Events from the year 1755 in Scotland.
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- 18 January – James Hamilton, 7th Duke of Hamilton (died 1769)
- 21 February – Anne Grant, poet (died 1838)
- 25 June – Archibald Gracie merchant and shipowner (died 1829 in the United States)
- August 5 – James Playfair, Scottish Neoclassical architect (died 1794)
- 17 August – William Paterson, soldier, colonial governor in Australia, explorer and botanist (died 1810 at sea)
- 4 September – Mary FitzMaurice, 4th Countess of Orkney, née O'Brien (died 1831)
- October – George Galloway, poet and playwright
- November – John Dunlop, merchant and songwriter (died 1820)
- 25 February – 11-year-old David Allan begins to study painting at the new Foulis Academy in Glasgow.[5]
- David Dalrymple, as editor, publishes Edom of Gordon: an ancient Scottish poem.
"Experiments upon Magnesia Alba, Quicklime, and Some Other Alcaline Substances", published 1756.