Lost in Math: A Book Review

I recently finished reading a thought-provoking book by theoretical physicist Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray. Hossenfelder writes in an engaging and accessible style, and I hope you will enjoy reading this book as much as I did. Do we have a crisis in physics and cosmology? You be the judge. She presents convincing arguments.

The basic premise of Hossenfelder’s book is that when theoretical physicists and cosmologists lack empirical data to validate their theories, they have to rely on other approaches—”beauty”, “symmetry”, “simplicity”, “naturalness“, “elegance”—mathematics. Just because these approaches have been remarkably successful in the past is no guarantee they will lead to further progress.

One structural element that contributes to the book’s appeal is Hossenfelder’s interviews with prominent theoretical physicists and cosmologists: Gian Francesco Giudice, Michael Krämer, Gordon Kane, Keith Olive, Nima Arkani-Hamed, Steven Weinberg, Chad Orzel, Frank Wilczek, Garrett Lisi, Joseph Polchinski, Xiao-Gang Wen, Katie Mack, George Ellis, and Doyne Farmer. And, throughout the book, she quotes many other physicists, past and present, as well. This is a well-researched book by an expert in the field.

I also like her “In Brief” summaries of key points at the end of each chapter. And her occasional self-deprecating, brief, soliloquies, which I find reassuring. This book is never about the care and feeding of the author’s ego, but rather giving voice to largely unspoken fears that theoretical physics is stagnating. And an academic environment hell-bent on preserving the status quo isn’t helping matters, either.

Anthropic Principle

Do we live in a universe fine-tuned for life? If so, is it the only possible universe that would support life? Recent work indicates that there may be more than one set of parameters that could lead to a life-supporting universe.

Beauty is in the Eye of the Beholder

Is our sense of what is “beautiful” a reliable guide to gaining a deeper understanding of nature? Or does it sometimes lead us astray? We know from history that it does.

In the past, symmetries have been very useful. Past and present, they are considered beautiful

When we don’t have data to guide our theory development, aesthetic criteria are used. Caveat emptor.

Experiment and Theory

Traditionally, experiment and observation have driven theory. Now, increasingly, theory drives experiment, and the experiments are getting more difficult, more expensive, and more time consuming to do—if they can be done at all.


The rapid expansion of the universe at the time of the Big Bang is known as cosmic inflation, or, simply, inflation. Though there is some evidence to support inflation, that evidence is not yet compelling.


Mathematics creates a logically consistent universe all its own. Some of it can actually be used to describe our physical universe. What math is the right math?

Math is very useful for describing nature, but is math itself “real”, or is it just a useful tool? This is an ancient question.

Memorable Quotations

“I went into physics because I don’t understand human behavior.” (p. 2)

“If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.” (p. 9)

“In our search for new ideas, beauty plays many roles. It’s a guide, a reward, a motivation. It is also a systematic bias.” (p. 10)

On artificial intelligence: “Being unintuitive shouldn’t be held against a theory. Like lack of aesthetic appeal, it is a hurdle to progress. Maybe this one isn’t a hurdle we can overcome. Maybe we’re stuck in the foundations of physics because we’ve reached the limits of what humans can comprehend. Maybe it’s time to pass the torch.” (p. 132)

“The current organization of academia encourages scientists to join already dominant research programs and discourages any critique of one’s own research area.” (p. 170)


The idea that our universe of just one of a great many universes is presently the most controversial idea in physics.

Particles and Interactions

What is truly interesting is not the particles themselves, but the interactions between particles.


Physicists and astrophysicists are sloppy philosophers and could stand to benefit from a better understanding of the philosophical assumptions and implications of their work.

Physics isn’t Math

Sure, physics contains a lot of math, but that math has traditionally been well-grounded in observational science. Is math driving physics more than experiment and observation today?

Quantum Mechanics

Nobody really understands quantum mechanics. Everybody’s amazed but no one is happy. It works splendidly well. The quantum world is weird. Waves and particles don’t really exist, but everything (perhaps even the universe itself) is describable by a probabilistic “wave function” that has properties of both and yet is neither. Then there’s the many-worlds interpretation of quantum mechanics, and quantum entanglement

Science and the Scientific Method

In areas of physics where experiments are too difficult, expensive, or impossible to do, some physicists seem to be abandoning the scientific method as the central pillar of scientific inquiry. Faith in beauty, faith in mathematics, faith in naturalness, faith in symmetry. How is this any different than religion?

If scientists can evaluate a theory using other criteria than that theory’s ability to describe observation, how is that science?


Some areas of physics haven’t seen any new data for decades. In such an environment, theories can and do run amok.

Standard Model (of particle physics)

Ugly, contrived, ad hoc, baroque, overly flexible, unfinished, too many unexplained parameters. These are some of the words used to describe the standard model of particle physics. And, yet, the standard model describes the elementary particles we see in nature and their interactions with extraordinary exactitude.

String Theory

String theory dates back at least to the 1970s, and its origins go back to the 1940s. To date, there is still no experimental evidence to support it. String theory is not able to predict basic features of the standard model. That’s a problem.

Triple Threat: Crises in Physics, Astrophysics, and Cosmology?

Physics: Sure, the Large Hadron Collider (LHC) at CERN gave us the Higgs boson, but little else. No new physics. No supersymmetry particles. Embarrassments like the diphoton anomaly. Do we need a bigger collider? Perhaps. Do we need new ideas? Likely.

Astrophysics: We’ve spent decades trying to understand what dark matter is, to no avail. No dark matter particles have been found.

Cosmology: We have no testable idea as to what dark energy is. Plenty of theories, though.

See Hossenfelder’s recent comments on the LHC and dark matter in her op-ed, “The Uncertain Future of Particle Physics” in the January 23, 2019 issue of The New York Times.

The book concludes with three appendices:

  • Appendix A: The Standard Model Particles
  • Appendix B: The Trouble with Naturalness
  • Appendix C: What You Can Do To Help

Hossenfelder gives some excellent practical advice in Appendix C. This appendix is divided into three sections of action items:

  • As a scientist
  • As a higher ed administrator, science policy maker, journal editor, or representative of a funding body
  • As a science writer or member of the public

I’m really glad she wrote this book. As an insider, it takes courage to criticize the status quo.

Hossenfelder, S., Lost in Math: How Beauty Leads Physics Astray, Basic Books, New York (2018).
Hossenfelder, Sabine. “The Uncertain Future of Particle Physics.” The New York Times 23 Jan 2019. https://www.nytimes.com/2019/01/23/opinion/particle-physics-large-hadron-collider.html.


Fermilab is a name well known to all physicists.  When I was an astrophysics undergraduate student at Iowa State University in Ames, Iowa in the mid-to-late 1970s, I remember that several members of our large high energy physics group made frequent trips to Fermilab, including Bill Kernan and Alex Firestone.  At the time, it was the best place in the world to do high energy physics.  What is high energy physics?  Basically, it is the creation and study of new and normally unseen elementary particles formed by colliding subatomic particles into one another at very high velocities (kinetic energies).

Wilson Hall, Fermilab, March 4, 2018.  Photo by Lynda Schweikert

On Sunday, March 4, a group of us from the Iowa County Astronomers met up at Fermilab for an afternoon tour of this amazing facility.  We were all grateful that John Heasley had organized the tour, and that Lynda Schweikert photo-documented our visit.

Our group at Fermilab. Our wonderful tour guide is third from left, and club organizer John Heasley is sixth from right. Photo by Lynda Schweikert, fourth from left.

Our afternoon began with an engaging talk by Jim Annis, Senior Scientist with the Experimental Astrophysics Group: “Kilonova-2017: The birth of multi-messenger astronomy using gravitational waves, x-rays, optical, infrared and radio waves to see and hear neutron stars”.  Here he is showing a computer simulation of an orbiting  pair of neutron stars coalescing, an event first observed by the LIGO and Virgo gravitational wave detectors on 17 August 2017 (GW170817), and subsequently studied across the entire electromagnetic spectrum.

Dr. Jim Annis describing the neutron star merger detected on 17 Aug 2017. Photograph by Lynda Schweikert.

One of the amazing factinos I remember from his talk: even though neutrinos were not directly detected from the GW170817 event, the matter in colliding neutron stars is so dense that neutrinos push material outwards in what is called a neutrino wind.  Yes, these are the same neutrinos that could pass through a light year of solid lead and only have a 50% chance of being absorbed or deflected, and pass through your body at the rate of 100 trillion every second with nary a notice.

Even though CERN has now eclipsed Fermilab as the world’s highest-energy particle physics laboratory, Fermilab is making a new name for itself as the world’s premier facility for producing and studying neutrinos.  This is a fitting tribute to Enrico Fermi (1901-1954)—after whom Fermilab is named—as Fermi coined (or at least popularized) the term “neutrino” for these elusive particles in July 1932.

Basic research is so important to the advancement of human knowledge, and funding it generally requires public/government funding because practical benefits are often years or decades away; therefore such work is seldom taken up by businesses interested in short term profit.  However, as our tour guide informed us, the equipment and technology that has to be developed to do the basic research often leads to practical applications in other fields on a much shorter time frame.

Main Control Room at Fermilab. Photograph by Lynda Schweikert.

Thoughts Inspired by Leon Lederman: A Footnote

I had the great privilege in October 2004 of attending a talk given by Leon Lederman (1922-), winner of the 1988 Nobel Prize in Physics and director emeritus of Fermilab.  I listened intently and took a lot of notes, but what I remember best besides his charm and engaging speaking style was his idea for restructuring high school science education.  The growing scientific illiteracy in American society, and the growth of dogmatic religious doctrine, is alarming.  Lederman advocates that all U.S. high school students should be required to take a conceptual physics & astronomy course in 9th grade, chemistry in 10th grade, and biology in 11th grade. Then, in 12th grade, students with a strong interest in science would take one or more advanced science courses.

Teaching conceptual physics (and astronomy) first would better develop scientific thinking skills and lay a better groundwork for chemistry, which in turn would lay a better groundwork for biology.  Whether or not a student chooses a career in science, our future prosperity as a society depends, in large part, on citizens being well-informed about science & technology matters that affect all of our lives.  We also need to be well-equipped to assimilate new information as it comes along.

It is in this context that I was delighted to read Leon Lederman’s commentary, “Science education and the future of humankind” as the last article in the first biweekly issue of Science News (April 21, 2008). He writes:

Can we modify our educational system so that all high school graduates emerge with a science way of thinking?  Let me try to be more specific.  Consider Galileo’s great discovery (immortalized as Newton’s First Law): “An isolated body will continue its state of motion forever.”  What could be more counterintuitive?  The creative act was to realize that our experience is irrelevant because in our normal experience, objects are never isolated—balls stop rolling, horses must pull carts to continue the motion.  However, Galileo’s deeper intuition suspected simplicity in the law governing moving bodies, and his insightful surmise was that if one could isolate the body, it would indeed continue moving forever.  Galileo and his followers for the past 400 years have demonstrated how scientists must construct new intuitions in order to know how the world works.

I’d like to take Lederman’s comments one step further.  Whether it be science, politics, economics, philosophy, or religion, we must realize that most ignorance is learned.  We all have blind spots you could drive a truck through.  Our perceptions masquerade as truth but sometimes upon closer inspection prove to be faulty.  Therefore, we must learn to question everything, accepting only those tenets that survive careful, ongoing scrutiny.  We must learn to reject, unlearn if you will, old intuitions and beliefs that are harmful to others or that have outlived their usefulness in the world.  We must develop new intuitions, even though at first they might seem counterintuitive, that are well supported by facts and that emphasize the greater good.  We must, all of us, construct new intuitions in order to make our world a better place—for everyone.