28 2. Basic notions of representation theory
advances with his id´ ee fixe, Lie finally acquired the mathematical
weaponry needed to answer the challenge of the Erlangen Program
and to tackle the theory of continuous transformation groups.
Living on the outskirts of Europe, Lie felt quite marginalized in
the European mathematics community. No students and very few for-
eign colleagues were interested in his research. He wrote his papers
in German but published them almost exclusively in Norwegian jour-
nals, preferring publication speed over wide accessibility. A few years
later he learned, however, that one French mathematician had won
the Grand Prix from the Acad´ emie des Sciences for independently
obtained results that yielded some special cases of Lie’s work on dif-
ferential equations. Lie realized that his Norwegian publications were
not the greatest publicity vehicle, and that he needed to make his
work better known in Europe. “If only I could collect together and
edit all my results,” he wistfully wrote to Klein [22, p. 77]. Klein’s
practical mind quickly found a solution. Klein, who then taught at
Leipzig, arranged for the young mathematician Friedrich Engel, a re-
cent doctoral student of his colleague, to go to Christiania and to
render Lie a helping mathematical hand.
Lie and Engel met twice daily for a polite conversation about
transformation groups. As Engel recalled, Lie carried his theory al-
most entirely in his head and dictated to Engel an outline of each
chapter, “a sort of skeleton, to be clothed by me with flesh and blood”
[22, p. 77]. Lie read and revised Engel’s notes, eventually producing
the first draft of a book-length manuscript.
When Klein left Leipzig to take up a professorship at G¨ottingen,
he arranged for the vacated chair of geometry to be offered to Lie.
Lie somewhat reluctantly left his homeland and arrived at Leipzig
with the intention of building “a healthy mathematical school” there
[22, p. 226]. He continued his collaboration with Engel, which cul-
minated in the publication of their joint three-volume work, Theorie
der Transformationsgruppen.
Lie’s ideas began to spread around Europe, finding a particularly
fertile ground in Paris. Inspired by Lie, Henri Poincar´ e remarked that
all mathematics was a tale about groups, and
Emile Picard wrote to
Lie, “Paris is becoming a center for groups; it is all fermenting in
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