Why becoming lost in math is a danger to science and scientists

The thesis of Sabine Hossenfelder’s new book “Lost in Math: how beauty leads physics astray” is one that is whispered between academics across the world. It starts with hushed confessions by scientists and applied mathematicians that we don’t understand string theory or dark matter. Then it builds to questions about the meaning of the pages of calculations produced by theoretical physicists. What do these theories really predict? Are these researchers just lost in math?

Gossip at faculty board meetings is cheap. And the fact is that most academics looking in on theoretical physics from the outside (including professors of applied maths, such as myself) are not really qualified to make such criticism. It requires someone on the inside to look at exactly what is going on. A whistleblower. And this is exactly the job Sabine performs. She has worked deep inside theoretical and experimental physics and now she is taking a long hard look at the subject she has been working on.

In her book, Sabine carefully explains the physics to us, revealing where maths has and hasn’t succeeded. The problems we whisper to each other are real: thousands of scientific papers are being written about a supersymmetry that no-one has seen any trace of and somewhere between 0 to 90% of our galaxy appears to be made of dark matter and energy that theoreticians have invented so as to keep their models from being wrong. That’s before we start getting in to the oddities of quantum mechanics and the potential existence of multiverses.

With the ‘lost in math’ hypothesis established, Sabine travels around the world and lets the physicists working on the theory address her criticisms. But what they do is talk themselves deeper and deeper in to a hole. We hear stories about bets on whether or not particles exist, we hear arguments about whose theory is ugliest, we hear assertions that theories must be true based entirely on the fact that constants should typically be around one and we hear about the imposing personalities of leading theoretical physicists. But, despite the construction of the Large Hadron Collider to search for new experimental breakthroughs, we hear very little about successful theoretical predictions. The Higgs boson, predicted in 1964, could prove to be the last successful prediction originating from the type of mathematical thinking currently adopted.

Sabine doesn’t shy away from discussing how academic politics and social norms seep in to the rise of meaningless mathematical physics. She points out that theoreticians are cheap and uncontroversial. It is very expensive to do experiments, so hiring a ‘clever’ white man (my stereotyping, not the author’s) who churns out lots of incomprehensible articles is value for money in a system where success is judged by scientific ‘outputs’, and not by genuine progress. She also discusses how the historic success of maths in physics has created a culture of over mathematising the subject. This culture is then self-perpetuating, with success in maths being conflated with success in science.

Sabine stays close to her own research area of fundamental physics. But much of her analysis could, in fact, be applied to other areas in which physicists have got involved. And here I am qualified to make similar criticisms of my own.

For example, the massive interest of physicists in ‘network science’ has produced some interesting and applicable ideas such as small worlds and polarisation. But it is has also led to tens of thousands of theoretical papers being written about small variations on models that provide no new insights and are not coupled to applications. In the research area I am closest to, collective animal behaviour, some physics research groups such as Tamas Viscek’s group in Budapest and the Starflag project in Rome have combined theory and experiment to create new insights, but this is again accompanied by pages and pages of accumulating theory in which meaningless models are analysed in the large n limit. The latest physplaining is applying renormalization groups to neural networks, resulting in dubious claims of a fundamental physics of human intelligence.

Maths and theoretical physics has a lot to offer the applied sciences, but we (far too often) stretch our mathematical analogies too far.

The one thing that Sabine doesn’t offer is a clear alternative. But, more worryingly, nor do most of the physicists she talks to. Revealingly, with the exception of theoretical astrophysicist and blogger, Katie Mack, none of the people she interviews ask for her opinion. This makes discussion of an alternative difficult. Instead, the grand old men and younger rock stars of physics repeat well-rehearsed defenses of what they are doing, carefully refining their notions of beauty in order to fit the questions she poses.

Their arguments can be paraphrased as: “No, we didn’t mean that theories are true because they are beautiful, it is just that they are beautiful and we can use this as a guide”. But, as Sabine points out, beauty is in the eye of the beholder, and there is no rational reason to trust it as a scientific guide.

What is most shocking about this book is its existence. It was written after Hossenfelder became disillusioned with her field, while failing to secure tenure-track employment at a University. It is a sad indictment of modern physics that a thoughtful, insightful woman like Sabine Hossenfelder, who has published widely and has a genuinely valuable take on the future of physics, has such difficulty securing a permanent scientific position. At the same time, at a department near you, another mathematical ‘genius’, who no-one understands and who looks down on experiments, is currently being hired to explain theoretical connections entirely devoid of physical meaning.

Theory only exists to help us understand the world. If we let mathematical elegance determine ‘good’ theory then we will lose many good scientists along the way.