James Waddell Alexander II was an important mathematician and topologist of the pre-WW II era and part of an influential Princeton topology elite, which included Oswald Veblen, Solomon Lefschetz, and others. He was one of the first members of the Institute for Advanced Study (1933–1951), and also a professor at Princeton University (1920–1951).

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  • 1888-09-19 (xsd:date)
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  • 1971-09-23 (xsd:date)
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  • 1888-09-19 (xsd:date)
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  • 1971-09-23 (xsd:date)
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  • James Waddell Alexander II was an important mathematician and topologist of the pre-WW II era and part of an influential Princeton topology elite, which included Oswald Veblen, Solomon Lefschetz, and others. He was one of the first members of the Institute for Advanced Study (1933–1951), and also a professor at Princeton University (1920–1951). He was a pioneer in algebraic topology, setting the foundations for Henri Poincaré's ideas on homology theory and furthering it by founding cohomology theory, which developed gradually in the decade after he gave a definition of cochain. For this, in 1928 he was awarded the Bôcher Memorial Prize. He also contributed to the beginnings of knot theory by inventing the Alexander invariant of a knot, which in modern terms is a graded module obtained from the homology of a "cyclic covering" of the knot complement. From this invariant, he defined the first of the polynomial knot invariants. With Garland Briggs, he also gave a combinatorial description of knot invariance based on certain moves, now (against the history) called the Reidemeister moves; and also a means of computing homological invariants from the knot diagram. Alexander was also a noted mountaineer, having succeeded in many major ascents, e.g. in the Swiss Alps and Colorado Rockies. The Alexander's Chimney, in the Rocky Mountain National Park, is named after him. When in Princeton, he liked to climb the university buildings, and always left his office window on the top floor of Fine Hall open so that he could enter by climbing the building. Alexander came from an old, distinguished Princeton family. He was the only child of the American portrait painter John White Alexander and Elizabeth Alexander. His maternal grandfather, James Waddell Alexander, was the president of the Equitable Life Assurance Society. Alexander's affluence and upbringing allowed him to interact with high society in America and elsewhere. He married Natalia Levitzkaja in 1917, a Russian woman, and they would frequently spend time, until 1937, in the Chamonix area of France, where he would also climb mountains and hills. Towards the end of his life, Alexander became a recluse. He was known as a socialist and his prominence brought him to the attention of McCarthyists. The atmosphere of the McCarthy era pushed him into a greater seclusion. He was not seen in public after 1954, when he appeared to sign a letter supporting J. Robert Oppenheimer.
  • James Waddell Alexander II war ein bedeutender Topologe, Professor an der Princeton-Universität und eines der ersten Mitglieder des Institute for Advanced Study.
  • James Waddell Alexander II oli merkittävä topologi toista maailmansotaa edeltäneellä ajalla ja osa vaikutusvaltaista Princetonilaista topologieliittiä, johon kuuluivat Oswald Veblen, Solomon Lefschetz ja muita. Hän oli yksi Princetonilaisen-tutkimuskeskuksen ensimmäisistä jäsenistä. Hän toimi myös Princetonin yliopiston professorina.
  • James Waddell Alexander II was een wiskundige en topoloog uit de periode tussen de beide wereldoorlogen. Hij maakte deel uit van de invloedrijke kring van topologen in Princeton. Zijn collega's daar waren Oswald Veblen, Solomon Lefschetz en anderen. Hij was een van de eerste leden van de Institute for Advanced Study (1933-1951) en van 1920 tot 1955 hoogleraar aan de Universiteit van Princeton.
  • Дже́ймс Уэ́дделл Алекса́ндер — американский математик. Основные работы лежат в области алгебраической топологии. Доказал топологическую инвариантность симплициальных гомологий, поставив на твёрдый фундамент топологические работы А. Пуанкаре. Исследовал «двойственность Александера» — связь между гомологическими свойствами взаимно дополнительных подмножеств топологического пространства (для полиэдров). Александер также ввёл понятие когомологии, которое приобрело большое значение в топологии и особенно в гомологической алгебре (Независимо от него это понятие ввёл А. Н. Колмогоров). Был одним из основателем теории узлов, где ввёл инвариант Александера. С основания знаменитого Института перспективных исследований в Принстоне, был одним из его членов. Был известен также как альпинист (его имя носит кратер Александера в Скалистых горах). Будучи человеком левых взглядов подвергался нападкам во время сенатора Маккарти, в 1954 подписал письмо в защиту Р. Оппенгеймера.
  • 詹姆斯·韋德爾·亞歷山大（James Waddell Alexander II）（1888年9月19日－1971年9月23日），美國拓撲學家，普林斯頓高等研究院最早期的成員之一。 他的學術生涯大部分時間都在普林斯頓大學。他在那裡學習數學和物理，1910年和1911年取得學士和碩士學位後又留在那裡任導師，後來曾到歐洲留學。1915年在普林斯頓取得博士學位，在母校任教。兩次世界大戰期間，他都參與了軍事工作。 在數學上，他是代數拓撲學專家： 證明了單純形的同調是拓撲不變。 紐結理論： Reidemeister moves 亞歷山大多項式 同調論的創立者之一 提出亞歷山大帶角球 在數學之外，他亦喜愛攀山，踏足過阿爾卑斯山脈和洛磯山脈。洛磯山公園內的Alexander's Chimney便是以他命名。在普林斯頓時，他的辦公室窗戶總是開着，以便他從地上攀進去。 他可謂來自上流社會。父親約翰·懷特·亞歷山大（John White Alexander）是美國人像畫家，同樣叫詹姆斯·韋德爾·亞歷山大的祖父是美國公平人壽保險協會主席。豐富的遺產令他在不領薪金的情況之下仍能成為百萬富翁。 由於他是社會主義者，在當時麥卡錫主義盛行的時代，令他1951年退休後不得不隱居。1954年他簽署了一封支持羅伯特·奧本海默的信，以後就沒公開出現。
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  • James Waddell Alexander II
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  • James Waddell Alexander II was an important mathematician and topologist of the pre-WW II era and part of an influential Princeton topology elite, which included Oswald Veblen, Solomon Lefschetz, and others. He was one of the first members of the Institute for Advanced Study (1933–1951), and also a professor at Princeton University (1920–1951).
  • James Waddell Alexander II war ein bedeutender Topologe, Professor an der Princeton-Universität und eines der ersten Mitglieder des Institute for Advanced Study.
  • James Waddell Alexander II oli merkittävä topologi toista maailmansotaa edeltäneellä ajalla ja osa vaikutusvaltaista Princetonilaista topologieliittiä, johon kuuluivat Oswald Veblen, Solomon Lefschetz ja muita. Hän oli yksi Princetonilaisen-tutkimuskeskuksen ensimmäisistä jäsenistä. Hän toimi myös Princetonin yliopiston professorina.
  • James Waddell Alexander II was een wiskundige en topoloog uit de periode tussen de beide wereldoorlogen. Hij maakte deel uit van de invloedrijke kring van topologen in Princeton. Zijn collega's daar waren Oswald Veblen, Solomon Lefschetz en anderen. Hij was een van de eerste leden van de Institute for Advanced Study (1933-1951) en van 1920 tot 1955 hoogleraar aan de Universiteit van Princeton.
  • Дже́ймс Уэ́дделл Алекса́ндер — американский математик. Основные работы лежат в области алгебраической топологии. Доказал топологическую инвариантность симплициальных гомологий, поставив на твёрдый фундамент топологические работы А. Пуанкаре.
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  • James Waddell Alexander II
  • James Alexander (Mathematiker)
  • James Waddell Alexander
  • James Alexander
  • Александер, Джеймс Уэдделл
  • 詹姆斯·韋德爾·亞歷山大
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