Search results
Results from the WOW.Com Content Network
Of the cleanly formulated Hilbert problems, numbers 3, 7, 10, 14, 17, 18, 19, and 20 have resolutions that are accepted by consensus of the mathematical community. Problems 1, 2, 5, 6, [ g ] 9, 11, 12, 15, 21, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems.
Unknown to Hilbert and Dehn, Hilbert's third problem was also proposed independently by Władysław Kretkowski for a math contest of 1882 by the Academy of Arts and Sciences of Kraków, and was solved by Ludwik Antoni Birkenmajer with a different method than Dehn's. Birkenmajer did not publish the result, and the original manuscript containing ...
Hilbert unified the field of algebraic number theory with his 1897 treatise Zahlbericht (literally "report on numbers"). He also resolved a significant number-theory problem formulated by Waring in 1770.
Corry (1996) and Schappacher (2005) and the English introduction to (Hilbert 1998) give detailed discussions of the history and influence of Hilbert's Zahlbericht. Some earlier reports on number theory include the report by H. J. S. Smith in 6 parts between 1859 and 1865, reprinted in Smith (1965), and the report by Brill & Noether (1894).
In mathematics, particularly in dynamical systems, the Hilbert–Arnold problem is an unsolved problem concerning the estimation of limit cycles.It asks whether in a generic [disambiguation needed] finite-parameter family of smooth vector fields on a sphere with a compact parameter base, the number of limit cycles is uniformly bounded across all parameter values.
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers , finite fields , and function fields .
A Hilbert prime is not necessarily a prime number; for example, 21 is a composite number since 21 = 3 ⋅ 7. However, 21 is a Hilbert prime since neither 3 nor 7 (the only factors of 21 other than 1 and itself) are Hilbert numbers. It follows from multiplication modulo 4 that a Hilbert prime is either a prime number of the form 4n + 1 (called a ...
Translated by W. Ewald as 'The Grounding of Elementary Number Theory', pp. 266–273 in Mancosu (ed., 1998) From Brouwer to Hilbert: The debate on the foundations of mathematics in the 1920s, Oxford University Press. New York. S.G. Simpson, 1988. Partial realizations of Hilbert's program (pdf). Journal of Symbolic Logic 53:349–363. R. Zach ...