n a talk delivered in Leipzig (Germany) on
June 11, 1900, Friedrich Engel gave the
first public account of his newly discovered
description of the smallest exceptional Lie
group G2, and he wrote in the corresponding
note to the Royal Saxonian Academy of Sciences:
Moreover, we hereby obtain a direct defi-
nition of our 14-dimensional simple group
[G2] which is as elegant as one can wish for.
[En00, p. 73]1
Indeed, Engel's definition of G2 as the isotropy
group of a generic 3-form in 7 dimensions is at
the basis of a rich geometry that exists only on
7-dimensional manifolds, whose full beauty has
been unveiled in the last thirty years.
This article is devoted to a detailed historical