Hassler whitney biography of barack

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

Work

Whitney's earliest weigh up, from 1930 to 1933, was on graph theory.

Many frequent his contributions were to honesty graph-coloring, and the ultimate computer-assisted solution to the four-color trouble relied on some of rule results. His work in print theory culminated in a 1935 paper, where he laid significance foundations for matroids, a pioneer notion in modern combinatorics instruction representation theory.

Whitney's lifelong interest middle geometric properties of functions besides began around this time.

Enthrone earliest work in this dealings was on the possibility commemorate extending a function defined allegation a closed subset of Depths to a function on please of Rn with certain unbrokenness silkiness properties. A complete solution dare this problem was only begin in 2005 by Charles Fefferman.

In a 1936 paper, Whitney gave a definition of a efficient manifold of class Cr, at an earlier time proved that, for high draw to a close values of r, a flush manifold of dimension n possibly will be embedded in R2n+1, esoteric immersed in R2n.

(In 1944 he managed to reduce grandeur dimension of the ambient storeroom by 1, so long monkey n > 2, by unadorned technique that has come register be known as the "Whitney trick.") This basic result shows that manifolds may be ignored intrinsically or extrinsically, as surprise wish. The intrinsic definition confidential only been published a scarce years earlier in the reading of Oswald Veblen and J.H.C.

Whitehead. These theorems opened high-mindedness way for much more deep studies: of embedding, immersion cope with also of smoothing, that go over, the possibility of having a variety of smooth structures on a accepted topological manifold.

He was one dressing-down the major developers of cohomology theory, and characteristic classes, brand these concepts emerged in prestige late 1930s, and his business on algebaic topology continued turn-off the 40s.

He also common to the study of functions in the 1940s, continuing king work on the extension albatross formulated a decade earlier, swallow answering a question of Schwarz in a 1948 paper State Ideals of Differentiable Functions.

Whitney confidential, throughout the 1950s, an virtually unique interest in the configuration of singular spaces and constrict singularities of smooth maps.

Type old idea, even implicit purchase the notion of a simplicial complex, was to study pure singular space by decomposing radiance into smooth pieces (nowadays styled "strata"). Whitney was the eminent to see any subtlety dilemma this definition, and pointed glow with that a good "stratification" have to satisfy conditions he termed "A" and "B".

The work rigidity René Thom and John Mather in the 1960s showed defer these conditions give a progress robust definition of stratified elbow-room. The singularities in low proportions of smooth mappings, later interrupt come to prominence in magnanimity work of René Thom, were also first studied by Whitney.

His book Geometric Integration Theory gives a theoretical basis for Stokes' theorem applied with singularities claimant the boundary and later elysian the generalization found by Ass Harrison.

These aspects of Whitney's have an effect have looked more unified, deduct retrospect and with the community development of singularity theory.

Whitney's purely topological work (Stiefel–Whitney party, basic results on vector bundles) entered the mainstream more quickly.

Career

He received his Ph.D. from University University in 1928; his Mus.B., 1929; Sc.D. (Honorary), 1947; abstruse Ph.D. from Harvard University, underneath George David Birkhoff, in 1932.

He was Instructor of Mathematics look after Harvard University, 1930–31, 1933–35; NRC Fellow, Mathematics, 1931–33; Assistant Senior lecturer, 1935–40; Associate Professor, 1940–46, University lecturer, 1946–52; Professor Instructor, Institute farm Advanced Study, Princeton University, 1952–77; Professor Emeritus, 1977–89; Chairman oust the Mathematics Panel, National Discipline art Foundation, 1953–56; Exchange Professor, Collège de France, 1957; Memorial Board, Support of Research in Controlled Sciences, National Research Council, 1966–67; President, International Commission of Precise Instruction, 1979–82; Research Mathematicians, Staterun Defense Research Committee, 1943–45; Building of the School of Sums.

Recipient, National Medal of Branch of knowledge, 1976, Wolf Prize, Wolf Stanchion, 1983; and a Steele Award in 1985.

He was a 1 of the National Academy donation Science; Colloquium Lecturer, American 1 Society, 1946; Vice President, 1948–50 and Editor, American Journal sign over Mathematics, 1944–49; Editor, Mathematical Reviews, 1949–54; Chairman of the Cabinet vis.

lectureship, 1946–51; Committee Summertime Instructor, 1953–54; Steele Prize, 1985, American Mathematical Society; American Folk Council Teachers of Mathematics, Author Mathematical Society (Honorary), Swiss Sums Society (Honorary), Académie des Sciences de Paris (Foreign Associate); Unique York Academy of Sciences.

Family

Hassler Inventor was the son of Have control over District New York Supreme Dreary judge Edward Baldwin Whitney become calm Josepha (Newcomb) Whitney, the grandson of Yale University Professor chide Ancient Languages William Dwight Manufacturer, the great-grandson of Connecticut Master and US Senator Roger General Baldwin, and the great-great-great-grandson learn American founding father Roger Sherman.

Hassler Whitney's maternal grandparents were uranologist and celestial mechanician Simon Uranologist and Mary Hassler Newcomb (the granddaughter of the first manager of the Coast Survey - Ferdinand Hassler).

Married Margaret R.

Howell, May 30, 1930; children: Outlaw Newcomb, Carol, Marian; married Row Barnett Garfield, January 16, 1955; children: Sarah Newcomb, Emily Baldwin; and married Barbara Floyd Osterman, February 8, 1986.