Geometry under Siege

  • Donald J. Albers


“Euclid Must Go!” With these words Jean Dieudonné attacked the standard one-year course in Euclidean geometry at a 1959 international conference devoted to improving mathematical education. Naturally his comments provoked a great controversy. His remarks at that meeting help to explain the battle that followed:

Let us assume for the sake of argument that one had to teach plane Euclidean geometry to mature minds from another world who had never heard of it... Then the whole course might, I think, be tackled in two or three of them being occupied by the description of the axiom system, one by its useful consequences and possibly a third one by a few mildly interesting exercises.

Everything else which now fills volumes of “elementary geometry”...and by that I mean, for instance, everything about triangles (it is perfectly feasible and desirable to describe the whole theory without even defining a triangle!) almost everything about inversion, systems of circles, conics, etc.,...has just as much relevance to what mathematicians (pure and applied) are doing today as magic squares or chess problems! [1]


Mathematics Teacher Euclidean Geometry Axiom System High School Teacher Geometric Intuition 
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  1. [1]
    Fehr, Howard F. (Ed.) New Thinking in School Mathematics: Organization for Economic Cooperation and Development. Report of the Royaumont Seminar, Paris, OECD, 1960.Google Scholar
  2. [2]
    Fawcett, Harold P. The Nature of Proof. Thirteenth Yearbook of the National Council of Teachers of Mathematics. Columbia University, 1938.Google Scholar
  3. [3]
    Gearhart, George. “What do mathematics teachers think about the high school geometry controversy?” Mathematics Teacher 68 (1975) 486–493.Google Scholar
  4. [4]
    Spivak, Michael. A Comprehensive Introduction to Differential Geometry, Vol. 5. Boston: Publish or Perish Press, 1975.Google Scholar

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Donald J. Albers

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