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| 1930 |
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| Vannevar Bush (1890–1974) and his associates placed into operation a “differential analyzer,” the first modern analog computer. | 1 |
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| 1931 |
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| Ernest O. Lawrence (1901–58) invented the cyclotron, a device for accelerating atomic particles, which has become the fundamental research tool in high-energy physics and has made possible the creation of transuranium elements. | 2 |
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| 1931 |
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| Kurt Gödel (1906–78) published Uber formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, showing that in any formal mathematical system in which elementary arithmetic can be done, there are theorems whose truth or falsity cannot be proved. | 3 |
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| 1932 |
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| Karl Jansky reported the reception of radio waves from cosmic sources, making radio astronomy possible. | 4 |
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| 1938–39 |
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| Otto Hahn (1879–1968) and Otto Strassmann bombarded uranium with neutrons and found an isotope of barium in the product (1938). Lise Meitner (1878–1968) and Otto Frisch (1904–79) explained this result by assuming the fission of the uranium nucleus (nuclear fission). | 5 |
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| 1939 |
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| Nicolas Bourbaki (pseudonym assumed by a group of mathematicians) published the first of a long series of expository works on modern mathematics. | 6 |
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| 1939 |
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| Hans A. Bethe (b. 1906) and Carl von Weizsäcker (b. 1912) independently proposed two sets of nuclear reactions to account for stellar energies: the carbon-nitrogen cycle and the proton-proton chain. | 7 |
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| 1939–45 |
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| World War II research needs stimulated the formation of large groups or teams of research workers to concentrate effort on single problems, such as radar and the atomic bomb. Such group research has become a common feature of postwar science. | 8 |
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| 1940 |
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| Gödel, in The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory, proved that transfinite methods could not introduce inconsistencies into mathematics. | 9 |
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| 1942 |
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| Enrico Fermi (1901–54) and associates built the first controlled self-sustaining nuclear reactor. Fermi was one of the chief architects of the theory of the atomic nucleus. | 10 |
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| 1944 |
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| Mark I, the Harvard-IBM Automatic Sequence Controlled Calculator, was put into operation at Harvard University. This was the first large-scale digital calculating machine. | 11 |
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| 1945 |
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| Vannevar Bush issued the report Science: The Endless Frontier, recommending the creation of a U.S. foundation for the support and encouragement of basic research and education in science. In 1950 the U.S. Congress established the National Science Foundation to implement this recommendation. | 12 |
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