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.

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