1791 in science
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- Jean Baptiste François Pierre Bulliard begins publication of Histoire des champignons de la France, a significant text in mycology.
- Luigi Galvani publishes his discoveries in "animal electricity" (Galvanism).
- Nicolas Leblanc patents the Leblanc process for the production of soda ash (sodium carbonate) from common salt (sodium chloride).
- The element Titanium is discovered included in ilmenite in Cornwall, England, by local amateur geologist Rev. William Gregor.
- March – In France, the National Constituent Assembly accepts the recommendation of its Commission of Weights and Measures that the nation should adopt the metric system.
- Pierre Prévost shows that all bodies radiate heat, no matter how hot or cold they are.
- Sir John Sinclair's Statistical Account of Scotland begins publication, introducing the term Statistics into English.
- March 20 – John Farey, English mechanical engineer and technical writer (died 1851)
- April 9 – George Peacock, English mathematician (died 1858)
- April 27 – Samuel F. B. Morse, American inventor (died 1872)
- July 13 – Allan Cunningham, English botanist and explorer (died 1839)
- September 4 – Robert Knox, Scottish anatomist (died 1862)
- September 22 – Michael Faraday, English chemist and physicist (died 1867)
- September 23 – Johann Franz Encke, German astronomer (died 1865)
- December 26 – Charles Babbage, English mathematician and inventor of computing machines (died 1871)
- In the treatise "De viribus electricitatis in motu musculari commentarius" ("Commentary on the Force of Electricity on Muscular Motion") published in the proceedings of the Institute of Sciences at Bologna (vol. 7) and separately at Modena the following year.
- Reported to the Royal Geological Society of Cornwall and in Crell's Annalen. Emsley, John (2001). "Titanium". Nature's Building Blocks: An A-Z Guide to the Elements. Oxford University Press. p. 452. ISBN 0-19-850340-7.
- British patent no. 1825.
- Ball, Philip (2004). Critical Mass. Farrar, Straus & Giroux. p. 53. ISBN 0-374-53041-6.