In his mid-life, Arbuthnot, complaining of the work of
Edmund Curll, among others, who commissioned and invented a biography as soon as an author died, said, "Biography is one of the new terrors of death," and so a biography of Arbuthnot is made difficult by his own reluctance to leave records.
Alexander Pope noted to
Joseph Spence that Arbuthnot allowed his infant children to play with, and even burn, his writings. Throughout his professional life, Arbuthnot exhibited a strong humility and social conviviality, and his friends often complained that he did not take sufficient credit for his own work. Arbuthnot was born in
Arbuthnot,
Kincardineshire, on the north-eastern coast of Scotland, son of Margaret (née Lammie) and Rev Alexander Arbuthnot, an
Episcopalian priest. He may have graduated with an arts degree from
Marischal College in 1685. Where Arbuthnot's brothers took part in
Jacobite causes in 1689, he remained with his father. These brothers included Robert, who fled after fighting for
King James VII in 1689 and became a banker in
Rouen and half-brother George, who fled to France and became a wine merchant. However, when
William and Mary came to the throne and the Scottish and English parliaments required all ministers to swear allegiance to them as king and queen, Arbuthnot's father did not comply. As a
non-juror, he was removed from his church, and John was there to take care of affairs when, in 1691, his father died. Arbuthnot went to
London in 1691, where he is supposed to have supported himself by teaching mathematics (which had been his formal course of study). He lodged with William Pate, whom Swift knew and called a "
bel esprit". He published
Of the Laws of Chance in 1692, translated from
Christiaan Huygens's
De ratiociniis in ludo aleae. This was the first work on probability published in English. The work, which applied the field of
probability to common games, was a success, and Arbuthnot became the private tutor of one Edward Jeffreys, son of Jeffrey Jeffreys, an
MP. He remained Jeffreys's tutor when the latter attended
University College, Oxford in 1694, and he there met the variety of scholars then teaching mathematics and medicine, including Dr
John Radcliffe,
Isaac Newton, and
Samuel Pepys. However, Arbuthnot lacked the money to be a full-time student and was already well educated, although informally. He went to the
University of St Andrews and enrolled as a doctoral student in
medicine on 11 September 1696. The
very same day he defended seven theses on medicine and was awarded the doctorate. He first wrote
satire in 1697, when he answered Dr
John Woodward's
An essay towards a natural history of the earth and terrestrial bodies, especially minerals... with ''An Examination of Dr Woodward's Account &c.'' He poked fun at the arrogance of the work and Woodward's misguided,
Aristotelian insistence that what is theoretically attractive must be actually true. In 1701, Arbuthnot wrote another mathematical work,
An essay on the usefulness of mathematical learning, in a letter from a gentleman in the city to his friend in Oxford. The work was moderately successful, and Arbuthnot praises mathematics as a method of freeing the mind from
superstition. In 1702, he was at
Epsom when
Prince George of Denmark, husband of
Queen Anne fell ill. According to tradition, Arbuthnot treated the prince successfully. According to tradition again, this treatment earned him an invitation to court. Also around 1702, he married Margaret, whose maiden name is possibly Wemyss. Although there are no baptismal records, it seems that his first son, George (named in honour of the prince), was born in 1703. He was elected to be a Fellow of the
Royal Society in 1704. Also thanks to the Queen's presence, he was made an MD at
Cambridge University on 16 April 1705. Arbuthnot was an amiable individual, and Swift said that the only fault an enemy could lay upon him was a slight waddle in his walk. His conviviality and his royal connections made him an important figure in the Royal Society. In 1705, Arbuthnot became physician extraordinary to Queen Anne, and at the same time was put on the board trying to publish the
Historia coelestius. Newton and
Edmund Halley wanted it published immediately, to support their work on orbits, while
John Flamsteed, the Royal Astronomer whose observations they were, wanted to keep the data secret until he had perfected it. The result was that Arbuthnot used his leverage as friend and physician to Prince George, whose money was paying for the publication, to force Flamsteed to allow it out, albeit with serious errors, in 1712. Also as a scholar, Arbuthnot took up an interest in antiquities and published
Tables of Grecian, Roman, and Jewish measures, weights and coins; reduced to the English standard in 1705, 1707, 1709, and, expanded with a preface (which indicated that his second son, Charles, was born in 1705), in 1727 and 1747. Although Arbuthnot was not a
Jacobite after the fashion of his brothers, he was a
Tory, for national and familial reasons. Anne was advised (and many said controlled) by
Sarah Churchill, Duchess of Marlborough, who was a champion of
Whig causes. In 1706, the Duchess of Marlborough fell out with Anne—a
schism which the Tories were pleased to encourage. The marriage of lady-in-waiting Abigail Hill to
Samuel Masham, which was the first overt sign of Anne's displeasure with Sarah Churchill, took place in Arbuthnot's apartments at
St James's Palace. The reasons for the choice of apartment and the degree of involvement of Arbuthnot in either the love match or Anne's estrangement, are not clear. As a Scotsman, Arbuthnot served the crown by writing ''A sermon preach'd to the people at the Mercat Cross of Edinborough on the subject of the union. Ecclesiastes, Chapter 10, Verse 27.'' The work was designed to persuade Scots to accept the
Act of Union. When the Act passed, Arbuthnot was made a fellow of the Royal College of Physicians of Edinburgh. He was also made a
physician in ordinary to the Queen, which made him part of the
royal household. Arbuthnot returned to mathematics in 1710 with
An argument for Divine Providence, taken from the constant regularity observed in the births of both sexes (linked below) in the Royal Society's
Philosophical Transactions. In this paper, Arbuthnot examined birth records in London for each of the 82 years from 1629 to 1710 and the
human sex ratio at birth: in every year, the number of males born in London exceeded the number of females. If the probability of male and female birth were equal, the probability of the observed outcome would be 1/282. This vanishingly small number led Arbuthnot to believe that this phenomenon was not due to chance, but to divine providence: "From whence it follows, that it is Art, not Chance, that governs." This paper was a landmark in the
history of statistics; in modern terms he performed
statistical hypothesis testing, computing the
p-value (via a
sign test), interpreted it as
statistical significance, and rejected the
null hypothesis. This is credited as "… the first use of significance tests …", the first example of reasoning about statistical significance and moral certainty, ==As a Scriblerian==