But there are also significant flaws. Baker's slick journalistic style grates after a while - especially when we are forced to hear about him supping yet another coffee in a cafe as he waits for his next interviewee. And maybe it's because I'm a maths nerd, but I hoped for more detail about the maths involved. Baker's mathematical descriptions are often superficial, and indeed he seems to regard the maths as little more than magic. His numerati come across as sorcerers armed with mysterious, secret knowledge, not as scientists with tools that can be rationally analysed. This has the effect of making them seem more sinister than they are.

The book becomes more interesting when Baker turns his attention to the political implications of the numerati's activities. There are clear issues of civil liberties at stake, as well as of consent. Most of us have no idea how much of our lives are being tracked. If we did, we would probably be horrified. At the same time, it is hard to deny that the numerati do much that is good. Baker's analysis is pretty balanced, and he spells out why we should be grateful to the numerati, as well as concerned in some areas.

Increasingly, for example, the numerati use their skills to monitor health care; homes for the elderly are being wired with technology that can record fluctuations in weight or a decrease in mobility, triggering a hasty visit from a doctor. If you're joining a dating agency, you want to exploit the skills of mathematicians to find the perfect partner. And, as Baker points out in his chapter on the use of the numerati by pollsters, anything that helps politicians target individuals on issues that they care about, rather than simply trotting out bland platitudes, is a good thing.

The Fibonacci numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation
F_n=F_(n-1)+F_(n-2) (1)

with F_1=F_2=1. As a result of the definition (1), it is conventional to define F_0=0.

The Fibonacci numbers for n=1, 2, ... are 1, 1, 2, 3, 5, 8, 13, 21, ... (Sloane's A000045).

Fibonacci numbers can be viewed as a particular case of the Fibonacci polynomials F_n(x) with F_n=F_n(1).

Fibonacci numbers are implemented in Mathematica as Fibonacci[n].

The Fibonacci numbers are also a Lucas sequence U_n(1,-1), and are companions to the Lucas numbers (which satisfy the same recurrence equation).

For those with the ability to interpret it, this data trail is a goldmine. Advertisers and politicians have long dreamed of being able to target their messages - or products - at individuals on the basis of highly detailed information about them. Now this dream is becoming reality. By analysing the geometry of our mathematical pathways, mathematicians can cluster people with shared interests and passions, creating ever smaller, more specific groups to target.

For example, Baker talks to one of the numerati, Dave Morgan of AOL, who picked up a correlation between people visiting the Alamo Rent A Car website and surfing romantic movie sites. It isn't an obvious match; only in retrospect could it be traced to an escapist tendency. But once the pattern was identified, advertisers could find all sorts of clever ways to exploit it - for example, by bombarding this particular group with offers for weekend breaks in country hotels.

Baker argues that the numerati have become incredibly powerful in a range of fields, from the workplace to the voting booth, from health care to counter-terrorism. He even puts the maths to the test to see if a dating agency can pair him with his wife; when he eventually unchecks the box requesting someone several decades too young, Mrs Baker pops up top of the list. There is no denying that the digital revolution has opened up exciting new territory for mathematicians. The numerati are no fantasy; they exist. Baker is telling us about a phenomenon that is important and often overlooked. That makes his book urgent and exciting.