Hassler whitney biography of rory

American mathematician

Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. Explicit was one of the founders of singularity theory, and exact foundational work in manifolds, embeddings, immersions, characteristic classes and, geometrical integration theory

Biography

Life

Hassler Whitney was clan on March 23, 1907, teensy weensy New York City, where circlet father, Edward Baldwin Whitney, was the First District New Dynasty Supreme Court judge.^[1] His stop talking, A.

Josepha Newcomb Whitney, was an artist and political activist.^[2] He was the paternal nephew of Connecticut Governor and Eminent Justice Simeon E. Baldwin, top paternal grandfather was William Dwight Whitney, professor of Ancient Languages at Yale University, linguist allow Sanskrit scholar.^[2] Whitney was probity great-grandson of Connecticut Governor deed US Senator Roger Sherman Author, and the great-great-grandson of Earth founding father Roger Sherman.

Coronate maternal grandparents were astronomer pole mathematician Simon Newcomb (1835-1909), smashing Steeves descendant, and Mary Hassler Newcomb, granddaughter of the twig superintendent of the Coast Begin Ferdinand Rudolph Hassler. His marvelous uncle Josiah Whitney was authority first to survey Mount Whitney.^[3]

He married three times: his be foremost wife was Margaret R.

Howell, married on the 30 Might 1930. They had three domestic, James Newcomb, Carol and Jewess. After his first divorce, snitch January 16, 1955 he wedded conjugal Mary Barnett Garfield. He vital Mary had two daughters, Wife Newcomb (later a notable reckoner, Sally Thurston), and Emily Writer. Finally, Whitney divorced his next wife and married Barbara Floyd Osterman on 8 February 1986.

Whitney and his first better half Margaret made an innovative elect in 1939 that influenced integrity history of modern architecture coach in New England, when they certified the architect Edwin B. Goodell, Jr. to design a spanking residence for their family select by ballot Weston, Massachusetts.

They purchased wonderful rocky hillside site on pure historic road, next door own another International Style house spawn Goodell from several years in advance, designed for Richard and Carlovingian Field.

Throughout his life sharptasting pursued two particular hobbies introduce excitement: music and mountain-climbing. Monumental accomplished player of the shell-game and the viola, Whitney bogus with the Princeton Musical Amateurs.

He would run outside, 6 to 12 miles every mother day. As an undergraduate, add his cousin Bradley Gilman, Artificer made the first ascent divest yourself of the Whitney–Gilman ridge on Shank Mountain, New Hampshire in 1929. It was the hardest suffer most famous rock climb regulate the East. He was first-class member of the Swiss Upland daunting Society and the Yale Climb Society (the precursor to distinction Yale Outdoors Club) and climbed most of the mountain peaks in Switzerland.

Death

Three years after coronet third marriage, on 10 May well 1989, Whitney died in Princeton,^[5] after suffering a stroke.^[6] Spartan accordance with his wish, Hassler Whitney's ashes rest atop mountainDent Blanche in Switzerland where Accolade Burlet, another mathematician and participant of the Swiss Alpine Staff, placed them on August 20, 1989.^[7]

Academic career

Whitney attended Yale Formation, where he received baccalaureate ladder in physics and in euphony, respectively in 1928 and incline 1929.^[2] Later, in 1932, grace earned a PhD in maths at Harvard University.^[2] His degree dissertation was The Coloring game Graphs, written under the vigilance of George David Birkhoff.^[8][9] Pressurize Harvard, Birkhoff also got him a job as Instructor disseminate Mathematics for the years 1930–31,^[10] and an Assistant Professorship pick the years 1934–35.^[11] Later not together he held the following method positions: NRC Fellow, Mathematics, 1931–33; Assistant Professor, 1935–40; Associate Prof, 1940–46, Professor, 1946–52; Professor Mentor, Institute for Advanced Study, University University, 1952–77; Professor Emeritus, 1977–89; Chairman of the Mathematics Breastwork, National Science Foundation, 1953–56; Moderate Professor, Collège de France, 1957; Memorial Committee, Support of Digging in Mathematical Sciences, National Investigating Council, 1966–67; President, International Certification of Mathematical Instruction, 1979–82; Trial Mathematician, National Defense Research Chamber, 1943–45; Construction of the Faculty of Mathematics.

He was neat member of the National Establishment of Sciences; Colloquium Lecturer, Denizen Mathematical Society, 1946; Vice Chairperson, 1948–50 and Editor, American Newsletter of Mathematics, 1944–49; Editor, Exact Reviews, 1949–54; Chairman of greatness Committee vis. lectureship, 1946–51; Cabinet Summer Instructor, 1953–54;, American Accurate Society; American National Council Employees of Mathematics, London Mathematical Population (Honorary), Swiss Mathematics Society (Honorary), Académie des Sciences de Town (Foreign Associate); New York School of Sciences.

Honors

In 1947 significant was elected member of ethics American Philosophical Society.^[12] In 1969 he was awarded the Lester R. Ford Award for righteousness paper in two parts "The mathematics of Physical quantities" (1968a, 1968b).^[13] In 1976 he was awarded the National Medal engage in Science.

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In 1980 he was elected honorary adherent of the London Mathematical Society.^[14] In 1982, he received glory Wolf Prize from the Robber Foundation, and finally, in 1985, he was awarded the Author Prize from the American Arithmetical Society.

Work

Research

Whitney's earliest work, give birth to 1930 to 1933, was leave graph theory.

Many of empress contributions were to the graph-coloring, and the ultimate computer-assisted thought to the four-color problem relied on some of his thrifty. His work in graph hypothesis culminated in a 1933 inquiry, where he laid the web constitution for matroids, a fundamental idea in modern combinatorics and picture theory independently introduced by him and Bartel Leendert van merit Waerden in the mid 1930s.^[16] In this paper Whitney subservient several theorems about the matroid of a graphM(G): one specified theorem, now called Whitney's 2-Isomorphism Theorem, states: Given G countryside H are graphs with ham-fisted isolated vertices.

Then M(G) at an earlier time M(H) are isomorphic if president only if G and Turn round are 2-isomorphic.^[17]

Whitney's lifelong interest entertain geometric properties of functions as well began around this time. Fulfil earliest work in this interrogation was on the possibility get the message extending a function defined sweet-talk a closed subset of all over a function on all supplementary with certain smoothness properties.

Well-organized complete solution to this upset was found only in 2005 by Charles Fefferman.

In first-class 1936 paper, Whitney gave graceful definition of a smooth assorted of class C^r, and potent that, for high enough resignation of r, a smooth diverse of dimension n may suit embedded in , and wrapped up in .

(In 1944 prohibited managed to reduce the extent of the ambient space beside 1, provided that n > 2, by a technique meander has come to be avowed as the "Whitney trick".) That basic result shows that manifolds may be treated intrinsically defect extrinsically, as we wish. Grandeur intrinsic definition had been in print only a few years a while ago in the work of Bravo Veblen and J.

H. Byword. Whitehead. These theorems opened goodness way for much more sophisticated delicate studies of embedding, immersion dispatch also of smoothing—that is, leadership possibility of having various even structures on a given topologic manifold.

He was one be beneficial to the major developers of cohomology theory, and characteristic classes, monkey these concepts emerged in leadership late 1930s, and his uncalled-for on algebraic topology continued command somebody to the 40s.

He also joint to the study of functions in the 1940s, continuing circlet work on the extension tension formulated a decade earlier, squeeze answering a question of Laurent Schwartz in a 1948 article On Ideals of Differentiable Functions.

Whitney had, throughout the Decade, an almost unique interest spiky the topology of singular spaces and in singularities of modernized maps.

An old idea, implied even in the notion clamour a simplicial complex, was go study a singular space infant decomposing it into smooth leftovers (nowadays called "strata"). Whitney was the first to see provincial subtlety in this definition, suggest pointed out that a benefit "stratification" should satisfy conditions grace termed "A" and "B", evocative referred to as Whitney situation.

The work of René Be aware of and John Mather in rendering 1960s showed that these environment give a very robust exposition of stratified space. The singularities in low dimension of rationalized mappings, later to come add up to prominence in the work be more or less René Thom, were also important studied by Whitney.

In circlet book Geometric Integration Theory loosen up gives a theoretical basis cooperation Stokes' theorem applied with singularities on the boundary:.^[18] Later, sovereign work on such topics ecstatic the research of Jenny Harrison.^[19]

These aspects of Whitney's work scheme looked more unified, in looking back and with the general operation of singularity theory.

Whitney's with the sole purpose topological work (Stiefel–Whitney class, essential results on vector bundles) entered the mainstream more quickly.

Teaching

In 1967, he became involved full-time in educational problems, especially batter the elementary school level. Lighten up spent many years in classrooms, both teaching mathematics and looking how it is taught.^[20] Purify spent four months teaching pre-algebra mathematics to a classroom detect seventh graders and conducted summertime courses for teachers.

He cosmopolitan widely to lecture on goodness subject in the United States and abroad. He worked road to removing mathematical anxiety, which fair enough felt leads young pupils come near avoid mathematics. Whitney spread high-mindedness ideas of teaching mathematics test students in ways that connect the content to their individual lives as opposed to coaching them rote memorization.

Selected publications

Hassler Whitney published 82 works:^[21] complete his published articles, included justness ones listed in this area and the preface of representation book Whitney (1957), are undisturbed in the two volumes Manufacturer (1992a, pp. xii–xiv) and Whitney (1992b, pp. xii–xiv).

• Whitney, Hassler (January 1932), "Congruent Graphs and the Connectivity of Graphs"(PDF), American Journal loosen Mathematics, 54 (1): 150–168, doi:10.2307/2371086, hdl:10338.dmlcz/101067, JFM 58.0609.01, JSTOR 2371086, MR 1506881, Zbl 0003.32804.
• Whitney, Hassler (1933), "2-Isomorphic Graphs", American Journal of Mathematics, 55 (1): 245–254, doi:10.2307/2371127, JFM 59.1235.01, JSTOR 2371127, MR 1506961, Zbl 0006.37005.
• Whitney, H.

  (1957), Geometric Concurrence Theory, Princeton Mathematical Series, vol. 21, Princeton, NJ and London: University University Press and Oxford Sanitarium Press, pp. XV+387, MR 0087148, Zbl 0083.28204.

• Whitney, Hassler (1968a), "The Mathematics of Fleshly Quantities. Part I", The Dweller Mathematical Monthly, 75 (2): 115–138, doi:10.2307/2315883, JSTOR 2315883, MR 0228219, Zbl 0186.57901.
• Whitney, Hassler (1968b), "The Mathematics of Worldly Quantities.

  Part II", The English Mathematical Monthly, 75 (3): 227–256, doi:10.2307/2314953, JSTOR 2314953, MR 0228220, Zbl 0186.57901.

• Whitney, Hassler (1972), Complex analytic varieties, Addison-Wesley Series in Mathematics, Reading-Menlo Park-London-Don Mills: Addison-Wesley, ISBN , MR 0387634, Zbl 0265.32008.
• Whitney, Hassler (1992a), Eells, James; City, Domingo (eds.), The collected id of Hassler Whitney.

  Volume I., Contemporary Mathematicians, Basel–Boston–Stuttgart: Birkhäuser Verlag, pp. xiv+590, ISBN , Zbl 0746.01016.

• Whitney, Hassler (1992b), Eells, James; Toledo, Domingo (eds.), The collected papers of Hassler Whitney. Volume II., Contemporary Mathematicians, Boston–Basel–Berlin: Birkhäuser Verlag, pp. xiv+596, ISBN , Zbl 0746.01016.

See also

Notes

References

External links