Studied at Marischal College, Aberdeen, then took a medical degree at the University of St Andrews graduating in 1696. He translated Huygens' tract on probability in 1692 and extended it by adding to it a few further games of chance. This was the first work on probability published in English. Arbuthnot went to London and gave lessons in mathematics. Around this time (1700) he published Essay towards a natural history of the Earth and Essay on the usefulness of mathematical learning. He was elected a Fellow of the Royal Society in 1704.
In 1705 he was appointed physician to Queen Anne. He continued his scientific work submitting a paper to the Royal Society in 1710 discussing the slight excess of male births over female births. This paper is perhaps the first application of probability to social statistics. In this paper he claims to demonstrate that divine providence, not chance, governs the sex ratio at birth.
Arbuthnot's main fame is on his reputation as a wit and on his satirical writings. With Alexander Pope, Jonathan Swift, John Gay and Thomas Parnell he founded the Scriblerus Club in 1714, whose purpose was to satirise bad poetry and pedantry. The club was short-lived.
After Queen Anne died, despite Arbuthnot attending her in her final illness, he went to France for a while. He then returned to England to become a physician to other important people.
In addition to satirical works he also published some serious medical work in his last few years.