Note: This review is by my husband Jim.
Ian Stewart is an English mathematician who writes entertaining books on the importance of mathematics in just about every aspect of life. He demonstrates, with hardly an equation in sight, how math forms the basis for discoveries ranging from technological advances on earth to the ability to visit the moon; from predicting the nature of atoms to learning about the workings of galaxies.
The core theme of the book is that:
“…there are mathematical patterns in the motions and structure of both celestial and terrestrial bodies, from the smallest dust particle to the universe as a whole. Understanding those patterns allows us not just to explain the cosmos, but also to explore it, exploit it, and protect ourselves against it.
Arguably the greatest breakthrough is to realise that there are patterns. After that, you know what to look for, and while it may be difficult to pin the answers down, the problems become a matter of technique.”
Thus he describes, for example, (1) how Newton’s invention of calculus enabled him to “prove” or at least gain insight into why planetary orbits were (as Kepler had shown) elliptical rather than circular; (2) how mathematical perturbations in the orbit of Uranus led to the discovery of Neptune; (3) how Einstein’s general relativity field equations implied the existence of black holes; and (4) how math has been instrumental in many other somewhat less famous astronomical theories and phenomena. [And, although the author doesn’t mention this particular application, it is math that can decide the important question of whether two smaller pizzas is better than ordering one big pizza.]
Interestingly, Stewart also argues that the mathematical basis for the existence of “dark matter” may not be on the rock solid ground that some commentators have implied. Of course, the problem with dark matter is that it is not composed of atoms or the familiar elementary particles that interact with light, so it cannot be detected except by measuring its theorized influence on what we can see. But Stewart argues that explanations other than the existence of dark matter could also account for perturbations in expected calculations. [This book was published in 2016; some advances in understanding dark matter have been made since that date.]
Stewart writes, “The main thrust of Calculating the Cosmos is the need for, and the astonishing success of, mathematical reasoning in astronomy and cosmology.” But he also shows where accepted scientific reasoning has led to false conclusions in the past, such as when astronomers sought a planet between Mercury and the sun because of the precession of the perihelion of Mercury’s orbit: there is no such planet. He says that making mistakes is part of the scientific process, and that our scientific (as opposed to mathematical) knowledge is always tentative. He concludes:
“Maybe dark matter is a mistake. Maybe alien life can be radically different from anything we’ve ever encountered, possibly even than we can imagine.
The fun will be finding out.”
Evaluation: Those who avoid math are missing out on the vast worlds that open up through its application. It is a bit like having a whole new set of powerful lenses through which to see the world, or a whole new set of utensils, pots, and pans in your kitchen. What miraculous revelations can be made with such an elegant toolbox! Stewart helps you see just what ideas have been developed from the intersection of math and science. For me, there is little more exciting than learning about the unraveling of the secrets of the universe.
Published in the U.S. by Basic Books, an imprint of Perseus Books, a subsidiary of Hachette Book Group, 2018