David Hilbert is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
Hilbert is also known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.
THE FOUNDATIONS OF GEOMETRY
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BN ID:
2940016350462
- Publisher: OGB
- Publication date: 03/05/2013
- Sold by: Barnes & Noble
- Format: eBook
- File size: 8 MB
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A systematic discussion of the axioms upon which the Euclidean Geometry is based. By DAVID HILBERT, Professor of Mathematics, University of Göttingen. Translated by E. J. Townsend, University of Illinois.
Defining the elements of geometry, points, straight lines, and planes, as abstract things, David Hilbert sets up in this book a simple and complete set of independent axioms defining the mutual relations of these elements in accordance with the principles of geometry; that is, in accordance with our intuitions of space.
The purpose and importance of the work is his systematic discussion of the relations of these axioms to one another and the bearing of each upon the logical development of the Euclidean geometry.
The most important propositions of geometry are also demonstrated and in such a manner as to show exactly what axioms underlie and make possible the demonstration. The work is therefore not only of mathematical importance as a contribution to the purifying of mathematics from philosophical speculation, but it is of pedagogical importance in showing the simplest and most logical development of our analysis of space relations.
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