Composer: Peter Gregson

Performed by: the Infinity Choir, especially convened to record this composition.

Location: This piece and its historical context are closely linked with Emmanuel College, University of Cambridge.

This is a mix of 'Infinity' by Peter Gregson, recorded by Historyworks:


"Even we, that have our eyesight, can yet with more advantage apply our memory by night, in the dark, when all things are quiet; than by day, when sights and noises are apt to divert our thoughts." 

John Wallis, 'Arithmetica infinitorum' (1656).

Historical Context:

John Wallis was a gifted mathematician who lived between 1616 and 1703 and enrolled at Emmanuel College, University of Cambridge, at the age of just fifteen. Whilst studying from 1632 to 1640, Wallis read medicine, anatomy, and mathematics. He wrote a large number of mathematical, theological, and linguistic works and is known for his introduction and popularisation of the infinity symbol, commonly used in mathematics today.

In his work Arithmetica infinitorum (1655), he described a line as being made up of many small points that go on forever, in this case going on until infinity. This work on the infinitesimal quantity laid the foundations for the founding of infinitesimal calculus by Leibniz and Newton in the 1660s. Notable for his astonishing mental arithmetic ability, it was regular behaviour for Wallis to solve square roots before he fell asleep. 

On the night of 18 February 1671, exhausted by a year-long illness and alone in his bed, he began to test how big a number he could calculate the square root of in his head. Initially trying smaller numbers and succeeding, Wallis required a greater challenge.  A friend then suggested that Wallis calculate something large, leading him to try to square root a fifty-three digit number. Two days later, he recited the square root to 27 places from memory to his friend. However, after this feat of mental arithmetic, Wallis felt he couldn’t do any better and didn’t attempt any further large number calculations.

Image courtesy of the University of Cambridge.

To find out more about the history that has inspired this composition and its lyrics you can visit the Historyworks website.

Click on the film link below to access a fun film showing the route and the process of the Cycle of Songs journey:

Draft Score for Infinity can be found here

Piano reduction for Infinity Score: 

Soprano 1

Soprano 2

Soprano 3

Alto 1

Alto 2



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