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1675 (MDCLXXV) was a common year starting on Tuesday of the Gregorian calendar and a common year starting on Friday of the Julian calendar, the 1675th year of the Common Era (CE) and Anno Domini (AD) designations, the 675th year of the 2nd millennium, the 75th year of the 17th century, and the 6th year of the 1670s decade. As of the start of 1675, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 5 – Franco-Dutch War – Battle of Turckheim: In Turckheim, Alsace, France, the French defeat Austria and Brandenburg.
- January 29 – John Sassamon, an English-educated Native American Christian, dies at Assawampsett Pond, an event which will trigger a year-long war between the English American colonists of New England, and the Algonquian Native American tribes.
- March 30 – The guild organisation Maîtresses couturières is founded in Paris.
- April – English merchant Anthony de la Roché, blown off course after rounding Cape Horn eastabout, makes the first discovery of land south of the Antarctic Convergence, landing on South Georgia and (probably) Gough Island.
- June 8 – John Sassamon's alleged murderers are executed at Plymouth.
- June 11 – Armed Wampanoags are reported traveling around Swansea, Massachusetts.
- June 14–June 25 – Colonial authorities of Rhode Island, Plymouth, and Massachusetts attempt a negotiation with Metacomet (King Philip), leader of the Wampanoags, and seek guarantees of fidelity from the Nipmuck and Narragansett tribes.
- June 24 – King Philip's War breaks out, as the Wampanoags attack Swansea.
- June 26 – Massachusetts troops march to Swansea, to join the Plymouth troops.
- June 26–June 29 – Wampanoags assault Rehoboth and Taunton; the natives elude colonial troops and leave Mount Hope for Pocasset, Massachusetts. The Mohegan tribe travels to Boston, in order to side with the English colonists against the Wampanoags.
- June 28 – Battle of Fehrbellin: Brandenburg defeats the Swedes.
- July 15 – The Narragansett tribe signs a peace treaty with Connecticut.
- July 16–24 – An envoy from Massachusetts attempts to negotiate with the Nipmuck tribe.
- August 2–4 – The Nipmucks attack Massachusetts troops and besiege Brookfield, Massachusetts.
- August 10 – King Charles II of England places the foundation stone of the Royal Greenwich Observatory in London; construction begins.
- August 13 – The Massachusetts Council orders that Christian Indians are to be confined to designated praying towns.
- September 1–2 – While Wampanoags and Nipmucks attack Deerfield, Massachusetts, Captain Samuel Moseley commands Massachusetts troops in an attack on the Pennacook tribe.
- September 12 – English colonists abandon Deerfield, Squakeag, and Brookfield due to a coalition of Indian attacks.
- September 15 – The Bremen-Verden Campaign of the Northern Wars begins, with the invasion of Amt Wildeshausen by the Munster army, and their advance on Verden via the city of Bremen.
- September 18 – The Narragansetts sign a treaty with the English in Boston; meanwhile, Massachusetts troops are ambushed near Northampton, Massachusetts.
- October 5 – The Pocomtuc tribe attacks and destroys Springfield, Massachusetts.
- October 13 – The Massachusetts Council convenes and agrees that all Christian Indians should be ordered to move to Deer Island.
- October 29 - Gottfried Wilhelm Leibniz makes the first use of the long s (∫) as a symbol of the integral in calculus.
- November 2–12 – Commissioners of the Thirteen Colonies organize a united force to attack the Narragansett tribe.
- November 11
- December 19 – United colonial forces attack the Narragansetts at the Great Swamp Fight.
- January 16 – Louis de Rouvroy, duc de Saint-Simon, French writer (d. 1755)
- January 27 – Erik Benzelius the younger, Swedish priest (d. 1743)
- February 8 – Anna Moroni, Italian educator (b. 1613)
- February 21 – Franz Xaver Josef von Unertl, Bavarian politician (d. 1750)
- February 28 – Guillaume Delisle, French cartographer (d. 1726)
- March 31 – Pope Benedict XIV (d. 1758)
- May 29 – Humphry Ditton, English mathematician (d. 1715)
- June 1 – Francesco Scipione, marchese di Maffei, Italian archaeologist (d. 1755)
- July 5 – Mary Walcott, American accuser at the Salem witch trials
- July 12 – Evaristo Abaco, Italian composer (d. 1742)
- July 14 – Claude Alexandre de Bonneval, French soldier (d. 1747)
- September 2 – William Somervile, English poet (d. 1742)
- September 3 – Paul Dudley, Attorney-General of Massachusetts (d. 1751)
- September 27 – Dorothea Krag, Danish General Postmaster and noble (d. 1754)
- October 11 – Samuel Clarke, English philosopher (d. 1729)
- October 21 – Emperor Higashiyama of Japan (d. 1710)
- October 24 – Richard Temple, 1st Viscount Cobham, English soldier and politician (d. 1749)
- date unknown
- January 9 – Francesco Maria Brancaccio, Catholic cardinal (b. 1592)
- January 26 – Domenico II Contarini, Doge of Venice (b. 1585)
- February 9 – Gerhard Douw, Dutch painter (b. 1613)
- February 10 – Gervase Holles, English Member of Parliament (b. 1607)
- March 14 – Francis Davies, British bishop (b. 1605)
- March 18 – Arthur Chichester, 1st Earl of Donegall, Irish soldier (b. 1606)
- April 8 – Veit Erbermann, German theologian (b. 1597)
- April 10 – Dorothea of Saxe-Altenburg, Duchess of Saxe-Altenburg by births and by marriage Duchess of Saxe-Eisenach (b. 1601)
- April 12 – Richard Bennett, British Colonial Governor of Virginia (b. 1609)
- May 1 – Jonathan Rashleigh, English politician (b. 1591)
- May 6 – August Philipp, Duke of Schleswig-Holstein-Sonderburg-Beck, Danish-German prince and member of the House of Oldenburg (b. 1612)
- May 18
- May 27 – Gaspard Dughet, French painter (b. 1613)
- June 5 – John Mordaunt, 1st Viscount Mordaunt, English politician (b. 1626)
- June 11
- June 12 – Charles Emmanuel II, Duke of Savoy (b. 1634)
- July 14 – Daniel Hallé, French painter (b. 1614)
- July 20 – Giles Strangways, English politician (b. 1615)
- July 25 – Johan Stiernhöök, Swedish lawyer (b. 1596)
- July 27 – Henri de la Tour d'Auvergne, Vicomte de Turenne, Marshal of France (b. 1611)
- July 28 – Bulstrode Whitelocke, English lawyer (b. 1605)
- August 5 – Brynjólfur Sveinsson, Icelandic bishop and scholar (b. 1605)
- August 16 – António Luís de Meneses, 1st Marquis of Marialva, Portuguese general and noble (b. 1596)
- August 29 – Joachim Irgens von Westervick, Dano–Norwegian nobleman (b. 1611)
- September 8
- September 18 – Charles IV, Duke of Lorraine (b. 1604)
- September 23 – Valentin Conrart, French founder of the Académie française (b. 1603)
- October 10 – Tommaso Tamburini, Italian theologian (b. 1591)
- October 15 – William Wadsworth, American colonial pioneer (b. 1594)
- October 26 – William Sprague, English co-founder of Charlestown, Massachusetts (b. 1609)
- October 27 – Gilles de Roberval, French mathematician (b. 1602)
- November – Feodosia Morozova, Russian religious dissident martyr (b. 1632)
- November 1 – Guru Tegh Bahadur, 9th Sikh Guru (b. 1621)
- November 4 – Remigius van Leemput, painter from the Southern Netherlands (b. 1607)
- November 10 – Leopoldo de' Medici, Italian Catholic cardinal (b. 1617)
- November 11 – Thomas Willis, English doctor who played an important part in the history of anatomy (b. 1621)
- November 15 – Preben von Ahnen, German-born civil servant and landowner in Norway (b. 1606)
- November 21 – George William, Duke of Liegnitz (b. 1660)
- November 28 – Basil Feilding, 2nd Earl of Denbigh, English Civil War soldier
- November 28 – Leonard Hoar, American President of Harvard University (b. 1630)
- November 30
- December 6 – John Lightfoot, English churchman, scholar (b. 1602)
- December 15 (bur.) – Johannes Vermeer, Dutch painter (b. 1632)
- December 16 – Armand-Nompar de Caumont, duc de La Force, Marshal of France (b. 1580)
- December 23 – Caesar, duc de Choiseul, French marshal and diplomat (b. 1602)
- date unknown – Margareta Beijer, director of the Swedish Royal Post Office (b. 1625)
- ^ Headland, Robert (1992). The Island of South Georgia (2nd ed.). Cambridge University Press. ISBN 0-521-42474-7.
- ^ de Seixas y Lovera, Francisco (1690). Descripcion geographica, y derrotero de la region austral Magallanica. Madrid: Antonio de Zafra.
- ^ Wace, N. M. (1969). "The discovery, exploitation and settlement of the Tristan da Cunha Islands". Proceedings of the Royal Geographical Society of Australasia (South Australian Branch). 10: 11–40.