# Euler's mathematical functions replicated using modern technology

## Euler's mathematical functions replicated using modern technology

Leonhard Euler (15 April 1707 – 18 September 1783) was a Swiss mathematician who made important and influential contributions to calculus, graph theory, number theory, and applied mathematics. He was also interested in how mathematics could be applied to music.

Drawing on both his musical training and mathematical knowledge, Euler published the book *Tentamen*, in Latin, in 1739, describing a new theory of music explained through well-founded mathematical principles of harmony.

277 years later, Professor David De Roure has reproduced Euler's results using contemporary computer algebra techniques, successfully confirming Euler's manual calculations (and identifying one omitted number).

Euler's "suavitatis gradus" function is now published in the On-line Encylopedia of Integer Sequences as sequence A275314 where it is defined in terms of other fundamental sequences.

The gradus function is used in calculation of musical consonance, and is one of the mathematical ideas that would have been available to Ada Lovelace and Charles Babbage - it is now being utilised in the Centre's Numbers Into Notes software.