London, September, 1853. A cholera outbreak has decimated Soho, killing 10% of the population and wiping out entire families in days. Current medical theories assert that the disease is spread by "bad air" emanating from the stinking open sewers. But one physician, John Snow, has a different theory: that cholera is spread through contaminated water. And he is just about to use mathematics to prove that he is right.
Statistics can mislead, and who'd know this better than mathematicians? It's ironic, then, that mathematics itself has fallen victim to the seductive lure of crude numbers. Mathematicians' work is being measured, ranked and judged on the basis of a single measurement: the
number of times research papers are cited by others. And mathematicians are not happy about it.
Many things in life are more than the sum of their parts. Whether its the behaviour of crowds of people, flocking birds or shoaling fish, the unpredictable patterns of the weather or the complex structure of the Internet, it's often the interaction between things, rather than the things themselves, that generates complexity. It's a challenge to science, whose traditional approach of taking things apart and looking at the individual bits doesn't work when faced with emergent complexity. But there are mathematical techniques to understand this phenomenon.
What would you think if the nice café latte in your cup suddenly separated itself out into one half containing just milk and the other containing just coffee? Probably that you, or the world, have just gone crazy. There is, perhaps, a theoretical chance that after stirring the coffee all the swirling atoms in your cup just happen to find themselves in the right place for this to occur, but this chance is astronomically small.