A. de M. on Niels Henrik Abel

“He was sent in 1815 to the cathedral school of Christiania, where he did not show any remarkable sign of progress, until 1818 when M. Holmboe, a newly-appointed professor of mathematics, afterwards the writer of Abel's life, and editor of his works, discovered his talent for mathematics, and aided him in pursuing those sciences beyond the elements.”

“In the obituary published by Crelle, in his "Journal," he states distinctly that the large number of important memoirs which Abel had ready for publication was the immediate reason of the "Journal" being undertaken.”

“Nothing can be a severer trial to a mathematician's character than the publication of his loose papers; but, however crude the speculation, Abel is never lowered. He had read comparatively so little, that all which he has left bears the stamp of his own most original power; and there is not much which fails to leave the impression made on Legendre by his treatment of elliptic functions. ...The frankness of the acknowledgment made by Legendre, and the spirited manner in which the old man set to work to incorporate the new discoveries into his own books, will never be forgotten by any biographer of Abel. It is unnecessary to specify the particular methods of the latter; all who study the subject of elliptic functions are fully aware how much is due to him.”

“He appears to have fully developed in his own mind the subject of the separation of symbols of operation and quantity, not indeed to the extent of founding its results upon an algebraical theory, but to that of giving the theory a wider amount of application. He was a daring generalizer, and sometimes went too far: had he lived, he would have corrected some of his writings. And yet he appears to have been deeply impressed with the notion that a great part of mathematical analysis is rendered unsound by the employment of divergent series.”