1720 in science
- May – First patient admitted to the Westminster Public Infirmary, predecessor of St George's Hospital, London.
- Dr Steevens' Hospital is established at Kilmainham, Dublin.
- Great Plague of Marseille, the last major outbreak of bubonic plague in Europe.
- Willem 's Gravesande publishes Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam, an introduction to Newtonian physics, in Leiden.
- A theodolite is developed by Jonathan Sisson of England.
- Pinchbeck is invented by English watchmaker Christopher Pinchbeck; it is an alloy of 83% copper and 17% zinc, creating a strong, hard-wearing metal which has the appearance and weight of 20 carat gold.
- An early chronograph is invented which has only mechanical parts in it.
- Henry de Saumarez (of the Channel Islands) produces an instrument called the Marine Surveyor intended to measure a ship's velocity.
- A single-action five-pedal harp is developed by Jacob Hochbrucker of Bavaria which can raise the pitch of the selected strings by a half step.
- approx. date – Joseph Williamson uses a differential gear in a clock.
- March 13 – Charles Bonnet, Swiss naturalist and philosophical writer (died 1793)
- July 18 – Gilbert White, English naturalist (died 1793)
- October 8 – Geneviève Thiroux d'Arconville, French novelist, translator and chemist (d. 1805)
- December ? – James Hargreaves, English inventor (died 1778)
- approx. date – Dmitry Ivanovich Vinogradov, Russian chemist (died 1758)
- December 29 – Maria Margarethe Kirch, German astronomer (born 1670)
- David Gregory, Scottish physician and inventor (born 1625)