During the 17th century, when the scientific revolution was in full swing, people started to talk about the “laws of nature”. Newton set the example when, in the Principia, he proposed his three “axioms, or laws of motion” (axioms surely being a nod to Euclid). Then, throughout the 18th and 19th centuries many laws were propounded. In the 20th century, however, law-naming became less popular in science.

But why the word “law”? What, if any, is the connection with the laws of a nation? National or even international laws are things that we are supposed to obey but often do not. Yet nature cannot help but “obey” its laws. Perhaps Newton and his contemporaries thought of the laws of nature as being God-given, and so therefore unbreakable.

There are also several other words that scientists apply to ideas that they deem important: in addition to axiom, we have hypothesis, principle, equation, theory, theorem and model. The usual practice is to reserve the word “law” for something that can be formulated in one or two sentences, with at most one simple mathematical equation. This, at any rate, is roughly the criterion for inclusion in noted science writer Clifford Pickover’s latest book, Archimedes to Hawking: Laws of Science and the Great Minds Behind Them. Pickover’s other criteria seem to be that a law should be at least moderately important and should hold true — with the usual caveats about appropriate circumstances and approximations.

Some of the deepest ideas in science, however, are too subtle to be encapsulated as a law — for example Darwin’s theory of evolution and Einstein’s theories of relativity. Even Newton’s laws are preceded by eight definitions and a “scholium”, or explanatory comment, asserting that space, time and motion are absolute. Indeed, the latter could be called Newton’s zeroth law.

Schrödinger’s equation, on the other hand, is short enough when written in symbols but is difficult to translate as a sentence, and even harder to explain, so it does not qualify as a law. The Navier–Stokes equations of fluid flow are presumably too mathematical and complex to be included, and even the apparent simplicity of E=mc² is deceptive.

Pickover’s book presents 40 scientific laws together with explanations of what they mean and short biographies of those who developed them. Applications of these laws are also described, even recent ones. The laws are all from the physical sciences, but I think it is a pity that, say, Mendel’s laws of genetics or Crick’s “central dogma” (another interesting word there) about the flow of information in molecular biology have been excluded.

The list starts with Archimedes and Kepler, whose three laws of planetary motion were not, incidentally, called “laws” by either him or Newton. The 19th century provides 25 laws and the 20th century only four, with the last being Hubble’s law in 1929. After that the flow dries up. Is this because of a different theological view, or because scientists became more modest (for example, naming particle physics’ most successful theory the Standard Model)?

The book ends with short sections on 47 “great contenders” — a sort of reserve list. However, I think that some of these deserve a place in the original selection. Pauli’s exclusion principle might have been called a law (and Heisenberg’s principle did indeed get picked), and either Maupertuis’ rule of least action or Hamilton’s related principle are surely as important as they come.

Stephen Hawking only gets in as a great contender, although the laws of black-hole thermodynamics that he helped formulate are nice examples of late 20th-century laws. Another possibility from the second half of the 20th century might have been the “CPT theorem”, which asserts, roughly, that every charged particle has an oppositely charged mirror antiparticle with otherwise identical properties.

The laws in the book could be classified into two sorts: those (like Boyle’s law) that are consequences of some more general theory; and those that have not been explained in this way (or at least not yet). I am not sure that any of the laws in the main list are of this second type, but some of the great contenders are and the latter sort perhaps have more claim to be “fundamental”.

Pickover’s book contains all sorts of interesting information and asides. For example, David Brewster (of the law of reflection of polarized light) invented the kaleidoscope, but he failed to benefit from its wide popularity because his patent was faulty. There are also many quotations and some, which are of a philosophical nature, are used as “conversation starters” between the chapters. The reader might well get interested in either the science or the history, and there are plenty of references for further reading. However, some line diagrams might have helped explain the more mathematical laws.

A question that often came to my mind as I read the book, and which I did not always find answered, is whether a law was first derived in just an empirical way, and if so, whether it was later derived from a bigger theory. I notice that many of the laws state just a proportionality between two quantities, which suggests that their inventors were attracted by simplicity. Poiseuille’s law about fluid flow through a tube is an exception, with a fourth-power dependence on the radius.

With such a wide range, this book cannot be expected to be equally authoritative about everything that it covers. However, like some of the quotations given, it is an excellent conversation starter.