Mathematical Problems : Lecture delivered before the International Congress of…
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"Mathematical Problems" by David Hilbert is a lecture delivered in 1900. Hilbert presented twenty-three unsolved mathematical problems that would shape twentieth-century mathematics. Delivered at the International Congress of Mathematicians in Paris, the lecture outlined challenges ranging from number theory to geometry. Some problems were solved quickly, while others remain unsolved today. Several problems proved too vague for definitive answers, yet work on these questions earned mathematicians the highest honors and continues to
drive mathematical research. (This is an automatically generated summary.)
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About this eBook
| 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. |
| Note | Wikipedia page about this book: en.wikipedia.org/wiki/Hilbert%27s_problems |
| 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 |
| ISBN (HTML) | 979-8-238-71655-8 |
| Release Date | Sep 15, 2023 |
| Copyright | Public domain in the USA. |
| Downloads | 289 downloads in the last 30 days. |
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