RePoSS #11: The Mathematics of Niels Henrik Abel: Continuation ...

2.3. The European tour 27
the French Revolution. Later in the application procedure, Göttingen, the seat of the
German champion of mathematics GAUSS was added to the travel plan.
In his first period of creative mathematical production, 1823–24, while inspired
by HANSTEEN and DEGEN (see above), ABEL devoted his attention to the theory of
integration in the tradition of EULER’S Institutiones calculi integralis and LEGENDRE’S
Traité de calcul integral. By 1824, ABEL had documented his “exceptional abilities in the
mathematical sciences” 29 an example of which HANSTEEN presented to the collegium
in the form of a manuscript. ABEL had hoped that — besides the travel grant — the
collegium would support publication of the result which he believed had international
importance and could serve as a door opener on his tour. However, the collegium
decided to only support a travel grant for ABEL to go to the Continent. There was only
one condition; the grant was only to begin in 1825; until then ABEL had to prepare by
studying the “learned languages”, which in particular meant French. 30
2.3.1 Objectives and plans
In the application to the collegium, sources to the contemporary Norwegian rank-
ing of the mathematical centres may be found. The choices were mainly made by
ABEL’S benefactors, the mathematics professors HANSTEEN and RASMUSSEN. When
they first proposed sending ABEL abroad they suggested that he should go to “the
places abroad where the most distinguished mathematicians of our time are located,
perhaps primarily to Paris”. 31 In ABEL’S official application to the King, he wrote:
“After I have thus in this country by the use of the available tools sought to
approach the erected goal, it would be very beneficial to me to acquaint myself,
during a stay abroad at different universities in particular in Paris where so many
distinguished mathematicians are located, with the newest creations in the science
[mathematics] and enjoy the guidance of those men who in our time have brought
it [mathematics] to such a remarkable height.” 32
Only of July 4th 1825 did the idea of sending ABEL to Göttingen enter into the ap-
plication when the collegium applied for the grant to be made effective. ABEL submit-
ted a more detailed travel plan which RASMUSSEN was supposed to comment upon
to the collegium; this plan is no longer extant. 33 Two months later, on September 7,
ABEL embarked on his European tour.
29 HANSTEEN’S opinion as expressed in the accommodating letter from the collegium academicum to
the department of the church (N. H. Abel, 1902d, 7).
30 (ibid., 12).
31 (ibid., 7).
32 “Efter at jeg saaledes her i Landet ved de her forhaanden værende Hjelpemidler har stræbet at
nærme mig det foresatte Maal, vilde det være mig særdeles gavnligt ved et Ophold i Udlandet ved
forskjellige Universiteter, især i Paris hvor saa mange i udmærkede Mathematikere findes, at blive
bekjendt med de nyeste Frembringelser i Videnskaben og nyde de Mænds Veiledning som i vor
Tidsalder have bragt den til en saa betydelig Høide.” (ibid., 13).
33 (ibid., 20, footnote).