Supportive Quantitative Methods

To Err is Human

Ah ne'er so dire a Thirst of Glory boast,

Nor in the Critick let the Man be lost!

Good-Nature and Good-Sense must ever join;

To err is Humane; to Forgive, Divine.

(Alexander Pope, An Essay on Criticism, Part II, 1711)

Why all this Mathematics?

  • Living in small groups is easy…
  • With some basic mental accounting we can keep track of property rights.
  • It is also possible to have some barter trade.
  • But not much more…
  • One cannot organize a city of thousands without some form of bookkeeping.

The Sumerian City of Uruk

  • Ancient Sumer is one of the earliest cradles of civilization.
  • It emerged between the fertile lands of Tigris and Euphrates around 5000 BC. in modern-day Iraq.
  • The abundance of crops led to surpluses and created a need to build storage facilities for the stockpile.
  • The first early urban settlements were formed.
  • Among them was Uruk.
  • It is estimated that Uruk may have had 40000 residents in 3100 BC., making it the largest city in the world at the time.


  • How did the people of Uruk keep track of their stockpile?
  • The earliest proto-writing (elaborate bookkeeping system) texts come from the city of Uruk c. 3500 BC.
  • They consisted of symbols scratched on clay tablets.
  • They record the distribution of bread, wheat… and beer.

The Accountant

  • Some of the records were written by a person named Kushim.
  • Their signature on 18 tablets indicates that Kushim was responsible for a warehouse with beer brewing materials.
  • Nisa, their supervisor, also signed these tablets.
  • To fulfill their roles, Kushim and Nisa had to perform a lot of mathematical calculations.
  • They were not always correct!

The Oldest Mistake Ever Recorded

Costly Errors in Finance Mathematics

  • Errors in mathematics can get very costly.
  • In 1999, the $125 Million Mars Climate Orbiter crashed due to a conversion error between the imperial and metric measurement systems.
  • An integer overflow led to the explosion of the European Space Agency’s Ariane 5 rocket in 1996.
  • Although mistakes in large engineering projects receive more attention, mistakes in finance and economics can also be very costly.

The Great Recession

  • After the collapse of Lehman Brothers in 2008, monetary authorities in the US and the EU strengthened their regulatory supervision.
  • Up to 2007, stress tests were used internally by banks for their self-assessment.
  • After the crisis, central banks started conducting their own stress tests to assess how well banks are able to cope with financial and economic shocks.
  • For instance, ECB is conducting multiple stress tests for the EU banking sector each year (Bank 2023).

Some Good News

  • In March 2014, Bank of America (BoA) announced its very positive performance for the recently conducted stress tests.
  • It was the first time that BoA passed the Federal Reserve's (Fed) stress test since the 2008 financial crisis.
  • The results were so good that the bank announced
    • it will boost the dividend payments to its shareholders, and
    • buy back stocks up to $4 billion.
  • Neither the dividends were paid, nor any buyback operations were conducted.

Structured Bonds

  • In 2009, BoA acquired structured bonds owned by Merril Lynch.
  • An accounting review of the stress test data revealed certain inconsistencies in the valuations of these bonds (Christina, Dan, and Ryan 2014).
  • BoA reported that it miscalculated a measure of the capital on its books due to an incorrect adjustment on the bond's future values.

A Math Error with a $9 Billion Valuation

  • In April 2009, BoA retracted its previous announcement.
  • Fed required BoA to resubmit its report and capital action plans.
  • The bank's shareholders were not very happy with this error.
  • The day when the news of the error went public, the bank's stock value plummeted by $9 billion (5% of its total value).


Bank, European Central. 2023. “Stress Tests.” European Central Bank - Banking Supervision.
Christina, Rexrode, Fitzpatrick Dan, and Tracy Ryan. 2014. “Bank of America Suspends Buyback, Dividend Increase.” The Wall Street Journal. Dow Jones & Company.
Parker, Matt. 2019. Humble Pi: A Comedy of Maths Errors. Penguin Books Limited.