"At nearly the same time with Abel, Jacobi published articles on elliptic functions. Legendre's favourite subject, so long neglected, was at last to be enriched by some extraordinary discoveries. The advantage to be derived by inverting the elliptic integral of the first kind and treating it as a function of its amplitude (now called elliptic function) was recognised by Abel, and a few months later also by Jacobi. A second fruitful idea, also arrived at independently by both, is the introduction of imaginaries leading to the observation that the new functions simulated at once trigonometric and exponential functions. For it was shown that while trigonometric functions had only a real period, and exponential only an imaginary, elliptic functions had both sorts of periods. These two discoveries were the foundations upon which Abel and Jacobi, each in his own way, erected beautiful new structures. Abel developed the curious expressions representing elliptic functions by infinite series or quotients of infinite products."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Florian Cajori, A History of Mathematics (1893)
https://en.wikiquote.org/wiki/Niels_Henrik_Abel
Revision History
No revisions have been submitted for this quote.
Categories
Niels Henrik Abel
Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This question was one of the outstanding open problems of his day, and had been unresolved for 250 years. He was also an innovator in the field of elliptic functions, discoverer of Abelian functions. Despite his achievem
35 quotes on TrueQuotesView all quotes by Niels Henrik Abel →
Related Quotes
"Lety5 - ay4 + by3 - cy2 + dy - e = 0be the general equation of the fifth degree and suppose that it can be solved alg…"
"My work in the future must be devoted entirely to pure mathematics in its abstract meaning. I shall apply all my stre…"
"On the whole, Divergant series are the work of the Devil and it's a Shame that one dares base any Demonstration on th…"
"On the whole, I do not like the French as well as the Germans; the French are extremely reserved toward strangers... …"
"It is readily seen that any theory written by Laplace will be superior to all produced of lower standing. It appears …"
"His memoirs on elliptic functions, originally published in Crelle's Journal (of which he was one of the founders), tr…"
"The name of Abelian function has been given to the higher transcendents of multiple periodicity which were first disc…"
"Abel criticised the use of infinite series, and discovered the well-known theorem which furnishes a test for the vali…"
"Like Jacobi and many other young men who became eminent mathematicians, Abel found the first exercise of his talent i…"
"The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several…"