16th-Century Mathematician Invented Logarithms

Prof. Enrique Gonzalez-Velasco Image by Edwin L. Aguirre
Prof. Enrique González-Velasco

By Edwin L. Aguirre

Math Prof. Enrique González-Velasco believes you can learn a lot about math by looking at its roots. His latest scholarly work takes a deep dive into the contributions of the influential mathematician John Napier, who is credited with inventing logarithms and bringing the decimal point into common use.

González-Velasco co-authored “The Life and Works of John Napier” with Brian Rice of Horsham, West Sussex, and Alexander Corrigan of the University of Edinburgh’s School of Divinity, both in the U.K. The 994-page book was published by Springer earlier this year.

González-Velasco, who holds doctorates in applied mathematics and telecommunications engineering from Brown University and Spain’s Polytechnic University of Madrid, respectively, joined the UMass Lowell faculty in 1977. Here, he shares some insights into his work.

Q: Who is John Napier and why is he an important figure in mathematics?

A: John Napier of Merchiston was a Scottish theologian and mathematician who is best known for his invention of logarithms, which are a convenient way of computing with large numbers. By greatly reducing the time and improving the accuracy of such laborious computations, he provided astronomers, navigators, scientists, engineers, surveyors and actuaries with an indispensable tool to advance their work.

Napier is also renowned, among many others, for inventing “Napier’s Bones,” the world’s first practical, manually operated calculator, and for making common the use of the decimal point in arithmetic and mathematics. He also invented two other calculating devices to simplify computations – the chessboard abacus and the Promptuary for multiplication.

John Napier Image by Edinburgh Napier University
John Napier (1550–1617)

Q: What inspired you to write about Napier and his works?

A: It wasn’t so much as inspiration but it was a direct request from Brian Rice, who is a descendant of Napier, that motivated me to collaborate on this project. Noticing that 2017 marks the 400th anniversary of Napier’s death – on April 4 – Brian approached me and Alex, asking us to prepare a volume containing the complete works of Napier, plus several explanatory introductions and appendices.

Q: Why were you chosen to co-author the book?

A: Brian chose me because he was familiar with my previous book, “Journey through Mathematics: Creative Episodes in its History,” which was published in 2011, also by Springer. The book’s second chapter is devoted to the history of logarithms. I became extremely interested and enthusiastic about the Napier project and, after completing my chapter on “Mathematical Introduction,” I took the text of Napier’s mathematical works by copying and pasting from modern and old translations. Then I started on typesetting most of the 994 pages of the volume, all but pages 99 to 390, formatting the pages, fonts and symbols in the style of the Latin originals. I think the final result is a beauty.

Q: What is special about this work?

A: The book brings together for the first time all of Napier’s works into a single volume in English. Napier’s four mathematical works were originally published in Latin: two during his lifetime [1550–1617], one shortly after he died and one over 200 years later.

The book also contains many new findings about Napier’s life to provide the most complete biography of this enigmatic character, whose reputation has previously been overshadowed by rumor and speculation. As Brian has pointed out, “Mark Napier’s ‘Memoirs of John Napier of Merchiston,’ published in 1834 and generally considered the standard work on Napier, is not as objective a work as one might suppose. The common view of Napier – often seen on the internet and in some books as a warlock, sorcerer or necromancer – is also largely due to Mark Napier and it was our intention to rectify this.”

Q: What are you like as a teacher?

A: I don’t know what I can say about myself as a teacher. I’ve been doing it for 49 years, and I always try to do my best. My own opinion is that I succeed most of the time, but I must admit that I am demanding, which is the only way to have the students learn the most they can.