The year 1759 in science and technology involved several significant events.

• Halley's Comet returns; a team of three mathematicians, Alexis Clairaut, Jérome Lalande and Nicole Reine Lepaute, have – for the first time – predicted the date.

• Caspar Friedrich Wolff's dissertation at the University of Halle Theoria Generationis supports the theory of epigenesis.^[1]

• Kew Gardens established in England by Augusta of Saxe-Coburg, the mother of George III.^[2]

• Giovanni Arduino proposes dividing the geological history of Earth into four periods: Primitive, Secondary, Tertiary and Volcanic, or Quaternary.^[3]

• June 15 – The first vascular surgery in history is performed by a Dr. Hallowell at Newcastle upon Tyne in England, who uses suture repair rather than a tying off with a ligature to repair an aneurysm on a patient's brachial artery.^[4][5] The new procedure of reconstructing a damaged artery replaces the practice of ligation that had risked the amputation of a limb or organ failure.^[6]
• Angélique du Coudray publishes Abrégé de l'art des accouchements ("The Art of Obstetrics").

• Posthumous publication of Émilie du Châtelet's French translation and commentary on Newton's Principia, Principes mathématiques de la philosophie naturelle.

• English clockmaker John Harrison produces his "No. 1 sea watch" ("H4"), the first successful marine chronometer.^[7]

• James Brindley is engaged by the Duke of Bridgewater to construct a canal to transport coal to Manchester from the duke's mines at Worsley, in North West England.
• October 16 – Smeaton's Tower, John Smeaton's Eddystone Lighthouse off the coast of South West England, is first illuminated.^[8]

• Copley Medal: John Smeaton^[9]

• January 29 – Louis Augustin Guillaume Bosc, French botanist (died 1828)
• July 19 – Jacques Anselme Dorthès, French physician, entomologist and naturalist (died 1794)^[10]
• August 12 – Thomas Andrew Knight, English horticulturalist (died 1838)
• September 19 – William Kirby, English entomologist (died 1850)
• December 2 – James Edward Smith, English botanist (died 1828)
• Date unknown – Maria Petraccini, Italian anatomist and physician (died 1791)

• February 16 – Bartholomew Mosse, Irish surgeon (born 1712)
• April 6 – Johann Gottfried Zinn, German anatomist and botanist (born 1727)
• July 27 – Pierre Louis Maupertuis, French mathematician (born 1698)
• September 10 – Ferdinand Konščak, Croatian explorer (born 1703)
• November 29 – Nicolaus I Bernoulli, Swiss mathematician (born 1687)