World Library  
Flag as Inappropriate
Email this Article

Hassler Whitney


Hassler Whitney

Hassler Whitney
Born (1907-03-23)March 23, 1907
New York City
Died May 10, 1989(1989-05-10) (aged 82)
Princeton, New Jersey
Fields Mathematics
Institutions Harvard University
Institute for Advanced Study
Princeton University
National Science Foundation
National Defense Research Committee
Alma mater Yale University
Doctoral advisor George David Birkhoff
Doctoral students James Eells
Wilfred Kaplan
Paul Olum
Herbert Robbins
Known for Algebraic topology
Differential topology
Graph theory
Geometric measure theory
Singularity theory
Notable awards National Medal of Science (1976)
Wolf Prize (1983)
Leroy P. Steele Prize (1985)

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


  • Biography 1
    • Life 1.1
      • Death 1.1.1
    • Academic career 1.2
    • Honors 1.3
  • Work 2
    • Research 2.1
    • Teaching activity 2.2
      • Teaching the youth 2.2.1
  • Selected publications 3
  • See also 4
  • Notes 5
  • References 6
    • Biographical references 6.1
    • Scientific references 6.2
  • External links 7



Hassler Whitney was born on March 23, 1907, in New York City, where his father Edward Baldwin Whitney was the First District New York Supreme Court judge.[1] His mother, Josepha (Newcomb) Whitney, was an artist and active in politics.[2] His paternal grandfather was William Dwight Whitney, professor of Ancient Languages at Yale University, linguist, and Sanskrit scholar.[2] Whitney was the great grandson of Connecticut Governor and US Senator Roger Sherman Baldwin, and the great-great-grandson of American founding father Roger Sherman. His maternal grandparents were astronomer and mathematician Simon Newcomb (1835-1909), a Steeves descendant, and Mary Hassler Newcomb, granddaughter of the first superintendent of the Coast Survey Ferdinand Rudolph Hassler. His great uncle Josiah Whitney was the first to survey Mount Whitney.[3]

He married three times: his first wife was Margaret R. Howell, married on the 30 May 1930. They had three children, James Newcomb, Carol and Marian. After his first divorce, on January 16, 1955 he married Mary Barnett Garfield. He and Mary had two daughters, Sarah Newcomb and Emily Baldwin. Finally, Whitney divorced his second wife and married Barbara Floyd Osterman on 8 February 1986.

Throughout his life he pursued two particular hobbies with excitement: music and mountain-climbing. An accomplished player of the violin and the viola, Whitney played with the Princeton Musical Amateurs. He would run outside, 6 to 12 miles every other day. As an undergraduate, with his cousin Bradley Gilman, Whitney made the first ascent of the Whitney-Gilman ridge on Cannon Mountain, New Hampshire in 1929. It was the hardest and most famous rock climb in the East. He was a member of the Swiss Alpine Society and climbed most of the mountain peaks in Switzerland.[4]


Three years after his third marriage, on 10 May 1989, Whitney died in Princeton,[5] after suffering a stroke.[6] In accordance with his wish, Hassler Whitney ashes rest atop mountain Dents Blanches in Switzerland where Oscar Burlet, another mathematician and member of the Swiss Alpine Club, placed them on August 20, 1989.[7]

Academic career

Whitney attended

  • Hassler Whitney at the Mathematics Genealogy Project
  • .  
  • Hassler Whitney Page - Whitney Research Group
  • Interview with Hassler Whitney about his experiences at Princeton
  • Hassler Whitney — The First Century of the International Commission on Mathematical Instruction

External links

  • Chirka, Evgeniǐ Mikhaǐlovich (1989), Complex analytic sets, Mathematics and Its Application (Soviet Series) 46, .  
  • .  
  • Nadis, Steve; : ISBN 978-0-674-72655-0). e-book ( 
  • Oxley, James (1992), Matroid Theory, Oxford Graduate Texts in Mathematics 3, Oxford: .  
  • Shields, Allen (1988), "Differentiable manifolds: Weyl and Whitney",  .

Scientific references

  •  .
  • Fisher, Elizabeth (9 November 2012), Full list of Honorary Members (PDF), .  
  • Fowler, Glenn (May 12, 1989), "'"Hassler Whitney, Geometrician; He Eased 'Mathematics Anxiety,  .
  • Kendig, Keith (August 2013), "Hassler Whitney", Celebratio Mathematica 2013 (1), retrieved November 27, 2014 
  •  , available from Gallica.

Biographical references


  1. ^ Thom (1990, p. 474) and Chern (1994, p. 465).
  2. ^ a b c d Chern (1994, p. 465)
  3. ^ According to Chern (1994, p. 465) and Thom (1990, p. 474): Thom cites Josiah Whitney explicitly while Chern simply states that:-"... a great uncle was the first to survey Mount Whitney".
  4. ^ Fowler (1989).
  5. ^ Kendig (2013, p. 18) clarifies Princeton, NJ as his correct death place.
  6. ^ According to Kendig (2013, p. 18). Kendig writes also that being him apparently in good health, the physicians attributed the cause of the stroke to the treatments for prostate cancer he was undergoing.
  7. ^ The story on his resting place story is reported by Chern (1994, p. 467): see also Kendig (2013, p. 18).
  8. ^ O'Connor, JJ and E F Robertson. "Hassler Whitney". Retrieved 2013-04-16. 
  9. ^ See Kendig (2013, pp. 8–10).
  10. ^ See (Kendig 2013, p. 9).
  11. ^ See (Kendig 2013, pp. 9–10).
  12. ^ See (Chern 1994, p. 465).
  13. ^ Whitney (1992a, p. xi) and Whitney (1992b, p. xi), section, "Academic Appointments and Awards".
  14. ^ See the official list of honorary members redacted by Fisher (2012).
  15. ^ Whitney (1933).
  16. ^ According to Johnson, Will. "Matroids" (PDF). Retrieved 5 February 2013. .
  17. ^ According to Oxley (1992, pp. 147–153). Recall that two graphs G and G' are 2-isomorphic if one can be transformed into the other by applying operations of the following types:
  18. ^ See Federer's review (1958).
  19. ^  
  20. ^ Hechinger, Fred. "Learning Math by Thinking".June 10, 1986.!/2009/04/learning-math-by-thinking-hassler.html.
  21. ^ Complete bibliography in Whitney (1992a, pp. xii–xiv) and Whitney (1992b, pp. xii–xiv).


See also

  • Whitney, Hassler (January 1932), "Congruent Graphs and the Connectivity of Graphs",  .
  • Whitney, Hassler (1933), "2-Isomorphic Graphs",  .
  • Whitney, H. (1957), Geometric Integration Theory, Princeton Mathematical Series 21, Princeton, NJ and London: .  
  • Whitney, Hassler (1968a), "The Mathematics of Physical Quantities. Part I", .  
  • Whitney, Hassler (1968b), "The Mathematics of Physical Quantities. Part II", .  
  • Whitney, Hassler (1972), Complex analytic varieties, Addison-Wesley Series in Mathematics, .  
  • Whitney, Hassler (1992a), .  
  • Whitney, Hassler (1992b), .  

Hassler Whitney published 82 works:[21] all his published articles, included the ones listed in this section and the preface of the book Whitney (1957), are collected in the two volumes Whitney (1992a, pp. xii–xiv) and Whitney (1992b, pp. xii–xiv).

Selected publications

In 1967, he became involved full-time in educational problems, especially at the elementary school level. He spent many years in classrooms, both teaching mathematics and observing how it is taught.[20] He spent four months teaching pre-algebra mathematics to a classroom of seventh graders and conducted summer courses for teachers. He traveled widely to lecture on the subject in the United States and abroad. He worked toward removing the mathematics anxiety, which he felt leads young pupils to avoid mathematics. Whitney spread the ideas of teaching mathematics to students in ways that relate the content to their own lives as opposed to teaching them rote memorization.

Teaching the youth

Teaching activity

These aspects of Whitney's work have looked more unified, in retrospect and with the general development of singularity theory. Whitney's purely topological work (Stiefel–Whitney class, basic results on vector bundles) entered the mainstream more quickly.

In his book Geometric Integration Theory he gives a theoretical basis for Stokes' theorem applied with singularities on the boundary:[18] later, his work on such topics inspired the researches of Jenny Harrison.[19]

Whitney had, throughout the 1950s, an almost unique interest in the topology of singular spaces and in singularities of smooth maps. An old idea, implicit even in the notion of a simplicial complex, was to study a singular space by decomposing it into smooth pieces (nowadays called "strata"). Whitney was the first to see any subtlety in this definition, and pointed out that a good "stratification" should satisfy conditions he termed "A" and "B". The work of René Thom and John Mather in the 1960s showed that these conditions give a very robust definition of stratified space. The singularities in low dimension of smooth mappings, later to come to prominence in the work of René Thom, were also first studied by Whitney.

He was one of the major developers of cohomology theory, and characteristic classes, as these concepts emerged in the late 1930s, and his work on algebraic topology continued into the 40s. He also returned to the study of functions in the 1940s, continuing his work on the extension problems formulated a decade earlier, and answering a question of Laurent Schwartz in a 1948 paper On Ideals of Differentiable Functions.

In a 1936 paper, Whitney gave a definition of a smooth manifold of class C r, and proved that, for high enough values of r, a smooth manifold of dimension n may be embedded in ℝ2n+1, and immersed in ℝ2n. (In 1944 he managed to reduce the dimension of the ambient space by 1, provided that n > 2, by a technique that has come to be known as the "Whitney trick".) This basic result shows that manifolds may be treated intrinsically or extrinsically, as we wish. The intrinsic definition had been published only a few years earlier in the work of Oswald Veblen and J. H. C. Whitehead. These theorems opened the way for much more refined studies: of embedding, immersion and also of smoothing: that is, the possibility of having various smooth structures on a given topological manifold.

Whitney's lifelong interest in geometric properties of functions also began around this time. His earliest work in this subject was on the possibility of extending a function defined on a closed subset of ℝn to a function on all of ℝn with certain smoothness properties. A complete solution to this problem was found only in 2005 by Charles Fefferman.

Whitney's earliest work, from 1930 to 1933, was on graph theory. Many of his contributions were to the graph-coloring, and the ultimate computer-assisted solution to the four-color problem relied on some of his results. His work in graph theory culminated in a 1933 paper,[15] where he laid the foundations for matroids, a fundamental notion in modern combinatorics and representation theory independently introduced by him and Bartel Leendert van der Waerden in the mid 1930s.[16] In this paper Whitney proved several theorems about the matroid of a graph M(G): one such theorem, now called Whitney's 2-Isomorphism Theorem, states: Given G and H are graphs with no isolated vertices. Then M(G) and M(H) are isomorphic if and only if G and H are 2-isomorphic.[17]



In 1947 he was elected member of the American Philosophical Society.[12] In 1969 he was awarded the Lester R. Ford Award for the paper in two parts "The mathematics of Physical quantities" (1968a, 1968b).[13] In 1976 he was awarded the National Medal of Science. In 1980 he was elected honorary member of the London Mathematical Society.[14] In 1983 he received the Wolf Prize from the Wolf Foundation, and finally, in 1985, he was awarded the Steele Prize from the American Mathematical Society.


He was a member of the National Academy of Science; Colloquium Lecturer, American Mathematical Society, 1946; Vice President, 1948–50 and Editor, American Journal of Mathematics, 1944–49; Editor, Mathematical Reviews, 1949–54; Chairman of the Committee vis. lectureship, 1946–51; Committee Summer Instructor, 1953–54;, American Mathematical Society; American National Council Teachers of Mathematics, London Mathematical Society (Honorary), Swiss Mathematics Society (Honorary), Académie des Sciences de Paris (Foreign Associate); New York Academy of Sciences.

, 1943–45; Construction of the School of Mathematics. National Defense Research Committee, 1957; Memorial Committee, Support of Research in Mathematical Sciences, National Research Council, 1966–67; President, International Commission of Mathematical Instruction, 1979–82; Research Mathematician, Collège de France, 1953–56; Exchange Professor, National Science Foundation, 1952–77; Professor Emeritus, 1977–89; Chairman of the Mathematics Panel, Princeton University, Institute for Advanced Study Later on he held the following working positions: NRC Fellow, Mathematics, 1931–33; Assistant Professor, 1935–40; Associate Professor, 1940–46, Professor, 1946–52; Professor Instructor, [11] and an Assistant Professorship for the years 1934–35.[10] At Harvard, Birkhoff also got him a job as Instructor of Mathematics for the years 1930–31,[9][8]

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.