Redeeming the role of mathematics

9 October 2019

The Universe Speaks in Numbers: How Modern Math Reveals Nature’s Deepest Secrets, by Graham Farmelo, Basic Books

Pieces of E8 With applications in supergravity and string theory, the Lie group represented here is an example of mathematical complexity in theoretical physics that is not yet grounded in experiment. Credit: Jgmoxness

A currently popular sentiment in some quarters is that theoretical physics has dived too deeply into mathematics, and lost contact with the real world. Perhaps, it is surmised, the edifice of quantum gravity and string theory is in fact a contrived Rube-Goldberg machine, or a house of cards which is about to collapse – especially given that one of the supporting pillars, namely supersymmetry, has not been discovered at the LHC. Graham Farmelo’s new book sheds light on this issue.

The universe speaks in numbers, reads Farmelo’s title. With hindsight this allows a double interpretation: first, that it is primarily mathematical structure which underlies nature. On the other hand, one can read it as a caution that the universe speaks to us purely via measured numbers, and theorists should pay attention to that. The majority of physicists would likely support both interpretations, and agree that there is no real tension between them.

The author, who was a theoretical physicist before becoming an award-winning science writer, does not embark on a detailed scientific discussion of these matters, but provides a historical tour de force of the relationship between mathematics and physics, and their tightly correlated evolution. At the time of ancient Greeks there was no distinction between these fields, and it was only from about the 19th century onwards that they were viewed as separate. Evidently, a major factor was the growing role of experiments, which provided a firmer grounding in the physical world than what had previously been called natural philosophy.

Theoretical physicists should not allow themselves to be distracted by every surprising experimental finding

Paul Dirac

The book follows the mutual fertilisation of mathematics and physics through the last few centuries, as the disciplines gained momentum with Newton, and exploded in the 20th century. Along the way it peeks into the thinking of notable mathematicians and physicists, often with strong opinions. For example, Dirac, a favourite of the author, is quoted as reflecting both that “Einstein failed because his mathematical basis… was not broad enough” and that “theoretical physicists should not allow themselves to be distracted by every surprising experimental finding.” The belief that mathematical structure is at the heart of physics and that experimental results ought to have secondary importance holds sway in this section of the book. Such thinking is perhaps the result of selection bias, however, as only scientists with successful theories are remembered.

The detailed exposition makes the reader vividly aware that the relationship between mathematics and physics is a roller-coaster loaded with mutual admiration, contempt, misunderstandings, split-ups and re-marriages. Which brings us, towards the end of the book, to the current state of affairs in theoretical high-energy physics, which most of us in the profession would agree is characterised by extreme mathematical and intellectual sophistication, paired with a stunning lack of experimental support. After many decades of flourishing interplay, which provided, for example, the group-theoretical underpinning of the quark model, the geometry of gauge theories, the algebraic geometry of supersymmetric theories and finally strings, is there a new divorce ahead? It appears that some not only desire, but relish the lack of supporting experimental evidence. This concern is also expressed by the author, who criticises self-declared experts who “write with a confidence that belies the evident slightness of their understanding of the subject they are attacking”.

The last part of the book is the least readable. Based on personal interactions with physicists, the exposition becomes too detailed to be of use to the casual, or lay reader. While there is nothing wrong with the content, which is exciting, it will only be meaningful to people who are already familiar with the subject. On the positive side, however, it gives a lively and accurate snapshot of today’s sociology in theoretical particle physics, and of influential but less well known characters in the field.

The Universe Speaks in Numbers illuminates the role of mathematics in physics in an easy-to-grasp way, exhibiting in detail their interactive co-evolution until today. A worthwhile read for anybody, the book is best suited for particle physicists who are close to the field.


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