The notion of group is fundamental in our days, not only in
mathematics, but also in classical mechanics, electromagnetism,
theory of relativity, quantum mechanics, theory of elementary
particles, etc. This notion has developed during a century and this
development is connected with the names of great mathematicians as
E. Galois, A. L. Cauchy, C. F. Gauss, W. R. Hamilton, C. Jordan, S.
Lie, E. Cartan, H. Weyl, E. Wigner, and of many others. In
mathematics, as in other sciences, the simple and fertile ideas
make their way with difficulty and slowly; however, this long
history would have been of a minor interest, had the notion of
group remained connected only with rather restricted domains of
mathematics, those in which it occurred at the beginning. But at
present, groups have invaded almost all mathematical disciplines,
mechanics, the largest part of physics, of chemistry, etc. We may
say, without exaggeration, that this is the most important idea
that occurred in mathematics since the invention of infinitesimal
calculus; indeed, the notion of group expresses, in a precise and
operational form, the vague and universal ideas of regularity and
symmetry. The notion of group led to a profound understanding of
the character of the laws which govern natural phenomena,
permitting to formulate new laws, correcting certain inadequate
formulations and providing unitary and non contradictory
formulations for the investigated phenomena."
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