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.


Filed under Book Reviews, History of Mathematics, History of Physics

22 responses to “Mathematics or Physics–Mathematics vs. Physics–Mathematics and Physics

  1. Pingback: Mathematics or Physics–Mathematics vs. Physics–Mathematics and Physics — The Renaissance Mathematicus | Hacia una Cultura Científica

  2. Not the first time the debate has boiled over: you have Peter Woit’s Not Even Wrong (2006), and also Lee Smolin’s The Trouble with Physics (2008).

  3. brodix

    I object to my blog comments being used as a platform for pseudo-scientific balderdash, so I have removed your comment. Don’t try to repeat it!

  4. Jim Harrison

    Famously, Beethoven was deaf when he wrote some of his most famous works. A deaf music critic would be even more of a wonder. When it comes to evaluating the claims of theoretical physicists and advanced mathematics, I’m a deaf music critic. That admitted, I’ve struggled through enough textbooks on cosmology and string theory to recognize that they are finding enough coincidences in the pure math to stoke the suspicion that they’ve just gotta have something to do with the physical world. Maybe
    it’s an hallucination in whole or in part, but I wonder how those who reject the approach account for the intuitions of the math guys. I’ll read Farmelo’s book—I much enjoyed the Strangest Man..

    • String theory and modern cosmology present very different cases; you might almost call them polar opposites. The hypotheses of dark matter and dark energy were direct responses to observational data. (They’re still hypotheses—data never truly “speaks for itself”. Although dark energy looks more like a placeholder than a hypothesis.) String theory is a story of following the elegant math to see where it leads. It has yet to make a testable prediction. Its most dramatic success so far is in pure math (Seiberg-Witten invariants).

      • There is no evidence that dark energy (up there in the list of all-time stupid names) is anything other than the cosmological constant, which has been around for more than 100 years, appearing in the first-ever paper on relativistic cosmology. I’m not sure what you mean by “placeholder”. Do you mean that we don’t know what “causes” it? If so, how is that different from knowing what “causes” the gravitational constant to be non-zero?

      • Phillip, the difficulty with dark energy being simply Einstein’s cosmological constant is that it is so close to but not exactly zero. To get up to 120 orders of magnitude in cancellation, you need to go beyond the Standard Model (supersymmetry can do this, but it predicts particles we have not seen). Similarly, dark (that is non-baryonic) matter is needed to account for the rotation curves of galaxies unless you assume that gravity behaves differently at low accelerations (MOND).

      • @PhillipHelbig: Here’s what I meant.

        As we all know, Einstein introduced the cosmological constant to allow for a static universe. Once expansion was discovered, it fell into disfavor. You can catch the prevailing attitude in “the phone book” (Misner, Thorne, and Wheeler). Also of course we have the apocryphal Einstein quote, “my biggest blunder” (perhaps invented by Gamow).

        I remember reading posts on sci.physics.research from observational astronomers, complaining about how their theoretician colleagues mostly favored setting Λ=0, but the data seemed to be pointing in a different direction. Finally the evidence became pretty conclusive. After that, the phrase “dark energy” was born. That’s what I meant when I said that the dark energy (and dark matter) hypotheses were born out of observation, not elegant math.

        I called “dark energy” a placeholder to contrast it with “dark matter”. As I understand it, we have several rather plausible ideas for what dark matter could be. Theories to explain dark energy are much thinner on the ground.

        I would neither rule in nor rule out the notion that one day, we’ll have a convincing deeper explanation for why the expansion is accelerating. Calling it “dark energy” rather than “the cosmological constant” suggests that we will, which is why I called the term a placeholder.

      • With regard to the cosmological-constant problem, read and then ask yourself if there is still a problem. (You seem to be assuming that vacuum energy is somehow involved; that’s not conclusive.)

        MTW is of course a book on GR; relativists see cosmology as an application of GR while cosmologists see GR as just one element of cosmology. Also, that book is almost half a century old, but might provide a snapshot of the feelings of some people at that time.

        “Once expansion was discovered, it fell into disfavor.”

        Yes, but the universe is independent of what we think about it. The history of science if fascinating, in particular the history of cosmology (just now I’m reading an entire book on the entropic creation argument), but the universe is what it is, independent of the contingent paths by which we find out about it.

        “I remember reading posts on sci.physics.research from observational astronomers, complaining about how their theoretician colleagues mostly favored setting Λ=0, but the data seemed to be pointing in a different direction. Finally the evidence became pretty conclusive. After that, the phrase “dark energy” was born. That’s what I meant when I said that the dark energy (and dark matter) hypotheses were born out of observation, not elegant math.”

        This is essentially true, at least if one replaces “theoretician colleagues” by “some (influential) theoretician colleagues”. (I’ve been moderating sci.physics.research for 20 years!)

        “Theories to explain dark energy are much thinner on the ground.”

        Again, why do we need to explain it? In other words, why do some feel a need to explain why it is not zero and perhaps even its particular value, but don’t feel the same about, say, the gravitational constant?

      • You seem to be assuming that vacuum energy is somehow involved

        You’re mixing me up with Laurence Cox. I didn’t mention vacuum energy.

        As I said, I’m agnostic as to whether a “deeper explanation” for the value of Λ will ever be found. You’re convinced there is no such explanation. That’s fine, but of course that opinion is not universally shared. (Once upon a time, people sought a mechanical explanation for Newtonian gravity. We know how that played out.)

        I do wonder about your analogy with the gravitational constant. In natural units, its value is 1. That isn’t true for Λ, no?

      • My reply was to both Michael Weiss and Laurence Cox.

        I don’t deny that there is a deeper explanation, but the burden of proof is on those who think that there is.

        As for natural units, there are different sets of natural units. Saying that G is 1 in natural units is pretty much a tautology if such natural units are defined such that G is 1. There is no other way to arrive at G=1 than by assumption.

  5. okay i will try checking it out

  6. Pingback: Mathematics or Physics–Mathematics vs. Physics–Mathematics and Physics — The Renaissance Mathematicus – Rexton digital

  7. idpnsd

    I object to other people trying to use my blog as a pulpit to promote their arrant bullshit, so comment removed

  8. nwankwo emmanuel

    please i need to know more about atomic physics

  9. Pingback: Mathematics or Physics–Mathematics vs. Physics–Mathematics and Physics — The Renaissance Mathematicus – iyke's Blog

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