obsessed with mathematics that many theoretical physicists spend their careers working on theory that doesn't actually apply to the universe, because the maths is interesting. Even experimental physics can be tainted, as the driver for new expenditure in experiments, such as the proposed new collider at CERN, is not driven by discoveries but by these mathematically-directed theories. Graham Farmelo presents the opposite view here: that this speculative mathematical work is, in fact, a great success.

As I am very much in the Hossenfelder camp, I expected to find Farmelo's book rather irritating, as it's effectively a love letter to mathematically-obsessed theoretical physics - but in reality (an entertaining phrase, given the context) I found it both interesting and enjoyable. Farmelo has a clear enthusiasm for the wonders of higher abstract mathematics and takes us through the history of the transformation of physics from being driven by experiment and observation to being driven by mathematical theory with a light touch and some fascinating detail.

However, much though I enjoyed The Universe Speaks in Numbers, it hasn't changed my position. The book's subtitle is 'how modern maths reveals nature's deepest secrets' - but the problem is that it is failing to do so. We discover lots of new and interesting mathematics - with the physicists actually revealing new maths that surprised the mathematicians - but hardly anything that has come out of this mathematical work that has carried physics forward in the last 40 years. Modern maths isn't revealing nature's deepest secrets, it is revealing some of the secrets of more maths, and that isn't what physics should be about.

I think I can pinpoint where the worldview goes adrift from reality on page 127 of the book. Farmelo comments 'Most of [the remainder of the book] is not conventional science, in which theorists make predictions that experimenters test; rather, it is speculative science, still under development and often not yet susceptible to observational tests. But it is science nonetheless...' - I'm afraid I can't agree. Speculation isn't science. It may become science, so isn't necessarily worthless scientifically speaking, but it certainly isn't science at the moment, and hasn't succeeded in making the leap in several decades.

For example, as Hossenfelder points out in her book, string theory works best if the cosmological constant value that reflects the expansion or contraction of the universe is negative. Unfortunately it's actually positive, but most string theorists spend their time working with a negative cosmological constant. It makes for beautiful mathematics - but has nothing to do with our universe. It isn't science, it's maths.

I haven't lost hope for physics, where there is still plenty of excellent work going on. However, I don't share Farmelo's enthusiasm for building mathematical towers in the sky, piling speculation on speculation. This doesn't however, distract from the fact that this is an excellent summary of the current position and how we got here, and Farmelo manages to put the state of theoretical physics across without alienating someone with a very different view, which surely is an excellent achievement.

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Review by Brian Clegg