As the downturn takes hold, BBC Radio 4's More or Less programme looks at the maths behind the credit crunch. Read original article. Since 2007, presenter and economist Tim Harford has been exploring and explaining the numbers which have contributed to - and have characterised - the global economic downturn.
He met the mathematicians at the heart of the City - and found out why some say they are to blame for the financial crisis.
He uncovered the flaws of the bankers' bonus system, and discovered a mathematical error which might have led the banks into trouble.
He interviewed quantitative finance expert Paul Wilmott and The Financial Times journalist Gillian Tett.
And he met the guardians of what could be the financial world's most important number.
You can listen to all of Tim's reports here.
PAUL WILMOTT, QUANTITATIVE FINANCE EXPERT
Paul Wilmott is a lecturer in financial mathematics and runs the profession's most popular website.
He is a fan of quantitative finance - but he thinks that its misuse has played a part in creating the current banking crisis.
In November 2007, More or Less asked whether the financial mathematicians known as "quants" - short for quantitative analysts - were to blame for what was then being termed "the credit squeeze".
 | WHO ARE THE QUANTS? |
Paul Wilmott discussed his concerns with Professor William Perraudin of the Tanaka Business School at Imperial College London.
Tim Harford chaired the discussion.
The risks of risk management
In December 2008, Tim invited Paul Wilmott back to talk about the problems in more detail.
Banks and hedge funds rely on highly-paid mathematicians and economists - "quants" - to evaluate risk.
So why did they not they see the credit crunch coming?
Paul Wilmott says some mathematicians have a tendency to get fixated on the numbers, failing to think about the big picture.
| RISKY RISK MANAGEMENT |
He posed a scenario.
Imagine you are at a magic show. The magician takes an ordinary pack of 52 playing cards, and gives it to a man in the audience to shuffle. He then asks a volunteer to think of a card. "The ace of spades," she replies.
The magician turns to the man with the pack of cards and removes a single card from the deck. What is the probability that the card is the ace of spaces? 
To hear the answer listen to the interview, or read Paul Wilmott's article on the risks of risk management.
A fundamental mathematical error
Paul Wilmott says an additional cause of the credit crunch is that people simply got their sums wrong.
| GETTING THE SUMS WRONG |
He told
More or Less these errors might have contributed to the mispricing of financial derivatives, and thus to the travails of the banks, the credit crunch, and the economic downturn.
The maths of the bonus system
Many traders were paid bonuses if they made money.
And yet, collectively, their trades bankrupted some banks and nearly bankrupted many more.
| THE TRADER'S DILEMMA |
Why did traders, paid for performance, all make the same mistake at the same time?
Paul Wilmott set out the trader's dilemma.
AT HOME WITH THE QUANTS
In October 2007, Tim Harford got a glimpse into the world of the quants.
The most successful of these talented mathematicians will come up with mathematical formulae that make them and their bank or hedge fund employers millions of pounds per year.
They are highly secretive about their work, not wanting others to know the details of their systems.
| MEET THE QUANTS |
But one of them, William Hooper, invited Tim Harford into his beautiful London home.
Read more about quantitative analysts
A trader's apology
William Hooper has since left the world of finance to start his own business.
He has been reflecting on the global economic problems and the question of who is to blame - read A trader's apology.
GILLIAN TETT, THE FINANCIAL TIMES
Gillian Tett is an assistant editor of the Financial Times and oversees the global coverage of the financial markets.
Five years ago, she was shocked to discover what she says could best be described as an iceberg in the middle of the City.
The role of the media
She was studying media coverage of the City and began to realise journalists were doing lots of stories on stocks and shares, mergers and acquisitions, but nothing on what had become a much bigger part of finance - the credit and derivative markets.
She says business journalists were simply not covering the City in a representative way.
| THE FINANCIAL ICEBERG |
You had a small part of the financial system bobbing above the water but a vast shadowy mass of activity pretty much hidden beneath the waves.
And hidden not just from ordinary people, but hidden from politicians, from many regulators, and unfortunately from much of the media too.
UNDERSTANDING LIBOR
The London Interbank Offered Rate - LIBOR - has been dubbed the financial world's most important number.
Published each day in the UK, it is the rate at which the banks lend to each other and it influences over $150 trillion (£100 trillion) of funds worldwide.
The Libor number is compiled by putting together the estimates of the cost of borrowing from at least eight banks, and then discarding the highest and lowest of the sample to leave an average rate which then becomes the daily 'Libor Fix'.
| LIBOR |
But the figure's validity is being questioned, with critics dubbing it "the rate at which banks won't lend".
Tim Harford was granted exclusive access to the operations centre where the daily rate is compiled.
More or Less is broadcast on BBC Radio 4. To find out more, visit the programme website, or subscribe to the More or Lesspodcast.
Written by David Jetuah
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