Mathematical Work
Abel gave a proof of the binomial theorem valid for all numbers, extending Euler's result which had held only for rationals. At age 19, he showed there is no general algebraic solution for the roots of a quintic equation, or any general polynomial equation of degree greater than four, in terms of explicit algebraic operations. To do this, he invented (independently of Galois) an extremely important branch of mathematics known as group theory, which is invaluable not only in many areas of mathematics, but for much of physics as well. Among his other accomplishments, Abel wrote a monumental work on elliptic functions which, however, was not discovered until after his death. When asked how he developed his mathematical abilities so rapidly, he replied "by studying the masters, not their pupils." Abel said famously of Carl Friedrich Gauss's writing style, “He is like the fox, who effaces his tracks in the sand with his tail.”
Read more about this topic: Niels Henrik Abel
Famous quotes containing the words mathematical and/or work:
“As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.”
—Blaise Pascal (16231662)
“The theater needs continual reminders that there is nothing more debasing than the work of those who do well what is not worth doing at all.”
—Gore Vidal (b. 1925)