Mathematics or Physics–Mathematics vs. Physics–Mathematics and Physics

Graham Farmelo is a British physicist and science writer. He is the author of an excellent and highly praised biography of the British physicist P A M Dirac, The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius(Faber and Faber, 2009), which won a couple of book awards. He is also the author of a book Winston Churchill role in British war time nuclear research, Churchill’s Bomb:A hidden history of Britain’s first nuclear weapon programme (Faber and Faber, 2014), which was also well received and highly praised. Now he has published a new book on the relationship between mathematics and modern physics, The Universe Speaks in Numbers: How Modern Maths Reveals Nature’s Deepest Secrets (Faber and Faber, 2019).

I must admit that when I first took Farmelo’s new book into my hands it was with somewhat trepidation. Although, I studied mathematics to about BSc level that was quite a few years ago and these days my active knowledge of maths doesn’t extend much beyond A-Level and I never studied physics beyond A-Level and don’t ask what my grade was. However, I did study a lot of the history of early twentieth century physics before I moved back to the Renaissance. Would I be able to cope with Farmelo’s book? I needn’t have worried there are no complex mathematical or physical expressions or formulas. Although I would point out that this is not a book for the beginner with no knowledge; if your mind baulks at terms like gauge theory, string theory or super symmetry then you should approach this text with caution.

The book is Farmelo’s contribution to the debate about the use of higher mathematics to create advanced theories in physics that are not based on experimental evidence or even worse confirmable through experiment. It might well be regarded as a counterpoint to Sabine Hossenfelder’s much discussed Lost in Math: How Beauty Leads Physics Astray(Basic Books, 2018), which Farmelo actually mentions on the flyleaf to his book; although he obviously started researching and writing his volume long before the Hossenfelder tome appeared on the market. The almost concurrent appearance of the two contradictory works on the same topic shows that the debate that has been simmering just below the surface for a number of years has now boiled over into the public sphere.

Farmelo’s book is a historical survey of the relationship between advanced mathematics and theoretical physics since the seventeenth century, with an emphasis on the developments in the twentieth century. He is basically asking the questions, is it better when mathematics and physics develop separately or together and If together should mathematics or physics take the lead in that development. He investigated this questions using the words of the physicists and mathematicians from their published papers, from public lectures and from interviews, many of which for the most recent developments he conducted himself. He starts in the early seventeenth century with Kepler and Galileo, who, although they used mathematics to express their theories, he doesn’t think really understand or appreciate the close relationship between mathematics and physics. I actually disagree with him to some extent on this, as he knows. Disclosure: I actually read and discussed the opening section of the book with him, at his request, when he was writing it but I don’t think my minuscule contribution disqualifies me from reviewing it.

For Farmelo the true interrelationship between higher mathematics and advanced theories in physics begins with Isaac Newton. A fairly conventional viewpoint, after all Newton did title his magnum opus The Mathematical Principles of Natural Philosophy. I’m not going to give a decade by decade account of the contents, for that you will have to read the book but he, quite correctly, devotes a lot of space to James Clerk Maxwell in the nineteenth century, who can, with justification, be described as having taken the relationship between mathematics and physics to a whole new level.

Maxwell naturally leads to Albert Einstein, a man, who with his search for a purely mathematical grand unification theory provoked the accusation of having left the realm of experiment based and experimentally verifiable physics; an accusation that led many to accuse him of having lost the plot. As the author of a biography of Paul Dirac, Farmelo naturally devote quite a lot of space to the man, who might be regarded as the mathematical theoretical physicist par excellence and who, as Farmelo emphasises, preached a gospel of the necessity of mathematically beautiful theories, as to some extent Einstein had also done.

Farmelo takes us through the creation of quantum mechanics and the attempts to combine it with the theories of relativity, which takes the reader up to the early decades following the Second World War, roughly the middle of the book. Here the book takes a sharp turn away from the historical retelling of the emergence of modern theoretical physics to the attempts to create a fundamental theory of existence using purely mathematical methods, read string theory, M theory, supersymmetry and everything associated with them. This is exactly the development in modern physics that Hossenfelder rejects in her book.

Farmelo is very sympathetic to the mathematicians and physicists, who have taken this path but he is in his account very even handed, letting the critics have their say and not just the supporters. His account is very thorough and documents both the advances and the disappointments in the field over the most recent decades. He gives much emphasis to the fruitful co-operations and exchanges that have taken place between mathematicians and theoretical physicists. I must say that as somebody who has followed the debate at a distance, having read Farmelo’s detailed account I came out of it more sympathetic to Hossenfelder’s standpoint than his.

As always with his books Farmelo’s account is excellently researched, much of the more recent material is based on interviews he conducted with the participants, and very elegantly written. Despite the density of the material he is dealing with, his prose is light and often witty, which makes it easier to grapple with the complex themes he is discussing. I would certainly recommend this book to anybody interested in the developments in modern theoretical physics; maybe to be read together with Hossenfelder’s volume. I would also make an excellent present for any young school leaver contemplating studying physics or one that had already started on down that path.