Grundlagen der Geometrie

@article{MGrundlagenDG,
  title={Grundlagen der Geometrie},
  author={G. B. M.},
  journal={Nature},
  volume={80},
  pages={394-394}
}
THIS fascinating work has long since attained the rank of a classic, but attention may be directed to this new edition, which has various additions, mainly bibliographical, and seven supplements, which are reprints of papers by the author on topics related to that of his famous essay. Two of these can be enjoyed by readers with no exceptional mathematical knowledge. In the one on the equality of the base angles of an isosceles triangle, Dr. Hilbert proves, inter alia, the remarkable fact that… 

Survey of Non-Desarguesian Planes Charles Weibel

T he abstract study of projective geometry first arose in the work of J.-V. Poncelet (1822) and K. von Staudt (1847). About 100 years ago, axiomatic frameworks were developed by several people,

Perspective on Hilbert

  • D. Rowe
  • Art
    Perspectives on Science
  • 1997
As a discipline, the history of mathematics admits a wide variety of styles and methodologies. Even when the subject matter is reasonably well defined and clear, it can be fruitfully investigated in

A Most Interesting Draft for Hilbert and Bernays ’ “ Grundlagen der Mathematik

In 1934, in Bernays’ preface to the first edition of the first volume of Hilbert and Bernays’ monograph “Grundlagen der Mathematik”, a nearly completed draft of the the finally two-volume monograph

The last chapter of the Disquisitiones of Gauss

This exposition reviews what exactly Gauss asserted and what did he prove in the last chapter of {\sl Disquisitiones Arithmeticae} about dividing the circle into a given number of equal parts. In

On the Complexity of Hilbert's 17th Problem

TLDR
It is able to show, assuming a standard conjecture in complexity theory, that it is impossible that every non-negative, n-variate, degree four polynomial can be represented as a sum of squares of a small number of rational functions.

Angles in normed spaces

The concepts of angle, angle functions, and the question how to measure angles present old and well-established mathematical topics referring to the Euclidean space, and there exist also various

Axiomatizations of Hyperbolic and Absolute Geometries

A survey of finite first-order axiomatizations for hyperbolic and absolute geometries. 1. Hyperbolic Geometry Elementary Hyperbolic Geometry as conceived by Hilbert To axiomatize a geometry one needs

The twofold role of diagrams in Euclid’s plane geometry

TLDR
The purpose is to reformulate the thesis that many of Euclid’s geometric arguments are diagram-based in a quite general way, by describing what he takes to be the twofold role that diagrams play in Euclid's plane geometry (EPG).

Methods, concepts and ideas in mathematics : aspects of an evolution

ion from the individuals; they are then considered and studied in their totality from certain points of view. A next step is to study abstract totalities (sets). This is perhaps a general

Six mathematical gems from the history of distance geometry

TLDR
Heron's formula, Cauchy's theorem on the rigidity of polyhedra, Cayley's generalization of Heron's formulas to higher dimensions, Menger's characterization of abstract semi-metric spaces, and Schoenberg's equivalence of distance and positive semidefinite matrices are proved.
...