- September 9 – Nicolas Bernoulli first describes the St. Petersburg paradox in a letter to Pierre Raymond de Montmort.
- November 13 – James Waldegrave provides the first known minimax mixed strategy solution to a two-person game, in a letter to de Montmort.
- Jacob Bernoulli's best known work, Ars Conjectandi (The Art of Conjecture), is published posthumously by his nephew. It contains a mathematical proof of the law of large numbers, the Bernoulli numbers, and other important research in probability theory and enumeration.
- March 15 – Nicolas Louis de Lacaille, French astronomer (baptized December 28; died 1762)
- May 3 – Alexis Claude Clairaut, French mathematician (died 1765)
- May 25 – John Stuart, Lord Mount Stuart, Scottish politician and botanist (died 1792)
- September 10 – John Needham, English biologist (died 1781)
- Anthony Addington, English physician (died 1790)
- Jean Paul de Gua de Malves, French mathematician (died 1785)
- April 29 (bur.) – Francis Hauksbee, English scientific instrument maker and experimentalist (born 1660)
- April (end) – Edmund Dummer, English naval engineer (born 1651)
- July 7 – Henry Compton, English bishop and botanist (born 1632)
- August 26 (bur.) – Denis Papin, French-born physicist, mathematician and inventor (born 1647)
- October 20 – Archibald Pitcairne, Scottish physician (born 1652)