# John-Willard-Milnor

1130

280

215

28

<html lang="en" class="topic-desktop ui-chrome110 ui-chrome"><head></head><body data-leg="B" class="new-topic topic-desktop first-page-true user-ANONYMOUS user-ads md-desktop leg-b"><header id="header" class="bg-navy-dark"></header><main><div class="md-page-wrapper"><div id="content" class="md-content"><div class="md-article-container template-desktop"><div class="infinite-scroll-container article last"><article class="article-content container-lg qa-content px-0 pt-0 pb-40 py-lg-20 content " data-topic-id="383050"><div class="grid gx-0"><div class="col"><div class="h-100 ml-0 pr-sm-10 pr-lg-0 "><div class="h-100 grid gx-0 gx-sm-20"><div class="h-100 col-sm"><div class="h-100 infinite-pagination-container d-flex flex-column position-relative"><div class="grey-box w-100 grey-box-top
grey-box-bottom"><div class="grey-box-content mx-auto w-100"><div class="page2ref-true topic-content topic-type-BIOGRAPHY" data-student-article="false"><div class="reading-channel"><section data-level="1" id="ref1"><p class="topic-paragraph"><strong><span id="ref389127"></span>John Willard Milnor</strong> (born February 20, 1931, <span class="md-crosslink autoxref" data-show-preview="true">Orange</span>, <span class="md-crosslink autoxref" data-show-preview="true">New Jersey</span>, U.S.) is an American mathematician who was awarded the <span class="md-crosslink" data-show-preview="true">Fields Medal</span> in 1962 for his work in <span id="ref389128"></span><span class="md-crosslink">differential topology</span> and the <span class="md-crosslink" data-show-preview="true">Abel Prize</span> in 2011 for his work in topology, <span class="md-crosslink autoxref" data-show-preview="true">geometry</span>, and algebra.</p><p class="topic-paragraph">Milnor <span class="md-dictionary-link md-dictionary-tt-off eb" data-term="attended" data-type="EB">attended</span> <span class="md-crosslink" data-show-preview="true">Princeton University</span> (A.B., 1951; Ph.D., 1954), in New Jersey. He held an appointment at Princeton from 1954 to 1967 and, after several years at other institutions, joined the faculty at the Institute for Advanced Study, Princeton, in 1970. In 1989 he became director of the Institute for Mathematical Sciences at the <span class="md-crosslink autoxref" data-show-preview="true">State University of New York</span>, <span class="md-crosslink autoxref" data-show-preview="true">Stony Brook</span>.</p><p class="topic-paragraph">Milnor was awarded the Fields Medal at the International Congress of Mathematicians in Stockholm in 1962. His work was part of a revival of interest in a geometric approach to <span class="md-crosslink" data-show-preview="true">topology</span> in the 1950s. Early in the 20th century the field had been highly geometric, but in the 1930s and ’40s algebraic approaches dominated research. In particular, Milnor’s discovery of the 28 differentiable structures for the seven-dimensional sphere, <em>S</em><sup>7</sup>, in 1956 was instrumental in the development of the new field of <span class="md-dictionary-link md-dictionary-tt-off eb" data-term="differential" data-type="EB">differential</span> topology. Milnor dubbed these differentiable structures “<span id="ref1118351"></span>exotic spheres.” In 1963, in collaboration with French mathematician Michel Kervaire, he calculated the number of exotic spheres for dimensions greater than 4.</p><p class="topic-paragraph">Additionally, Milnor contributed to <span id="ref755493"></span><span class="md-crosslink" data-show-preview="true">algebraic geometry</span> on singular points of complex hypersurfaces, and in 1961 he showed that the <em>Hauptvermutung</em> (German: “main conjecture”), a principal conjecture in the theory of <span id="ref755494"></span><span class="md-crosslink" data-show-preview="true">manifolds</span> concerning triangulations of <em>n</em>-dimensional manifolds, which had been an open question since 1908, is not true for complexes in dimensions greater than 3. Beginning in the 1970s, he worked on <span class="md-crosslink" data-show-preview="true">complex dynamics</span>.</p><p class="topic-paragraph">Milnor was noted as an influential teacher, particularly through his books on the Morse theory and the <em>h</em>-cobordism theorem, which are universally regarded as models of mathematical <span class="md-dictionary-link md-dictionary-tt-off eb" data-term="exposition" data-type="EB">exposition</span>. His publications include <em>Differential Topology</em> (1958), <em>Morse Theory</em> (1963), <em>Topology from the Differentiable Viewpoint</em> (1965), and <em>Dynamics in One Complex Variable</em> (1999). His <em>Collected Papers</em> were published in five volumes from 1994 to 2010. He won the National Medal of Science in 1966.</p></section></div></div></div></div></div></div></div></div></div></div></article></div></div></div></div></main>