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| 1860–77 |
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| James Clerk Maxwell (1831–79) and Ludwig Boltzmann (1844–1906) developed statistical mechanics, a theory of the behavior of a gas considered as a collection of large numbers of molecules obeying the laws of classical mechanics. | 1 |
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| 1868 |
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| William Huggins (1824–1910), noting a slight shift toward the red in the spectrum of Sirius, calculated the radial velocity of a star for the first time. | 2 |
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| 1870–83 |
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| Georg Cantor (1845–1918) published his major works, founding the theory of sets (1870) and the theory of transfinite numbers (1883). | 3 |
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| 1872–82 |
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| Richard Dedekind (1831–1916) gave arithmetic definitions of irrational numbers (the Dedekind cut), constituting the first rigorous theory of irrationals. | 4 |
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| 1873 |
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| Johannes van der Waals (1837–1923) found an equation of state for imperfect gases. | 5 |
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| 1873 |
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| Maxwell published his Treatise on Electricity and Magnetism, in which he described the properties of the electromagnetic field in a series of equations (Maxwell equations) that entailed the electromagnetic theory of light. | 6 |
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| 1877 |
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| Giovanni Schiaparelli (1835–1910) observed long, straight, narrow, intersecting, dark lines on Mars, which he called canali. | 7 |
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| 1877–93 |
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| Francis Galton (1822–1911) and Karl Pearson (1857–1936) developed the major statistical tools of present-day social science, for example, regression (Galton, 1877), correlation coefficients (Galton, 1888), and moments and standard deviation (Pearson, 1893). | 8 |
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| 1878 |
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| William Crookes (1832–1919) showed that cathode rays proceed in straight lines, are capable of turning a small wheel, can be deflected by a magnet, can excite fluorescence in certain substances, and can heat and sometimes even melt some metals. | 9 |
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| 1884 |
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| Gottlob Frege (1848–1925) published Grundlagen der Arithmetik, in which arithmetical concepts were defined in logical terms. | 10 |
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| 1887 |
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| Heinrich Hertz (1857–94) demonstrated the existence of electromagnetic waves in the space about a discharging Leyden jar, and found that electromagnetic waves were propagated with the velocity of light as Maxwell had predicted (1873). Hertz's work led to modern radio communications. | 11 |
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| 1887 |
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| Albert Michelson (1852–1931) and Edward Morley (1838–1923) announced that they were unable to detect any effect of the earth's motion through the ether in experiments with an extremely sensitive interferometer. | 12 |
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