“Abel proposed himself the problem of finding all equations solvable by radicals, and succeeded in solving all equations with commutative groups, now called Abelian equations. Among Abel's other achievements are the discovery of the elliptic functions and their fundamental properties, his famous theorem on the integration of algebraic functions [and] theorems on power series.”
“The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the impossibility of it. However, if I am not mistaken...”
Niels Henrik Abel
“On the whole, I do not like the French as well as the Germans; the French are extremely reserved toward strangers... Everybody works for himself without concern for others. All want to instruct, and n...”
Niels Henrik Abel
“It is readily seen that any theory written by Laplace will be superior to all produced of lower standing. It appears to me that if one wants to make progress in mathematics, one should study the maste...”
Niels Henrik Abel
“Like Jacobi and many other young men who became eminent mathematicians, Abel found the first exercise of his talent in the attempt to solve by algebra the general equation of the fifth degree. ...His ...”
Niels Henrik Abel
“Abel had sent to Gauss his proof of 1824 of the impossibility of solving equations of the fifth degree, to which Gauss never paid any attention. This slight, and a haughtiness of spirit which he assoc...”
Niels Henrik Abel