Quelle tête celle du jeune Norvégien!
– Adrien-Marie Legendre (1752-1833)
Two of Abstract Algebra‘s most illustrious pioneers were Évariste Galois (1811–1832) and Niels Henrik Abel (1802-1829). There are many similarities between these two great thinkers: both Galois and Abel made important contributions at a very tender age, both died prematurely (Galois died in a duel at the age of 20, Abel died of tuberculosis at the age of 26), and neither Galois’ nor Abel’s work were fully appreciated until much after their tragic deaths. I will focus on Abel, Norway’s greatest mathematician.
[ Norwegian NK1483 stamp portraying Niels Henrik Abel ]
During his short life, Abel worked on various areas of Mathematics, such as functional equations, integral transforms, series, elliptic integrals, and the solution of algebraic equations. If you want to know more about Abel‘s work and contributions, I suggest you read Christian Houzel’s The Work of Niels Henrik Abel (PDF – 3.57 MB). Some of Niels Henrik Abel’s manuscripts are available at The Abel Prize:
- Recherches sur les fonctions elliptiques (PDF – 6.71 MB)
- Note sur quelques formules elliptiques (PDF – 1.47 MB)
- Recherches sur les fonctions elliptiques II (PDF – 4.52 MB)
If you are interested in the “Archaeology of Mathematics”, you might find the manuscripts quite interesting.