24/11/2017

Column in Folha: Mathematics can help fight crime.

The great English naturalist Charles Darwin (1809 – 1882) regretted not having studied mathematics in his youth because, he said, "people with that knowledge seem to have an extra sense," they see things that nobody else sees.

Years ago, I had a doctoral student who found a practical application for this idea: he told his colleagues who were finishing their theses that just by looking at them, I could spot the errors; I didn't even need to read the work.

It was a myth, of course, but it made others nervous – was that the intention? – and I want to believe that it motivated them to write more carefully.

But it is a fact that mathematicians can indeed discover errors and fraud in documents without needing to read them carefully.

That's what Wayne J. Nelson, an employee of the Arizona state treasury department, discovered in 1993, the hard way. He had been embezzling money through fake invoices and was very good at it: all the accounts were correct, and he only falsified small amounts to go unnoticed.

Even so, when the mathematicians looked at the values on his checks, they immediately realized something was wrong. The matter was investigated: it was discovered that Nelson had stolen more than US$2 million. He was tried and convicted.

The magic that mathematicians used is called Benford's law, named after the American engineer and physicist Frank A. Benford (1883 – 1948), although it was discovered much earlier by the Canadian astronomer and mathematician Simon Newcomb (1835 – 1909).

In 1881, Newcomb noticed that the logarithm tables he used were handled a great deal on pages with numbers beginning with 1 and 2, and less and less as the first digit of the logarithms increased. In a work of fiction, one might think that readers would lose interest in the story and give up reading. But in a logarithm table?

To explain the phenomenon, Newcomb suggested that logarithms starting with small digits are more likely, and proposed the following table:

To read the full text, visit the newspaper's website:

Folha allows each reader access to ten articles per month even without a subscription.