MARCUS DU SAUTOY:'You might think that catching criminals 'is all about finding physical evidence. 'Fingerprints, DNA.
MARCUS DU SAUTOY:'But even when these clues aren't available, 'a mathematical fingerprint is left behind.
MARCUS DU SAUTOY:'In 1888 the most notorious serial killer of all, Jack the Ripper, 'murdered five women in London's east end. 'He was never caught.
MARCUS DU SAUTOY:'Kim Rossmo has 20 years' experience as a detective inspector, 'and he specialises in catching serial killers.
MARCUS DU SAUTOY:'Although very rare, these criminals are notoriously hard to track down, 'because they often murder strangers 'in locations they have no obvious connection to.'
KIM ROSSMO:It's very common in the investigation of a serial murder case
KIM ROSSMO:to have hundreds, thousands, even tens of thousands of suspects. It's a needle in a haystack problem.
MARCUS DU SAUTOY:'But Rossmo is no ordinary cop,
MARCUS DU SAUTOY:'because he's a brilliant mathematician 'and uses numbers to understand the patterns 'that criminals leave behind.'
KIM ROSSMO:There's a logic in how the offender hunted for the victim, and the location where he committed the crime. If we can decode that, and if we can understand that pattern, we can use that information to help us focus a criminal investigation.
MARCUS DU SAUTOY:'To this day no one has been able to identify 'just who Jack the Ripper was, or where he lived,
MARCUS DU SAUTOY:'but based purely on the locations the murders took place, 'Rossmo thinks he could have tracked him down.
MARCUS DU SAUTOY:'Because he's noticed patterns in criminal behaviour 'that are as distinctive as a fingerprint,
MARCUS DU SAUTOY:'and he turned them into a mathematical formula 'based on probability.
MARCUS DU SAUTOY:'This formula calculates the likelihood 'that a criminal lives at a specific location 'based solely on where the crimes took place.
MARCUS DU SAUTOY:'The first half models what's known as the least effort principle.'
KIM ROSSMO:Inherently we're all lazy, and criminals just as much as anyone else. They want to accomplish their goals closer to home rather than further away.
MARCUS DU SAUTOY:'The probability gradually decreases the further you get from the crimes.
MARCUS DU SAUTOY:'The second half of the equation 'describes something called the buffer zone.
MARCUS DU SAUTOY:'Criminals avoid committing crimes too close to home 'for fear of drawing attention to themselves.
MARCUS DU SAUTOY:'It's the interaction of these two behaviours 'that allows Rossmo to calculate the most probable location 'of the criminals home.'
KIM ROSSMO:So naturally I was very interested in what would happen if I entered the locations of the five linked crimes into the equation.
MARCUS DU SAUTOY:'With a computer program based on his formula, 'Rossmo is creating a geographic profile 'to show the hotspots where the ripper was most likely to have lived.
MARCUS DU SAUTOY:'And it was this geographic profile that lead us here, 'to Flower and Dean Street.'
KIM ROSSMO:Flower and Dean Street should have been the epicentre of their search.
MARCUS DU SAUTOY:So do you think if you'd been alive at the end of the 19th Century and you'd had this equation, actually this guy might have been found?
KIM ROSSMO:Knowing what we know today about serial killers and with modern forensic techniques such as DNA I'm pretty sure that Jack the Ripper would have been caught if he was committing his crimes today.
MARCUS DU SAUTOY:'We may never know the truth about Jack the Ripper, 'but Rossmo's technique of geographic profiling 'has been used time and time again to help police all around the world 'narrow their search from an entire city to just a handful of streets.
MARCUS DU SAUTOY:'And at its heart lies pure mathematics.'
Marcus du Sautoy meets a detective with a PhD in mathematics who has created a probability function that can help narrow down the area in which a serial killer is likely to live.
The case of Jack the Ripper is outlined, and the probable street where he lives revealed.
The function is then broken down and the different elements explained: the least effort principle and the buffer zone.
This clip is from the series The Code.
Teacher Notes
Use as an enrichment clip as part of a series of lessons on probability and relative frequency.
This is a practical example of how probability functions and statistical models can be used to predict behaviour.
Students could discuss what other behaviours might be able to be predicted in this way, and whether it is ever possible for us to act outside of these models, leading to a discussion of free will.
Curriculum Notes
These clips will be relevant for teaching Maths at KS4 and GCSE in England, Wales and Northern Ireland and National 4/5 or Higher in Scotland.
The topics discussed will support OCR, Edexcel, AQA, WJEC in England and Wales, CCEA in Northern Ireland and SQA in Scotland.
