| 1845–1958 | Germany [earth sciences] | German naturalist and explorer Alexander von Humboldt lays the basis of modern geography with the publication of Kosmos/Cosmos, in which he arranges geographic knowledge in a systematic fashion. |
| 1911–1914 | USA, Mexico [statistics and demography] | 82,500 Mexicans emigrate to the USA. |
| 1913 | Sweden [railways] | The world's first diesel-electric locomotives begin running in Sweden. |
| 1913 | United Kingdom [materials] | The first stainless steel is cast in Britain, by Harry Brearley in Sheffield. |
| 1913 | [maths] | English philosopher Bertrand Russell publishes the final volume of Principia Mathematica/Principles of Mathematics in collaboration with another English mathematician and philosopher, Alfred North Whitehead. They attempt to derive the whole of mathematics from a logical foundation. |
| 1913 | [orchestral music] | The Austrian composer Anton Webern completes his Bagatelles for string quartet (Opus 9), 5 Stücke/Five Pieces for orchestra (Opus 10) and 6 Bagatelles for string quartet (Opus 11). |
| 1913 | Germany [photography] | German inventor Oskar Barnak devises the first 35-mm camera. It is not commercialized until 1924. |
| 1913 | England [physics] | English physicists William and Lawrence Bragg develop X-ray crystallography further by establishing laws that govern the orderly arrangement of atoms in crystals displays interference and diffraction patterns. They also demonstrate the wave nature of X-rays. |
| 1913 | USA, Germany [consumer products] | The first domestic refrigerators appear on the market in the USA and Germany. |
| 1913 | [fiction] | The US writer Eleanor Porter publishes her children's novel Polyanna. |
| 1913 | [fiction] | The French writer Alain-Fournier publishes his novel Le Grand Meaulnes/The Lost Domain. |
| 1913 | [fiction] | The English writer D H Lawrence publishes his novel Sons and Lovers. |
| 1913 | [fiction] | The French writer Marcel Proust publishes Du Côté de chez Swann/Swann's Way. This is the first volume of his multi-volume novel A la recherche du temps perdu/Remembrance of Things Past. |
| 1913 | United Kingdom [food and drink] | The London company Carter's Crisps launches potato crisps in Britain. |
| 1913 | United Kingdom [aircraft] | British firm Vickers introduce the Experimental Fighting Biplane No. 1. It is the first plane to have a machine gun mounted on it. |
| 1913 | [art] | The International Exhibition of Modern Art is held in New York City. Known as the ‘Armory Show’, it proves to be a controversial exhibition of post-Impressionist and cubist art, widely criticized as decadent. The exhibition plays an important role in introducing modern European art to the USA. |
| 1913 | [ballet] | The ballet Le Sacre du printemps/The Rite of Spring, by the Russian composer Igor Stravinsky and the Russian dancer Vaslav Nijinsky, is first performed, in Paris, France, under the Russian impresario Sergei Diaghilev. Nijinsky dances the central role. Audiences riot, judging the work to be crude and offensive. |
| 1913 | [chemistry] | English physicist Henry Gwyn-Jeffreys Moseley discovers the characteristic feature of an element, the atomic number. Moseley discovers that the X-ray spectra of the elements have a deviation that changes regularly through the periodic table. |
| 1913 | United Kingdom [cinema and film] | The British Board of Film Censors is established. It employs a simple system of classification, using U for universally appropriate films and A as an adults-only rating. |
| 1913 | [civic and commercial buildings] | The Woolworth Building, designed by the US architect Cass Gilbert, is completed in New York City. With 60 floors, it will be world's highest skyscraper until 1931. |
| 1913 | [sculpture] | The Italian artist Umberto Boccioni sculpts Unique Forms of Continuity in Space. |
| 9 January 1913 | [births and deaths] | Richard M(ilhous) Nixon, 37th president of the USA 1969–74, a Republican, the first president to resign, born in Yorba Linda, California (–1994). |
| 15 January 1913 | United Kingdom [social legislation] | Maternity, sickness, and unemployment benefits are introduced in Britain. |
| 18 February 1913 | Mexico [revolution] | The commander of the Mexican army, Victoriano Huerta, joins the rebel Mexican soldiers and forces President Francisco Madero to resign. He subsequently declares himself president, and civil war ensues. |
| 22 February 1913 | [births and deaths] | Ferdinand de Saussure, Swiss linguist whose ideas about the structure of language laid the foundation of modern linguistics, dies in Geneva, Switzerland (55). |
| 18 March 1913 | Greece [political events] | King George I of Greece is assassinated in newly occupied Thessaloníki (English Salonika) by a drunken Greek called Alexandros Skinas. |
| 3 April 1913 | United Kingdom [suffrage] | Militant suffragist Emmeline Pankhurst is imprisoned in Britain for inciting persons to place explosives outside the house of the chancellor of the Exchequer, David Lloyd George. |
| 20 May - 22 May 1913 | United Kingdom [gardens] | The Royal Horticultural Society holds the first Chelsea Flower Show, in London, England. |
| 30 May 1913 | Balkans [treaties] | A peace treaty between the Ottoman Empire and the Balkan states is signed in London, England, ending the First Balkan War. |
| 29 June 1913 | Bulgaria, Serbia, Greece [Balkan wars (1912–13)] | The Second Balkan War begins when Bulgaria attacks Serbian and Greek positions. |
| July 1913 | USA [magazines] | Billboard magazine is the first publication in the USA to print a weekly chart of best-selling popular songs. |
| 14 July 1913 | [births and deaths] | Gerald Ford, 38th president of the USA (1974–77), a Republican, born in Omaha, Nebraska. |
| 30 July 1913 | Balkans [Balkan wars (1912–13)] | The Balkan states sign an armistice in Bucharest, Romania, ending the Second Balkan War. |
| 10 August 1913 | Balkans [treaties] | The Balkan states sign a peace treaty in Bucharest, Romania, in which Serbia and Greece retain the areas of Macedonia they have taken from Bulgaria. |
| 18 September 1913 | Bulgaria, Anatolia, Ottoman Empire [treaties] | A Bulgarian–Ottoman treaty settles the frontier in Thrace, leaving Adrianople under Ottoman rule. |
| October 1913 | USA [industrialization] | Henry Ford introduces the assembly line process, reducing the time required to produce a Model T car from 12.5 to 1.5 hours. |
| 13 November 1913 | Greece, Anatolia, Ottoman Empire [treaties] | A Greek–Ottoman peace treaty following the Second Balkan War allows Greece to absorb Crete and all the Aegean islands except Tenedos, Imbros, and the Dodecanese. |
| 17 November 1913 | Panama [political events] | The first vessel passes through the Panama Canal. |
| 23 December 1913 | USA [legislation] | The US Congress passes the Glass-Owen Currency Act (Federal Reserve Bank Act), establishing a Federal Reserve Board with power over monetary policy and 12 district Federal Reserve banks, and creating the nation's first central banking system since the dissolution of the Second Bank of the United States in the 1830s. |