In search of the absolute

  • N. Ya. Vilenkin


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.


Classical Mathematic Continuum Hypothesis Existence Proof Decimal Digit Actual Infinite 
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  1. 1.
    Hurwitz, Adolf (1859–1919). German mathematician. Author of works in mathematical analysis, the theory of functions, algebra, and number theory.Google Scholar
  2. 2.
    Hadamard, Jacques (1865–1963). French mathematician. Author of outstanding works in the area of mathematical physics, the theory of functions, and number theory.Google Scholar
  3. 3.
    Burali-Forti, Cesaro (1861–1931). Italian mathematician.Google Scholar
  4. 4.
    Russell, Bertrand (1872–1970). English logician, philosopher, mathematician and social activist. Founder of logicism.Google Scholar
  5. 5.
    Shnirelman, Lev Henrikhovich (1905–1938). Soviet mathematician. Author of outstanding works in number theory, topology, and topological and quantitative methods of mathematical analysis.Google Scholar
  6. 6.
    Zermelo, Ernst (1871–1953). German mathematician. Author of works on set theory, the calculus of variations, and probability theory.Google Scholar
  7. 7.
    Baire, Rene (1874–1932). French mathematician. Worked in the area of the theory of functions of a real variable.Google Scholar
  8. 8.
    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.Google Scholar
  9. 9.
    Bourbaki, Nicolas. Pseudonym of a group of modern French mathematicians who have published a treatise of many volumes titled The elements of mathematics. Google Scholar
  10. 10.
    Gödel, Kurt (1906–1978). Abstract mathematician and logician.Google Scholar
  11. 11.
    Cohen, Paul (b. 1934). American mathematician. Proved the independence of the continuum hypothesis.Google Scholar
  12. 12.
    Bolyai, Jänos (1802–1860). Hungarian mathematician. Created hyperbolic geometry shortly after Lobachevski and independently of him.Google Scholar
  13. 13.
    Whitehead, Alfred (1861–1947). English mathematician and logician. Coauthor (with B. Russell) of Principia mathematica. Google Scholar
  14. 14.
    Quine, Willard (b. 1908). American mathematician. One of the greatest experts in mathematical logic and the foundations of mathematics.Google Scholar
  15. 15.
    Pólya, George (1887–1985). Hungarian mathematician. Author of works on functional analysis, mathematical statistics, and combinatorics.Google Scholar

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© Springer Science+Business Media New York 1995

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  • N. Ya. Vilenkin

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