Abstract
The success attained in the study of functions and curves with the help of set theory made it a full and equal member of the family of mathematical sciences. This recognition was acknowledged at the first international congress of mathematicians in Zurich in 1897. Hurwitz1 and Hadamard,2 the greatest experts in mathematical analysis, demonstrated in their lectures extremely varied applications of sets and disclosed their connection with the theory of so-called analytic functions. Three years later, at the next international mathematical congress, David Hilbert’s list of 23 of the most important unsolved mathematical problems included problems in set theory. In his lecture at the congress Henri Poincaré gave a high rating to Cantor’s works. Speaking of the role of intuition and logic in mathematics, he said that mathematics finds in set theory an absolutely permanent and reliable foundation, and now all that remains are the natural numbers and finite or infinite systems of such numbers. In his view, mathematics had become completely arithmetized and, finally, absolutely rigorous.
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References
Hurwitz, Adolf (1859–1919). German mathematician. Author of works in mathematical analysis, the theory of functions, algebra, and number theory.
Hadamard, Jacques (1865–1963). French mathematician. Author of outstanding works in the area of mathematical physics, the theory of functions, and number theory.
Burali-Forti, Cesaro (1861–1931). Italian mathematician.
Russell, Bertrand (1872–1970). English logician, philosopher, mathematician and social activist. Founder of logicism.
Shnirelman, Lev Henrikhovich (1905–1938). Soviet mathematician. Author of outstanding works in number theory, topology, and topological and quantitative methods of mathematical analysis.
Zermelo, Ernst (1871–1953). German mathematician. Author of works on set theory, the calculus of variations, and probability theory.
Baire, Rene (1874–1932). French mathematician. Worked in the area of the theory of functions of a real variable.
Kuratowski, Kazimierz (1896–1980). Polish mathematician. Author of works in the area of topology, the theory of functions of a real variable, and mathematical logic.
Bourbaki, Nicolas. Pseudonym of a group of modern French mathematicians who have published a treatise of many volumes titled The elements of mathematics.
Gödel, Kurt (1906–1978). Abstract mathematician and logician.
Cohen, Paul (b. 1934). American mathematician. Proved the independence of the continuum hypothesis.
Bolyai, Jänos (1802–1860). Hungarian mathematician. Created hyperbolic geometry shortly after Lobachevski and independently of him.
Whitehead, Alfred (1861–1947). English mathematician and logician. Coauthor (with B. Russell) of Principia mathematica.
Quine, Willard (b. 1908). American mathematician. One of the greatest experts in mathematical logic and the foundations of mathematics.
Pólya, George (1887–1985). Hungarian mathematician. Author of works on functional analysis, mathematical statistics, and combinatorics.
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Vilenkin, N.Y. (1995). In search of the absolute. In: In Search of Infinity. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0837-2_4
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DOI: https://doi.org/10.1007/978-1-4612-0837-2_4
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