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Geophysics

• May 23 – Volcanic eruption in the Santorini caldera begins.
• October 28 – The Hōei earthquake ruptures all segments of the Nankai megathrust simultaneously – the only earthquake known to have done this. It is the most powerful in Japan until 2011, with an estimated local magnitude of 8.6.
• December 16 – Hōei eruption, the last eruption of Mount Fuji in Japan, begins.

Mathematics

• Publication of Arithmetica universalis, the collected works of Isaac Newton on algebra.
• Abraham de Moivre derives de Moivre's formula.

Medicine

• John Floyer, in The Physician's Pulse Watch, introduces counting of pulse rate during one minute.
• Giovanni Maria Lancisi publishes De Subitaneis Mortibus (On Sudden Death), an early work in cardiology.
• Georg Ernst Stahl publishes Theoria medica vera: physiologiam & pathologiam.

Births

• January 11 – Vincenzo Riccati, Italian mathematician (died 1775)
• April 10 – John Pringle, Scottish physician (died 1782)
• April 15 – Leonhard Euler, Swiss mathematician (died 1783)
• April 26 – Johannes Burman, Dutch botanist (died 1780)
• May 23 – Carl Linnaeus, Swedish naturalist (died 1778)
• June 22 (bapt.) – Elizabeth Blackwell, Scottish-born botanical illustrator (died 1758)
• September 7 – Georges-Louis Leclerc, Comte de Buffon, French naturalist (died 1788)
• December 22 – Johann Amman, Swiss-Russian botanist (died 1741)
• date unknown – Benjamin Robins, English scientist and engineer (died 1751)

Deaths

• March 30 – Marquis de Vauban, French military engineer (born 1633)
• Maria Clara Eimmart, German astronomer, engraver and designer (born 1676)