© 2008

From Summetria to Symmetry: The Making of a Revolutionary Scientific Concept


  • Symmetry is a key concept in modern science

  • Its history has been distorted for various reasons

  • A critical account of the history of the concept sheds light on the dynamics of scientific change and the role of concepts in theory formation

  • The transition from the aesthetic concept of symmetry to its scientific usage is analyzed for the first time

  • Legendre’s pivotal role has not been noted at all in the secondary literature


Part of the Archimedes book series (ARIM, volume 20)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Giora Hon, Bernard R. Goldstein
      Pages 1-65
  3. Tradition: Ancient Perspectives and Their SurvivalintheEarlyModernEra

    1. Front Matter
      Pages 67-67
    2. Giora Hon, Bernard R. Goldstein
      Pages 69-91
    3. Giora Hon, Bernard R. Goldstein
      Pages 93-109
    4. Giora Hon, Bernard R. Goldstein
      Pages 111-155
  4. The Path to Revolution: Symmetry as a Modern Scientific Concept

    1. Front Matter
      Pages 177-177
    2. Giora Hon, Bernard R. Goldstein
      Pages 179-201
    3. Giora Hon, Bernard R. Goldstein
      Pages 263-293
  5. Back Matter
    Pages 295-335

About this book


The concept of symmetry is inherent to modern science, and its evolution has a complex history that richly exemplifies the dynamics of scientific change. This study is based on primary sources, presented in context: the authors examine closely the trajectory of the concept in the mathematical and scientific disciplines as well as its trajectory in art and architecture. The principal goal is to demonstrate that, despite the variety of usages in many different domains, there is a conceptual unity underlying the invocation of symmetry in the period from antiquity to the 1790s which is distinct from the scientific usages of this term that first emerged in France at the end of the 18th century. The key figure in revolutionizing the concept of symmetry is the mathematician, Adrien-Marie Legendre. His achievements in solid geometry (1794) are contrasted with the views of the philosopher, Immanuel Kant, on the directionality of space (1768).


History of Mathematics Immanuel Kant Legendre Moderne Perrault Scientific change Symmetry Vitruvius architecture science

Authors and affiliations

  1. 1.Dept. PhilosophyUniversity of HaifaIsrael
  2. 2.Fac. Art&SciencesUniversity of PittsburghPittsburghUSA

Bibliographic information


From the reviews:

“Hon and Goldstein’s book is, primarily, a historical study of the term ‘symmetry’ and the concepts associated with it up to the early 1800s. … a contribution to fruitful discussion between historians and philosophers of science. … For philosophers of science, such historical work is invaluable.”­­­ (Katherine Brading, Metascience, Vol. 19, March, 2010)