Project Gutenberg
2023-09-15
Public domain in the USA.
224
Hilbert, David
1862
1943
Hilbert, D. (David)
Newson, Mary Frances Winston
1869
1959
Winston, Mary Frances‏
Winston, Mary F.
Mathematical Problems : $b Lecture delivered before the International Congress of Mathematicians at Paris in 1900
$aLancaster & New York :$bThe Macmillan Company, $c1902.
Wikipedia page about this book: https://en.wikipedia.org/wiki/Hilbert%27s_problems
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.
Laura Natal Rodrigues (Images generously made available by The Internet Archive.)
https://archive.org/details/sim_american-mathematical-society-bulletin_1902-07_8/mode/1up
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