The Palpable Scholar

When William Whiston was fired from his position as the Lucasian Professor of Mathematics at the University of Cambridge in 1710, selecting a suitable replacement was hardly a simple matter. First established in 1663, the Lucasian Chair had already been held by some of the most eminent mathematicians in history, including Isaac Newton. The competition came down to two brilliant candidates, Nicholas Saunderson and Christopher Hussey though it would be Saunderson who won the vote to claim the position. In considering Saunderson at all, the Regents who selected him had to deal with two rather remarkable stumbling blocks. Not only did Saunderson have no academic degrees as such, he was also completely blind.

Born in Yorkshire in 1682, Nicholas Saunderson lost his sight as an infant due to smallpox. Not only did the disease leave him blind but his eyes needed to be removed as well. Practical programs for teaching blind children would not be developed for centuries though Saunderson's teachers managed to teach him to read and write by some unorthodox methods. According to one story, he learned his letters by tracing his fingers along the tombstones in a nearby cemetery.

The lack of any formal educational system for blind students meant that Nicholas Saunderson was forced to develop his own personal methods for learning. That included having friends read his textbooks to him since he could not read on his own (Braille would not be developed until the 19th century). Despite these barriers, he was an excellent student who became fluent in French, Latin and Greek as well as developing a special affinity for mathematics. In his spare time, he also became a skilled musician and gave performances with a flute. Since no university program could accomodate a blind student back then, he was largely educated at home after finishing his studies at the local free school. He was only able to continue with his mathematics training with the help of a mathematician friend, William West, who instructed him in algebra and geometry with his friends still reading the advanced textbooks to him.

By 1707, Saunderson became a good enough mathematician for his friends to encourage him to go to the University of Cambridge to continue his education. Unfortunately, his blindness and lack of funding kept him from registering though William Whiston was impressed enough by his ability to allow him to become a lecturer. Despite his lack of formal degrees, Nicholas Saunderson was an excellent teacher and his lectures were always extremely popular. He also began making his own original contributions to mathematics and became friends with some of the greatest mathematicians of his time, including Isaac Newton and Edmund Halley.

Essentially, he invented an entire new system he termed "palpable arithmetic" which involved developing his own tactile aid to examine mathematical concepts by touch alone. Using a specially-constructed "calculating table", basically a large pegboard allowing him to insert pegs and squares as needed, he could carry out complex arithmetic problems by touch. For problems in geometry, he used strings tied between pegs to represent geometric figures allowing him to work out complex mathematical problems on his own. By running his fingers over the board and changing the pegs and strings as needed, he was able to explore abstract concepts in fields as diverse as algebra, geometry and optics.

When Saunderson was chosen to replace Whiston in 1710, Queen Anne solved the problem of his lack of credentials by making him a Master of Arts. He was appointed to the Lucasian chair on the very next day and would spent the rest of his professional career at Cambridge. Ironically, while Whiston had been fired for his bizarre religious ideas, his successor was openly agnostic. He also had the good political sense his predecessor lacked. Despite his continuing needs for assistants to help him with written material, Saunderson maintained a heavy workload, including seven to eight hours a day of lecturing. He also became legendary for his ability to use his remaining senses in ways that seemed superhuman. According to one source, he could not only use sound to judge the size of a room and his location from the walls, but he also once "... distinguished in a set of Roman medals the genuine from the false, though they had ... deceived a connoisseur who had judged by eye."

As his recognition grew, so did the honours that was conferred on him. He became a Fellow of the Royal Society in 1719 and King George II personally travelled to Cambridge to meet Saunderson and to confer the LLD title on him in 1728. By then, he was already in failing health and his colleagues pressured him to write a book based on his lectures. As his health allowed, he managed to complete a two-volume work titled, Elements of Algebra, though he became ill with scurvy before the book could be completed. Whether the scurvy was due to his neglecting his own health or not, Nicholas Sauderson died on April 19, 1739 and his book was only published after his death.

While Elements of Algebra was the only book he wrote in his lifetime, Saunderson also left behind an enormous amount of material on differential and integral calculus which his son, John, later edited into a second book. Published in 1759, the book's full title was The Method of fluxions applied to a Select Number of Useful Problems, together with the Demonstration of Mr Cotes's forms of Fluents in the second part of his Logometria, the Analysis of the Problems in his Scholium Generale, and an Explanation of the Principal Propositions of Sir Isaac Newton's Philosophy (usually just called The Method of Fluxions for short).

Despite the example provided by Nicholas Saunderson and other blind scholars, special education for blind children would not be available for centuries except for whatever educators could improvise on their own. Certainly Saunderson's "palpable arithmetic" was never adopted by anyone except himself though it represents an ingenious way of getting around his inability to see. Along with his legacy as an educator and a mathematician, Nicholas Saunderson's life as a blind man helped combat rigid attitudes that often regarded blind people as having no value to society.

In his 1749 work, The Letter on the Blind for the Benefit of Those Who See, Denis Diderot devoted considerable attention to Nicholas Saunderson and his methods for overcoming blindness. Along with describing Saunderson's palpable arithmetic, including how his "calculating table" worked, Diderot discussed the different strategies Saunderson used to integrate himself into sighted society. Many of these strategies are similar to ones used by visually impaired people even today. Diderot's work represents one of the first true explorations of the psychology underlying blindness though it was primarily meant as a philosophical exercise (and which got him in trouble with government censors).

It may have have helped inspire the rise of the first true school for blind children in France in 1784. Though often underfunded, the school would slowly transform blind education and one of its students, Louis Braille, would also develop the tactile reading system that now bears his name. As the Braille system became used around the world and blind students began entering universities, many of the attitudes that had barred Nicholas Saunderson from being a university student would be overcome.

As one final note on the amazing legacy left behind by Nicholas Saunderson, a play based on his life opened in 2006. Written by a teacher living in the town where Saunderson was born and educated, the play provided modern audiences a glimpse into the life of this remarkable scholar. Still regarded as local celebrity, a local residential street and the science wing of the local grammar school all bear his name.