The year 1677 in science and technology involved some significant events.

• Publication of the first English star atlas, John Seller's Atlas Coelestis.

• Gottfried Wilhelm Leibniz gives a complete solution to the tangent problem.^[1]
• Publication of Cocker's Arithmetick: Being a Plain and Familiar Method Suitable to the Meanest Capacity for the Full Understanding of That Incomparable Art, As It Is Now Taught by the Ablest School-Masters in City and Country, attributed to Edward Cocker (died 1676). It will remain a standard grammar school textbook in England for more than 150 years.^[2]

• January 21 – A pamphlet on smallpox published in Boston becomes the first medical publication in the British colonies in North America.

• Antonie van Leeuwenhoek discovers the spermatozoon.

• Robert Plot publishes The Natural History of Oxford-shire, Being an Essay Toward the Natural History of England, in which he describes the fossilised femur of a human giant, now known to be from the dinosaur Megalosaurus.

• February 8 – Jacques Cassini, French astronomer (died 1756)
• September 17 – Stephen Hales, English physiologist and clergyman (died 1761)
• September 27 – Johann Gabriel Doppelmayr, German mathematician, astronomer and cartographer (died 1750)

• May 4 – Isaac Barrow, English mathematician (born 1630)
• May 23 (bur.) – John Kersey, English mathematician (born 1677)
• October 11 – Sir Cornelius Vermuyden, Dutch-born drainage engineer (born 1595).^[3]
• October 14 – Francis Glisson, English physician (born 1599?)