The year 1845 in science and technology involved some significant events, listed below.
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- February 17 (Old Style March 1) – Fyodor Pirotsky (died 1898), Ukrainian-born Russian military and electrical engineer and inventor.
- 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), French telegraph engineer.
- November 14 – Ulisse Dini (died 1918), Italian mathematician.
Palmer, Alan; Palmer, Veronica (1992). The Chronology of British History. London: Century Ltd. pp. 267–268. ISBN 0-7126-5616-2.