1731

January–June

• January 25 - A fire in Brussels at the Coudenberg Palace, at the time the home of the ruling Austrian Duchess of Brabant, destroys the building, including the state records stored therein.
• March 16 - The Treaty of Vienna is signed between the Holy Roman Empire, Great Britain, the Dutch Republic and Spain.
• April 1 - Battle of Dabhoi in India is fought between Sarsenapati Trimbakrao Dabhade and Bajirao Peshwa.
• April 2 - The town of Raynham, Massachusetts in Bristol County is entered as a new town by the governor and court of Massachusetts, New England, America.
• April 28 - A fire at White's Chocolate House, near St. James's Palace, destroys the historic club and the paintings therein, but is kept from spreading by the fast response of firemen.
• April - British trader Robert Jenkins has his ear cut off by Spanish coast guards in Cuba, casus belli for the War of Jenkins' Ear in 1739.
• June 4 - The English market town of Blandford Forum is destroyed by fire, with the exception of 26 houses. About one-third of the uninsured losses are paid for by the collection of disaster relief money.

  July–December

• July 1 - Benjamin Franklin and fellow-subscribers start the Library Company of Philadelphia.
• September 30 - The village of Barnwell, Cambridgeshire, is "burned down entirely" by a fire.
• October 23 - A fire at Ashburnham House in Westminster destroys 114 irreplaceable manuscripts and damages 98 others. Dr. Richard Bentley, the King's librarian and the House's owner, saves the only copy of the Codex Alexandrinus, carrying it under one arm as he leaps from a window. Dr. Bentley's ten year labor in translating the Greek Testament is ruined by the blaze. The remaining 844 manuscripts later form the heart of the collections of the British Library.

  Date unknown

• Royal Colony of North Carolina Governor George Burrington asks the North Carolina General Assembly to pass an act establishing a town on the Cape Fear River, in what is seen as a political move to shift the power away from the powerful Cape Fear plantation class. The town is laid out in 1733, and incorporated as Wilmington in 1740.
• English Captain Charles Gough rediscovers Gough Island in the South Atlantic.
• Laura Bassi becomes the first official female university teacher, on being appointed professor of anatomy at the University of Bologna, at the age of 21.
• John Bevis observes the Crab Nebula for the first time in the modern era.
• The Royal Theatre of Mantua is built by Ferdinando Galli Bibiena.
• Sextant first implemented to accurately determine latitude.

  Births

• January 3 - Angelo Emo, Venetian admiral and statesman
• February - Charles Churchill, English poet
• March 19 - Gabriela Silang, Filipino rebel leader and heroine
• April 8 - William Williams, signer of the Declaration of Independence
• May 8 - Beilby Porteus, Bishop of London and abolitionist
• June 2 - Martha Washington, First Lady of the United States
• June 2 - Dorothea Biehl, Danish writer
• July 16 - Samuel Huntington, Patriot in the American Revolution and politician
• August - Henry Constantine Jennings, English gambler and collector
• October 10 - Henry Cavendish, English scientist
• September 7 - Elisabetta de Gambarini, English composer
• November 9 - Benjamin Banneker, African-American astronomer, surveyor of the District of Columbia
• November 15 - William Cowper, English poet
• December 8 - František Xaver Dušek, Czech composer
• December 12 - Erasmus Darwin, English scientist and grandfather of Charles Darwin
• December 28 - José de Viera y Clavijo, Spanish writer
• Nikephoros Theotokis, Greek scholar and theologian
• Mikiel'Ang Grima - Maltese surgeon

  Deaths

• January 6 - Étienne François Geoffroy, French chemist
• January 20 - Antonio Farnese, Duke of Parma
• January 23 - Anna Lohe, Swedish banker
• January 27 - Bartolomeo Cristofori, Italian maker of musical instruments
• February 10 - George Carpenter, 1st Baron Carpenter, British Army general
• February 15 - Mary of Jesus de León y Delgado, Spanish Dominican lay sister and mystic
• February 22 - Frederik Ruysch, Dutch physician and anatomist
• March 5 - Abd al-Ghani al-Nabulsi, Sufi academic
• March 6 - Johann Melchior Dinglinger, German goldsmith
• March 8 - Ferdinand Brokoff, Czech sculptor
• March 12 - Ernest August, Duke of Schleswig-Holstein-Sonderburg-Augustenburg
• March 23 - Augustus William, Duke of Brunswick-Lüneburg
• c. April 24 - Daniel Defoe, English writer
• April 28
• * Johann Theodor Jablonski, German lexicographer
• * James Olmsted, Connecticut politician
• May 1 - Johann Ludwig Bach, German composer
• May 11 - Mary Astell, English feminist writer
• May 17 - Samuel Bradford, English churchman, Whig politician
• June 20 - Ned Ward, English writer, publican
• July 18 - Sir Walter Yonge, 3rd Baronet, English politician
• August 27 - Eudoxia Lopukhina, Russian Tsarina, divorced spouse of Peter the Great of Russia
• December 17 - George Lockhart, Scottish writer, spy and politician
• December 20 - Chhatrasal, Maharaja of Madhya Pradesh
• December 26 - Antoine Houdar de la Motte, French writer
• December 29 - Brook Taylor, English mathematician