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Jules Henri Poincaré (1854-1912)

Scientific field: Mathematics, Physics
Known for: Poincaré conjecture, Three-body problem, Topology, Special relativity

Jules Henri Poincaré was a French mathematician, one of the greatest mathematicians and mathematical physicists at the end of 19th century. He made a series of profound innovations in geometry, the theory of differential equations, electromagnetism, topology, and the philosophy of mathematics.

In the 1880s Poincaré began work on curves defined by a particular type of differential equation, in which he was the first to consider the global nature of the solution curves and their possible singular points (points where the differential equation is not properly defined). He investigated such questions as: Do the solutions spiral into or away from a point? Do they, like the hyperbola, at first approach a point and then swing past and recede from it? Do some solutions form closed loops? If so, do nearby curves spiral toward or away from these closed loops? He showed that the number and types of singular points are determined purely by the topological nature of the surface. In particular, it is only on the torus that the differential equations he was considering have no singular points.

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Andrey Nikolayevich Kolmogorov (1903-1987)

Scientific field: Mathematics
Known for: Information theory, Harmonic analysis, Number theory, Probability theory, Set theory

Andrey Kolmogorov was a Russian mathematician whose work influenced many branches of modern mathematics, and best remembered for a brilliant series of papers on the theory of probability.

Of the many areas of pure and applied mathematical research to which Kolmogorov contributed, probability theory is unquestionably the most important, in terms of both the depth and breadth of his contributions. In addition to his work on the foundations of probability, he contributed profound papers on stochastic processes, especially Markov processes. In Markov processes only the present state has any bearing upon the probability of future states; states are therefore said to retain no “memory” of past events. Kolmogorov invented a pair of functions to characterize the transition probabilities for a Markov process and showed that they amount to what he called an “instantaneous mean” and an “instantaneous variance”. Using these functions, he was able to write a set of partial differential equations to determine the probabilities of transition from one state to another. These equations provided an entirely new approach to the application of probability theory in physics, chemistry, civil engineering, and biology.

Kolmogorov’s interest in problems of turbulence in fluids (turbulent flow) arose in the late 1930s, when he realized that the recently developed stochastic field theory would be relevant to these problems. In 1941 and 1942 he contributed four papers to this area, in which his contributions were multiplied by a talented group of collaborators working under his direction.

During the 1930s, while continuing a prolific output of papers on particular mathematical topics, Kolmogorov began to write articles on methodological questions involving the theories of real analysis and probability. He also began to write expository articles for encyclopedias and journals aimed at a popular audience. After the end of World War II, established as one of the leading Soviet mathematicians, he began writing articles of historical and philosophical content. During the 1950s he contributed more than 80 articles to the second edition of the Great Soviet Encyclopedia.

In the mid-1950s Kolmogorov began to work on problems of information theory. He was inspired, in part, by the earlier nonrigorous work of the American engineer Claude Shannon. Working with Israil Gelfand and Akiva Yaglom, he was able to give a mathematical definition of the notion of quantity of information. In the 1960s he began writing articles on automata theory and theory of algorithms. The breadth of his culture and interests is shown by articles that he wrote at this time on the metrical structure of some of the masterpieces of Russian poetry.

The late 1960s marked Kolmogorov’s entrance into the theory of pedagogy, in which he was enormously influential through his textbooks and his service as a member of the U.S.S.R. Academy of Pedagogical Sciences. He cowrote and reviewed school textbooks and actively participated in reforming the mathematics curriculum in Soviet schools. Though suffering from Parkinson’s disease and nearly blind during the last few years of his life, he continued to take an active interest in the mathematical world until he died.

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Wolfgang Ernst Pauli (1900-1958)

Scientific field: Physics
Known for: Pauli exclusion principle

Austrian-born physicist, Wolfgang Pauli was the recipient of the 1945 Nobel Prize for Physics for his discovery in 1925 of the Pauli exclusion principle, which states that in an atom no two electrons can occupy the same quantum state simultaneously. This principle clearly relates the quantum theory to the observed properties of atoms.

When he was 20, Pauli wrote a 200-page encyclopaedia article on the theory of relativity. He was appointed a lecturer at the University of Hamburg in 1923, and the following year he proposed that a fourth quantum number, which may take on the numerical values +1/2 or −1/2, was necessary to specify electron energy states. It was later found that the two values represent the two possible directions of spin for fermions. In 1925 he introduced his exclusion principle, which immediately made clear the reason for the structure of the periodic table of the elements.

In 1928 Pauli became professor of theoretical physics at the Federal Institute of Technology, Zürich. Under his direction the institution became a great centre of research in theoretical physics during the years preceding World War II. In the late 1920s it was observed that when a beta particle (electron) is emitted from an atomic nucleus, there is generally some energy and momentum missing, a grave violation of the laws of conservation. Rather than allow these laws to be discarded, Pauli proposed in 1931 that the missing energy and momentum is carried away from the nucleus by some particle (later named the neutrino by Enrico Fermi) that is uncharged and has little or no mass and had gone unnoticed because it interacts with matter so seldom that it is nearly impossible to detect. This particle was not observed until 1956.

In 1940 Pauli was appointed to the chair of theoretical physics at the Institute for Advanced Study, Princeton, New Jersey, and in 1946 he became a naturalized citizen of the United States. Following World War II he returned to Zürich.

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Max Karl Ernst Ludwig Planck (1858-1947)

Scientific field: Physics
Known for: Planck’s constant, Quantum theory

Max Planck was a German theoretical physicist with many contributions to theoretical physics, but whose fame rests primarily on his role as originator of the quantum theory. This theory revolutionized our understanding of atomic and subatomic processes, just as Albert Einstein’s theory of relativity revolutionized our understanding of space and time. Together they constitute the fundamental theories of 20th-century physics.

In 1859–60 Kirchhoff had defined a blackbody as an object that reemits all of the radiant energy incident upon it; i.e., it is a perfect emitter and absorber of radiation. There was, therefore, something absolute about blackbody radiation, and by the 1890s various experimental and theoretical attempts had been made to determine its spectral energy distribution - the curve displaying how much radiant energy is emitted at different frequencies for a given temperature of the blackbody. Planck was particularly attracted to the formula found in 1896 by his colleague Wilhelm Wien at the Physikalisch-Technische Reichsanstalt (PTR) in Berlin-Charlottenburg, and he subsequently made a series of attempts to derive “Wien’s law” on the basis of the second law of thermodynamics. By October 1900, however, other colleagues at the PTR, the experimentalists Otto Richard Lummer, Ernst Pringsheim, Heinrich Rubens, and Ferdinand Kurlbaum, had found definite indications that Wien’s law, while valid at high frequencies, broke down completely at low frequencies.

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Julius Robert Oppenheimer (1904-1967)

Scientific field: Physics
Known for: Atomic bomb development, Tolman-Oppenheimer-Volkoff limit, Oppenheimer-Phillips process

Julius Robert Oppenheimer was an American theoretical physicist and science administrator, noted as director of the Los Alamos laboratory during development of the atomic bomb (1943–45) and as director of the Institute for Advanced Study, Princeton (1947–66).

In the 1920s the new quantum and relativity theories were engaging the attention of science. That mass was equivalent to energy and that matter could be both wavelike and corpuscular carried implications seen only dimly at that time. Oppenheimer’s early research was devoted in particular to energy processes of subatomic particles, including electrons, positrons, and cosmic rays. Since quantum theory had been proposed only a few years before, the university post provided him an excellent opportunity to devote his entire career to the exploration and development of its full significance. In addition, he trained a whole generation of U.S. physicists, who were greatly affected by his qualities of leadership and intellectual independence.

In August 1942 the U.S. Army was given the responsibility of organizing the efforts of British and U.S. physicists to seek a way to harness nuclear energy for military purposes, an effort that became known as the Manhattan Project. Oppenheimer was instructed to establish and administer a laboratory to carry out this assignment. The joint effort of outstanding scientists at Los Alamos culminated in the first nuclear explosion on July 16, 1945. In October of the same year, Oppenheimer resigned his post. In 1947 he became head of the Institute for Advanced Study at Princeton University and served from 1947 until 1952 as chairman of the General Advisory Committee of the Atomic Energy Commission, which in October 1949 opposed development of the hydrogen bomb.

In 1963 President Lyndon B. Johnson presented Oppenheimer with the Enrico Fermi Award of the Atomic Energy Commission. Oppenheimer retired from Princeton in 1966 and died of throat cancer the following year.

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