He was the son of a schoolmaster and with his maternal mathematical ancestor Thomas Fincke, he demonstrated his potential from an early age by being able to read books upside down. He passed the *Preliminary Examination* offered by the University of Copenhagen, with distinction, at age 14, after receiving dispensation to sit because he was younger than the usual minimum age.

For the next two years he taught alongside his father.

With a distant relative providing free board and lodgings, he prepared for and sat the University of Copenhagen entrance examination in 1896, which he passed with distinction. He won a scholarship to the University of Copenhagen and majored in mathematics, but also studied astronomy, physics and chemistry. He graduated in 1901 with an MA and subsequently taught at several schools over the next 7 years. He maintained his interest in mathematics and received an award for one paper that he submitted to the University of Copenhagen.

He was a member of the Danish Mathematicians' Association and through this met amateur mathematician Johan Jensen, the Chief Engineer of the Copenhagen Telephone Company, an offshoot of the International Bell Telephone Company. Erlang subsequently obtained employment with the company in 1908. He worked for the Copenhagen Telephone Company for almost 20 years, until his death after an abdominal operation.

It was while working for the Copenhagen Telephone Company that Erlang was presented with the classic problem of determining how many circuits were needed to provide an acceptable telephone service. However, his thinking went further in that he also realised that mathematics could be applied to assess how many operators were needed to handle a given volume of telephone calls. At that time most telephone exchanges used human operators and cord boards to switch telephone calls by means of jack plugs.

Out of necessity, Erlang was a hands-on researcher. He would conduct his own measurements and was prepared to climb into street manholes to do so.

Erlang was also an expert in both the history and calculation of the numerical tables of mathematical functions, particularly logarithms. He devised new calculation methods for certain forms of mathematical tables.

He developed his theory concerning telephone traffic over several years. His significant publications include:

- In 1909 - "The Theory of Probabilities and Telephone Conversations" - which proves that the Poisson distribution applies to random telephone traffic.
- In 1917 - "Solution of some Problems in the Theory of Probabilities of Significance in Automatic Telephone Exchanges" - which contains his classic formulae for loss and waiting time.

The British Post Office accepted his formula as the basis for calculating circuit facilities.

He was an associate of the British Institution of Electrical Engineers.

The unit of communication activity in these fields is now known as the erlang, in recognition of his achievements.

Ericsson Communications has also named the Erlang programming language, a programming language for large industrial real-time systems, in his honour.

His name is also given to the statistical probability distribution that arises from his work.

See also:

- Erlang programming language
- Erlang unit
- Erlang distribution
- Queueing theory
- Telecommunications traffic engineering.

- Biography - from St.Andrews University
- Biography - from Millennium Mathematics Project
- Erlang Distribution
- An Introduction to Erlang B and Erlang C by Ian Angus (PDF Document - Has terms and formulae plus biography)