**Published by:** Fourth Estate, 2003

Professor du Sautoy needs to write more books, because this is one of
the best-written popular science books I've read in a very long time.
It's the story of
the Riemann Hypothesis,
a nineteenth-century conjecture about the behaviour of prime numbers
(specifically, how often they crop up among the natural numbers) which
suggests that it is related to a type of equation called a *zeta
function*. Riemann died young and never got around to proving his
hypothesis. Instead, the problem soon found fame thanks to the way that
it resisted all attempts to find a decisive solution. Since
Fermat's Last Theorem
was finally proved by Sir Andrew Wiles in 1993, the Reimann Hypothesis
has become the Holy Grail of mathematics and is quite possibly the most
important unanswered question in science. It's proved intractable enough
to have become widely known outside the mathematics community, and it's
even played a central part in at least one
best-selling novel.

It's also intimately linked with the cryptographic algorithms that are used to protect the details of your credit card when you shop on the Internet, and Professor du Sautoy explains why it is that some areas of mathematical research aimed at proving the hypothesis have ended up being closely monitored by organizations such as the United States' National Security Agency.

Saying more about the history of the hypothesis would spoil things; the book is written like a whodunnit and the cast of characters includes many extraordinary figures from the field of maths. There are some familiar faces from physics, too. I was most surprised when Freeman Dyson made an appearance in the closing chapters.

I don't think it counts as a spoiler to reveal that as of today, the hypothesis remains unproven. But I was astonished by the directions the tale takes and the connections with seemingly unrelated areas of physics that have been discovered as a result of the heroic efforts to find a solution over the last two centuries. Even without a triumphant grand reveal at the end, this book is a delight from start to finish.

**Published by:** Houghton Mifflin, 2006

Another book from my charity shop science book haul. While this book is also about string theory, it examines the science from a markedly different perspective. Although the first few chapters are dedicated to where string theory came from and why it's so important, Smolin's main focus is on advancing a pretty solid argument that the theory has now taken over theoretical physics to the exclusion of pretty much all other theories. Smolin sets out why this is not a good thing, examining the sociological behaviours that are driving it. He's an excellent communicator. His writing is clear, easy to follow, and he conveys the roller-coaster ride of excitement and disillusionment that he personally experienced as a working theoretical physicist when the string theory revolution happened and the way people did physics started to change.

Although he assures the reader that this isn't meant as an attack on the science behind string theory or of the people working in the field, it's hard not to come away from the book feeling that an awful lot of very clever people have spent the last four decades barking up what might very well turn out to be the wrong tree. And they have done so for so long, Smolin argues, because it has become politically unacceptable for anyone to challenge consensus thinking on the subject. He sets out some pretty damning evidence for this extraordinary claim. String theory may well turn out to be one of the most expensive dead ends in the history of science.

Or it might not. The "Trouble with Physics" of the book's
title is not just related to the politics of modern science; it's also
the problem with the theory itself, which appears to be impossible to
test experimentally. It can't even be used to make useful predictions,
because the landscape of the underlying aspects of the theory is so
wide-ranging, the properties of reality it can define are so varied,
that nobody can identify which one we've ended up with, let alone
explain why. One problem associated with the theory is thought to have
around 10^{500} different solutions but it could be as many as
10^{272,000}, or
even higher. In trying to narrow things down, string theorists seem to
have done the opposite. That's not exactly what you'd expect (or want)
from a single, elegant theory of how the Universe works. The Emperor
might not be wearing any clothes, but nobody has yet managed to get
close enough to him to find out for certain.

What struck me most about the tale being told here is that the moment at
which the field of theoretical physics stalled corresponds to a quite
striking degree with the point at which the centre of activity in the
field shifted from Europe to the Americas. Smolin classes the shift as
being away from seers (disruptive visionaries like Einstein who thought
deeply about the philosophical aspects of their work) towards
craftspeople (who tend to be more attached to the *status quo*).
Ironically, the lack of seers has turned string theory into something
that looks remarkably like a cult, suffering from groupthink and
exclusion of the out-group almost as badly as the Republican Party.

When this book was first published, Smolin got a lot of flak for calling out what he saw as an endemic problem in modern physics. However, nearly two decades on from the book's debut, no progress seems to have been made in proving he was wrong.

**Published by:** Abacus, 1992.

I started this year with something from a recent charity shop haul of science books. It's an overview of string theory by the physicist and writer Dr. F. David Peat (1938-2017), and while it's somewhat out of date, it covers a lot of the history of the theory and its principal ideas. Roger Penrose's Twistor Theory and spin networks (which subsequently led to the development of Loop Quantum Gravity) feature prominently.

It's all a very dense read, and while I got the general gist of things,
a lot of the maths (and there's a *lot* of maths) went completely
over my head. Indeed, Peat bemoans the fact that as the 1980s progressed,
physics as he knew it was becomingly increasingly abstract; he more or
less gives up on the idea of depicting what the fundamental concepts
would look like, as many of the theory's fundamental entities don't
just exist in the three dimensions of space and time that we're
familiar with in every day life. However we are treated to an
introduction to one of modern physics's most eccentric invention,
the
trouser diagram.

And no, I am not making this up.