Abstract The article is devoted to the 125th anniversary of the Erlangen
program of F.
Klein. Its outstanding importance for development of mathematical science and
for formation of the modern mathematical concepts is pointed out. The influence
of the Erlangen program on creation of natural-scientific representations,
first of all physical, is analyzed. The special attention is given to the
role the Erlangen program has played in the history of mathematical education
in schools and universities.
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