Samuel Pepys lived during a very exciting time for many scientific fields, and mathematics was no exception. Consider that Isaac Newton, one of the giants in the field, was a contemporary and compatriot of Pepys, and you’ll get an idea of the strides being made at the time, as Classical scientific and mathematical concepts that had held sway for many centuries were being challenged and swept away.
Besides Newton, other notable English mathematicians of the time included Robert Boyle, John Collins, Jonas Moore, and John Wallis, all of whom Pepys knew through their association with The Royal Society (Pepys was president from 1684 to 1686).
Sam’s education, which was classically Classical in nature, did not focus on mathematics beyond the simplest of concepts. Though he was well able to keep his own and his lord’s accounts, it wasn’t until he entered the Navy Office that he realized he needed to learn higher forms of math, and so began receiving instruction from one-eyed, hard-drinking sailing master Richard Cooper, being introduced to the multiplication tables by him on 4 July 1662. The knowledge he gained from Cooper, combined with the knowledge gained from master shipbuilder Anthony Deane in measuring timber, enabled Sam to ferret out corruption and serve Charles II well. The Diary entry of 7 August 1663 is a good example of Sam flexing his new-found skills and tools.
One such tool was the slide rule. In 1663, he worked with “mathematical instrument maker” John Brown to design a custom-made rule, which Pepys called the “most useful that ever was made, and myself have the honour of being as it were the inventor of this form of it.”
Early in the Diary, after bringing the King back from Holland, Sam tells of a seaside ride with Edward “My Lord” Montagu and several companions during which the group laid wagers on the height of “a very high cliff by the sea-side.” Montagu “made a pretty good measure of it with two sticks, and found it to be not above thirty-five yards high,” losing the wager for himself, and winning it for Pepys, who had said the cliff was not as tall as St. Paul’s Cathedral, which Pepys said was “reckoned to be about ninety” yards high. How was Montagu able to do this without the aid of the modern devices we normally use for such tasks? Grahamt has a good explanation of it here.
The need to measure things accurately pops up again and again in the Diary, including the entry of 9 June 1663, where Pepys recalls a conversation with friendly rival John Creed about “a way found out by Mr. Jonas Moore” called “duodecimall arithmetique, which is properly applied to measuring, where all is ordered by inches, which are 12 in a foot, which I have a mind to learn.” This system of measuring things by twelves rather than tens (as in the decimal system) solved many problems in a system dominated by 12 inches to a foot. More on the duodecimal system can be found here.
Even more discussion on the system, as well as information about other mathematical figures (ahem) and concepts covered thus far in the Diary, can be found below.