Mathematical Problems : Lecture delivered before the International Congress of…

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Author Hilbert, David, 1862-1943
Translator Newson, Mary Frances Winston, 1869-1959
Title Mathematical Problems : Lecture delivered before the International Congress of Mathematicians at Paris in 1900
Original Publication Lancaster & New York: The Macmillan Company, 1902.
Contents Cantor's problem of the cardinal number of the continuum -- The compatibility of the arithmetical axioms -- The equality of the volumes of two tetrahedra of equal bases and equal altitudes -- Problem of the straight line as the shortest distance between two points -- Lie's concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group -- Mathematical treatment of the axioms of physics -- Irrationality and transcendence of certain numbers -- Problems of prime numbers -- Proof of the most general law of reciprocity in any number field -- Determination of the solvability of a diophantine equation -- Quadratic forms with any algebraic numerical coefficients -- Extension of Kronecker's theorem on abelian fields to any algebraic realm of rationality -- Impossibility of the solution of the general equation of the 7th degree by means of functions of only two arguments -- Proof of the finiteness of certain complete systems of functions -- Rigorous foundation of Schubert's enumerative calculus -- Problem of the topology of algebraic curves and surfaces -- Expression of definite forms by squares -- Building up of space from congruent polyhedra -- Are the solutions of regular problems in the calculus of variations always necessarily analytic?
The general problem of boundary values -- Proof of the existence of linear differential equations having a prescribed monodromic group -- Uniformizatiom of analytic relation's by means of automorphic functions -- Further development of the methods of the calculus of variations.
Credits Laura Natal Rodrigues (Images generously made available by The Internet Archive.)
Language English
LoC Class QA: Science: Mathematics
Subject Mathematics
Category Text
EBook-No. 71655
Release Date
Copyright Status Public domain in the USA.
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