The corresponding accountant, the man who invented π and the Earls of Macclesfield.

I recently stumbled over an exciting piece of news for all historians of the mathematics of the seventeenth century, Jackie Stedall and Philip Beeley have received a grant from the AHRC to edit and publish the correspondence of the English mathematician John Collins (1625 – 1683). Now anybody who is not up on the obscure aspects of seventeenth century mathematics is probably thinking who is John Collins and why should the publication of his correspondence be a reason to celebrate?

In the Early Modern Period before the advent of academic journals European scholars did not live in splendid isolation but spread, discussed and criticised each others newest thoughts by post. There existed a vast interlocking web of correspondence networks linking up the scholars in much the same way as the Internet does today but at a somewhat more leisurely pace.

The letters that scholars exchanged were often long detailed texts on their current research, resembling more a scientific paper than a conventional letter. These were also not private letters but were often conceived to be copied by the recipient and sent on by him to other interested parties in his own network. An early modern form of re-blogging or re-tweeting. Some scholar’s networks were so extensive that they are now referred to as ‘post offices’.  The most well known example of an early modern ‘post office’ is the French Minim Friar Marin Mersenne who appeared to be the hub around which the European scientific community revolved. He is particularly renowned for having championed Galileo’s physics. When he died letters from 79 different scientific correspondents were found in his monk’s cell in Paris. Even Mersenne’s prolific letter writing activities were over shadowed by another acolyte of Galileo, Mersenne’s countryman, Nicolas-Claude Fabri de Peiresc. We still have 10 000 of Peiresc’s letters.

Another European ‘post office’ was the German Jesuit professor of mathematics at the Collegio Romano, Athanasius Kircher. Kircher collected astronomical observations and other scientific information from all over the world and redistributed it to all of the leading astronomers of Europe, both Jesuit and non-Jesuit.

In England the first secretary of the Royal Society, Henry Oldenburg, also maintained a continent wide network of correspondents. In fact the contents of the early editions of the Philosophical Transactions, which Oldenburg started as a private enterprise to supplement his salary, consisted largely of letters of , often dubious, scientific merit from Oldenburg’s correspondents. His extensive foreign correspondence led to him, a German, being arrested and incarcerated on suspicion of being a spy for a time during the second Anglo-Dutch War in 1667. As we shall see John Collins came to serve as an assistant to Oldenburg dealing with the mathematical correspondence.

Collins, the son of an impoverished nonconformist minister, was born in Wood Eaton near Oxford in 1626. Unable to afford an advanced education he was apprenticed to the bookseller Thomas Allam. After Allam went bankrupt he became junior clerk under John Marr, clerk to the kitchens of the Prince of Wales, the future Charles II. Marr was an excellent mathematician and sundial maker and it was from him that Collin’s almost certainly received his mathematical education. During the civil war (1642 – 1649) he went to sea serving on an English merchantman engaged as a man-of-war in Venetian service. During this time he learnt navigation and taught himself accounting, mathematics and Latin.

Upon his return to England he earned his living in various positions as an accountant and began to develop a network of correspondents to acquire books and mathematical news. In 1667 Collins was elected to the Royal Society and for the next ten years he served the society as an unofficial secretary for matters mathematical. In this role he corresponded with most of the eminent mathematicians of Europe including Isaac Barrow (who christened him Mersennus Anglus), James Gregory, Christiaan Huygens, Gottfried Leibniz, John Pell, René de Sluze, Ehrenfried Tschirnhaus and possibly most important of all Isaac Newton. In fact it was Collins who outted, the then unknown, young Newton and dragged him out of his Cambridge seclusion into the seventeenth century mathematical community.

In 1669 Collins sent a new publication on analysis by Mercator (that’s Nicolaus the seventeenth century German mathematician and engineer not to be confused with Gerard the sixteenth century Dutch cartographer) to Isaac Barrow, then still the Lucasian professor of mathematics in Cambridge. Barrow responded by saying that he had a young colleague whose own work on the subject was far superior to Mercator’s. Collins thus obtained from Barrow a manuscript of Newton’s De analysi per aequationes numero terminorum infinitas (On Analysis by Infinite Series), which he proceeded to copy and distribute to a large number of European mathematicians including Leibniz. Thus making the world aware of the fact that there was a world-class mathematician in Cambridge and inadvertently igniting a slow fuse to the most notorious priority and plagiarism dispute in the history of mathematics.

Collins was also involved in the publishing business seeing several important mathematical and scientific works through the press: Thomas Salusbury’s Mathematical Collection (1661 – 1665), (including his translations of Galileo into English, which were also used by Newton), Isaac Barrow’s Lectiones opticae (1669) (prepared for publication by Newton), Lectiones geometricae (1670) and Archimedes (1675); John Wallis’ Mechanica (1669 –1671) and Algebra (1685); Jeremiah Horrocks’ Opera posthuma (1672 – 8); and others.

Collins was not a particularly skilled mathematician being more of a mathematical practitioner than a mathematician in the modern sense. He wrote and published works on accounting, surveying, navigating and dialling (the design and construction of sundials). He also wrote on the subject of trade.

Collins, who can best be described as a maths groupie, collected an extensive library of mathematical books and papers alongside his widespread correspondence. In the seventeenth century there was not the interest in papers and libraries of the deceased that exists today and there was a risk that Collins’ collection might have been dispersed after his death in 1683, enter William Jones.

William Jones, who was born on Anglesey in about 1675; was like Collins the son of an impoverished family with no prospects of an advanced education. However a local landowner recognised his mathematical talents and arranged a position for him at a London merchant’s counting house. He was sent by his employers to the West Indies and thus acquired a liking for the sea. From 1695 to 1702 he served as mathematics master on a man-of-war. Settling in London he became a private mathematics tutor publishing a book on navigation in 1702. In 1706 he published a textbook on the new calculus Synopsis palmarioum matheseos, or, A New Introduction to the Mathematics, which was the first book to include π as the ratio between the circumference and diameter of a circle; an honour often falsely attributed to Euler. William Oughtred had earlier used π to designate just the circumference. This publication probably first brought Jones into Newton’s inner circle.

In 1708 Jones bought up Collins’ collection of mathematical books, papers and letters. In 1711 he was elected to the Royal Society and appointed to the committee set up at the request of Leibniz to investigate the charges of plagiarism that had been made against him with respect to the invention of the calculus by Newton’s acolyte John Keill. Together with Newton, who should not have been involved at all being one of the disputing parties, Jones put together the Commercium  epistolicum (1712), which largely consisted of letters and papers from Collins’ collection and which, not unsurprisingly, found for Newton and against Leibniz. It did in fact contain a genuine smoking gun, the proof that Leibniz had received a copy of De analysi per aequationes numero terminorum infinitas from Collins, whereas Leibniz had always claimed to have had no knowledge of Newton’s early work.

Jones continued to work closely with Newton, acting as go between when relations became strained between Newton and Roger Cotes, when they were working on the second edition of Principia, and editing and publishing various of Newton’s other works.

Jones continued to earn his living as a private tutor and served for a time as mathematics teacher to Philip Yorke who would go on to become Lord Chancellor and the Earl of Hardwick. Through Yorke he was introduced to Lord Chief Justice Parker, who would become the first Earl of Macclesfield, and become tutor to his son George.

Involved in a political scandal Thomas Parker, who incidentally was one of Newton’s pallbearers, withdrew from public life and retired to his countryseat Shirburn Castle where Jones effectively became a member of the household. Parker was a great collector of books and built up a very impressive library. Meanwhile Jones continued to increase the Collins collection of mathematical books and papers.

Jones’ pupil George Parker, the second Earl of Macclesfield, was an avid amateur natural philosopher and astronomer, who added an observatory and a chemical laboratory to Shirburn Castle. In his role as a member of parliament he was instrumental in dragging Britain out of the Middle Ages and into the modern world by introducing the Gregorian calendar in 1752, two centuries after its adoption by Catholic Europe.

When he died Jones bequeathed the Collins-Jones mathematical collection to George Parker and it resided in the Shirburn Castle library for more than two hundred years largely inaccessible to historians. The astronomer and historian of mathematics Stephen Rigaud was granted access to Collins’ collection of letters and published some of them in his Correspondence of scientific men of the seventeenth century: including letters of Barrow, Flamsteed, Wallis, and Newton, printed from the originals in the collection of the Right Honourable the Earl of Macclesfield in 1841. The Macclesfield’s dissolved their priceless library at the beginning of the last decade, selling the scientific papers and letters to Cambridge University and the books by public auction. The three substantial volumes of the sales catalogue dealing with the mathematics books are themselves an invaluable history of mathematics resource (I know because a friend of mine owns them and I’m allowed to use them). That Collins’ letters collection is now going to receive the scholarly treatment it deserves is good news indeed for all historians of the seventeenth century and not just those of science or mathematics.