1845 in science
- January 14 – Physikalische Gesellschaft zu Berlin established and begins publishing Fortschritte der Physik and Verhandlungen.
- August 28 – The journal Scientific American begins publication.
- Alexander von Humboldt's Kosmos: Entwurf einer physischen Weltbeschreibung begins publication.
- April – Lord Rosse discovers that the nebula M51 has a spiral structure.
- September–October – Cornish mathematician John Couch Adams communicates to James Challis and George Biddell Airy his calculations demonstrating that a body (Neptune) is perturbing the orbit of Uranus.
- November 10 – Urbain Le Verrier presents to the Académie des sciences in Paris a memoir showing that existing theories fail to account for the motion of Uranus.
- Construction begins in Ireland of the "Leviathan of Parsonstown", a telescope built by Lord Rosse.
- August–September – Previously unknown Potato blight strikes the potato crop in Ireland: start of the Irish Potato Famine.
- March 17 – Stephen Perry patents the rubber band in England.
- Edmond Frémy discovers the oxidizing agent Frémy's salt.
- August – John Franklin's expedition with HMS Erebus and HMS Terror to find the Northwest Passage is last seen entering Baffin Bay prior to its mysterious disappearance.
- December 27 – Anesthesia is used in childbirth for the first time, by Dr Crawford Long in Jefferson, Georgia.
- September 13 – Michael Faraday discovers that an intense magnetic field can rotate the plane of polarized light.
- C. H. D. Buys Ballot confirms the Doppler effect for sound waves.
- Kirchhoff's circuit laws were first described in 1845 by German physicist Gustav Kirchhoff.
- July 26–August 10 – Isambard Kingdom Brunel’s iron steamship Great Britain makes the Transatlantic Crossing from Liverpool to New York, the first screw propelled vessel to make the passage.
- March 1 – Vasily Dokuchaev (died 1902), Russian geologist.
- March 3 – Georg Cantor (died 1918), Russian-born German mathematician.
- March 27 – Wilhelm Röntgen (died 1923), German physicist, discoverer of X-rays, Nobel laureate.
- April 21 – William Healey Dall (died 1927), American malacologist and explorer.
- May 4 – William Kingdon Clifford (died 1879), English geometer.
- May 16 – Élie Metchnikoff (died 1916), Russian-born microbiologist, Nobel laureate.
- June 16 – Heinrich Dressel (died 1920), German archaeologist.
- July 4 – Thomas Barnardo (died 1905), Irish-born physician and philanthropist.
- September 11 – Émile Baudot (died 1903), telegraph engineer.
- November 14 – Ulisse Dini (died 1918), Italian mathematician.
- January 11 – Etheldred Benett (born 1776), British geologist.
- March 13 – John Frederic Daniell (born 1790), English chemist and physicist.
- March 18 – 'Johnny Appleseed' (John Chapman) (born 1774), American nurseryman.
- April 10 – Thomas Sewall (born 1786), American anatomist.
- October 18 – Dominique, comte de Cassini (born 1748), French astronomer.
- Jean Henri Jaume Saint-Hilaire (born 1772), French botanist.
- Sheehan, William; Kollerstrom, Nicholas; Waff, Craig B. (2004-11-22). "The Case of the Pilfered Planet - Did the British steal Neptune?". Scientific American.
- Chisholm, Hugh, ed. (1911). "Adams, John Couch". Encyclopædia Britannica (11th ed.). Cambridge University Press.
- "BBC Short History of Ireland".
- Palmer, Alan; Veronica (1992). The Chronology of British History. London: Century Ltd. pp. 267–268. ISBN 0-7126-5616-2.
- Penguin Pocket On This Day. Penguin Reference Library. 2006. ISBN 0-14-102715-0.
- The Hutchinson Factfinder. Helicon. 1999. p. 549. ISBN 1-85986-000-1.
- Buys Ballot, C. H. D. (1845). "Akustische Versuche auf der Niederländischen Eisenbahn, nebst gelegentlichen Bemerkungen zur Theorie des Hrn. Prof. Doppler". Annalen der Physik und Chemie (in German). 11: 321–351.
- Fox, Stephen (2003). Transatlantic: Samuel Cunard, Isambard Brunel, and the Great Atlantic Steamships. HarperCollins. ISBN 978-0-06-019595-3.
- "Great Britain". The Ships List. Archived from the original on 2010-05-28. Retrieved 2010-10-01.
- "Obituaries". The Fort Wayne Sentinel. 67 (81). 22 March 1845.