Editing Norbert Wiener (section)

===Harvard and World War I===
The next year he returned to Harvard, while still continuing his philosophical studies. Back at Harvard, Wiener became influenced by [[Edward Vermilye Huntington]], whose mathematical interests ranged from axiomatic foundations to engineering problems. Harvard awarded Wiener a [[PhD]] in June&nbsp;1913, when he was only 19&nbsp;years old, for a dissertation on [[mathematical logic]] (a comparison of the work of [[Ernst Schröder (mathematician)|Ernst Schröder]] with that of [[Alfred North Whitehead]] and [[Bertrand Russell]]), supervised by Karl Schmidt, the essential results of which were published as {{harvp|Wiener|1914}}. He was one of the youngest to achieve such a feat. In that dissertation, he was the first to state publicly that [[ordered pair]]s can be defined in terms of elementary [[set theory]]. Hence [[relation (mathematics)|relations]] can be defined by set theory, thus the theory of relations does not require any axioms or primitive notions distinct from those of set theory. In 1921, [[Kazimierz Kuratowski]] proposed a simplification of Wiener's definition of ordered pairs, and that simplification has been in common use ever since. It is <math>\ \left( x, y \right) = \bigl\{ \left\{ x \right\}, \left\{x, y \right\}\ \bigr\} ~.</math>

In 1914, Wiener traveled to Europe, to be taught by [[Bertrand Russell]] and [[G. H. Hardy]] at [[University of Cambridge|Cambridge University]], and by [[David Hilbert]] and [[Edmund Landau]] at the [[University of Göttingen]]. At Göttingen he also attended three courses with [[Edmund Husserl]] "one on Kant's ethical writings, one on the principles of Ethics, and the seminar on Phenomenology." (Letter to Russell, c. June or July, 1914). During 1915–1916, he taught philosophy at Harvard, then was an engineer for [[General Electric]] and wrote for the ''[[Encyclopedia Americana]]''. Wiener was briefly a journalist for the ''[[Boston Herald]]'', where he wrote a feature story on the poor labor conditions for mill workers in [[Lawrence, Massachusetts]], but he was fired soon afterwards for his reluctance to write favorable articles about a politician the newspaper's owners sought to promote.<ref>{{harvnb|Conway|Siegelman|2005|p=45}}</ref>

Although Wiener eventually became a staunch pacifist, he eagerly contributed to the war effort in World War I. In 1916, with [[United States in World War I|America's entry into the war]] drawing closer, Wiener attended a training camp for potential military officers but failed to earn a commission. One year later Wiener again tried to join the military, but the government again rejected him due to his poor eyesight. In the summer of 1918, [[Oswald Veblen]] invited Wiener to work on [[ballistics]] at the [[Aberdeen Proving Ground]] in Maryland.<ref>{{harvnb|Conway|Siegelman|2005|pp=41–43}}</ref> Living and working with other mathematicians strengthened his interest in mathematics. However, Wiener was still eager to serve in uniform and decided to make one more attempt to enlist, this time as a common soldier. Wiener wrote in a letter to his parents, "I should consider myself a pretty cheap kind of a swine if I were willing to be an officer but unwilling to be a soldier."<ref>{{harvnb|Conway|Siegelman|2005|p=43}}</ref> This time the army accepted Wiener into its ranks and assigned him, by coincidence, to a unit stationed at Aberdeen, Maryland. World War I ended just days after Wiener's return to Aberdeen and Wiener was discharged from the military in February 1919.<ref>{{harvnb|Conway|Siegelman|2005|pp=43–44}}</ref>