1759 was a common year starting on Monday (see link for calendar).
- January 25 - Robert Burns, Scottish poet (d. 1796)
- February 15 - Friedrich August Wolf, philologist and archaeologist (d. 1824)
- May 20 - William Thornton, original architect of the United States Capitol (d. 1828)
- May 28 - William Pitt the Younger, British Prime Minister (d. 1806)
- September 19 - William Kirby, English entomologist (d. 1850)
- October 25 - Sophie Marie Dorothea of Württemberg, later Empress consort to Paul I of Russia (d. November 5, 1828)
- November 10 - Friedrich Schiller, German poet, historian, and dramatist (d. 1805)