Нильс Хенрик Абель цитаты

Нильс Хенрик Абель фото
0   0

Нильс Хенрик Абель

Дата рождения: 5. Август 1802
Дата смерти: 6. Апрель 1829

Реклама

Нильс Хе́нрик А́бель — норвежский математик.

Подобные авторы

Тур Хейердал фото
Тур Хейердал9
Известный путешественник.
Эдвард Григ фото
Эдвард Григ5
норвежский композитор периода романтизма, музыкальный дея...
Эдвард Мунк фото
Эдвард Мунк5
норвежский живописец и график, театральный художник, теор...
Давид Гильберт фото
Давид Гильберт7
немецкий математик
 Анаксагор фото
Анаксагор6
древнегреческий философ, математик и астроном, основополо...
Дьёрдь Пойа фото
Дьёрдь Пойа2
венгерский, швейцарский и американский математик
Симона Вейль фото
Симона Вейль17
французский философ и религиозный мыслитель

Цитаты Нильс Хенрик Абель

„My work in the future must be devoted entirely to pure mathematics in its abstract meaning. I shall apply all my strength to bring more light into the tremendous obscurity which one unquestionably finds in analysis. It lacks so completely all plan and system that it is peculiar that so many have studied it. The worst of it is, it has never been treated stringently. There are very few theorems in advanced analysis which have been demonstrated in a logically tenable manner. Everywhere one finds this miserable way of concluding from the special to the general, and it is extremely peculiar that such a procedure has led to do few of the so-called paradoxes. It is really interesting to seek the cause.
In analysis, one is largely occupied by functions which can be expressed as powers. As soon as other powers enter—this, however, is not often the case—then it does not work any more and a number of connected, incorrect theorems arise from false conclusions. I have examined several of them, and been so fortunate as to make this clear.... I have had to be extremely cautious, for the presumed theorems without strict proof... had taken such a stronghold in me, that I was continually in danger of using them without detailed verification.“

—  Niels Henrik Abel
Letter to Christoffer Hansteen (1826) as quoted by Øystein Ore, Niels Henrik Abel: Mathematician Extraordinary (1957) & in part by Morris Kline, Mathematical Thought from Ancient to Modern Times (1972) citing Œuvres, 2, 263-65

Реклама

„Lety5 - ay4 + by3 - cy2 + dy - e = 0be the general equation of the fifth degree and suppose that it can be solved algebraically,—i. e., that y can be expressed as a function of the quantities a, b, c, d, and e, composed of radicals. In this case, it is clear that y can be written in the formy = p + p1R1/m + p2R2/m +...+ pm-1R(m-1)/m,m being a prime number, and R, p, p1, p2, etc. being functions of the same form as y. We can continue in this way until we reach rational functions of a, b, c, d, and e. [Note: main body of proof is excluded]
... we can find y expressed as a rational function of Z, a, b, c, d, and e. Now such a function can always be reduced to the formy = P + R1/5 + P2R2/5 + P3R3/5 + P4R4/5, where P, R, P2, P3, and P4 are functions or the form p + p1S1/2, where p, p1 and S are rational functions of a, b, c, d, and e. From this value of y we obtainR1/5 = 1/5(y1 + α4y2 + α3y3 + α2y4 + α y5) = (p + p1S1/2)1/5,whereα4 + α3 + α2 + α + 1 = 0.Now the first member has 120 different values, while the second member has only 10; hence y can not have the form that we have found: but we have proved that y must necessarily have this form, if the proposed equation can be solved: hence we conclude that
It is impossible to solve the general equation of the fifth degree in terms of radicals.
It follows immediately from this theorem, that it is also impossible to solve the general equations of degrees higher than the fifth, in terms of radicals.“

—  Niels Henrik Abel
A Memoir on Algebraic Equations, Proving the Impossibility of a Solution of the General Equation of the Fifth Degree (1824) Tr. W. H. Langdon, as quote in A Source Book in Mathematics (1929) ed. David Eugene Smith

Сегодня годовщина
Отто Лилиенталь фото
Отто Лилиенталь1
немецкий инженер 1848 - 1896
Лариса Андреевна Гузеева фото
Лариса Андреевна Гузеева21
советская и российская актриса театра и кино, телеведущая 1959
Джон Рокфеллер фото
Джон Рокфеллер27
американский предприниматель, филантроп, первый долларовы... 1839 - 1937
Генрих Гиммлер фото
Генрих Гиммлер2
один из главных политических и военных деятелей Третьего ... 1900 - 1945
Другие 62 годовщин
Подобные авторы
Тур Хейердал фото
Тур Хейердал9
Известный путешественник.
Эдвард Григ фото
Эдвард Григ5
норвежский композитор периода романтизма, музыкальный дея...
Эдвард Мунк фото
Эдвард Мунк5
норвежский живописец и график, театральный художник, теор...
Давид Гильберт фото
Давид Гильберт7
немецкий математик