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Hassler Whitney

Hassler Whitney is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hassler Whitney rather than just read about it. In short: Hassler Whitney (March 23, 1907 – May 10, 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.

Hassler Whitney — main illustration
Hassler Whitney — illustration

Key takeaways

  • Hassler Whitney belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Hassler Whitney to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Hassler Whitney from memory before moving on to harder problems.

Reference excerpt

Hassler Whitney (March 23, 1907 – May 10, 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

Life 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. His mother, A. Josepha Newcomb Whitney, was an artist and political activist. He was the paternal nephew of Connecticut Governor and Chief Justice Simeon E. Baldwin, his paternal grandfather was William Dwight Whitney, professor of Ancient Languages at Yale University, linguist and Sanskrit scholar. 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. 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 (later a notable statistician, Sally Thurston), and Emily Baldwin. Finally, Whitney divorced his second wife and married Barbara Floyd Osterman on 8 February 1986. Whitney and his first wife Margaret made an innovative decision in 1939 that influenced the history of modern architecture in New England, when they commissioned the architect Edwin B. Goodell, Jr. to design a new residence for their family in Weston, Massachusetts. They purchased a rocky hillside site on a historic road, next door to another International Style house by Goodell from several years earlier, designed for Richard and Caroline Field.

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 the Yale Mountaineering Society (the precursor to the Yale Outdoors Club) and climbed most of the mountain peaks in Switzerland.

Death Three years after his third marriage, on 10 May 1989, Whitney died in Princeton, after suffering a stroke. In accordance with his wish, Hassler Whitney's ashes rest atop mountain Dent Blanche in Switzerland where Oscar Burlet, another mathematician and member of the Swiss Alpine Club, placed them on August 20, 1989.

Academic career Whitney attended Yale University, where he received baccalaureate degrees in physics and in music, respectively in 1928 and in 1929. Later, in 1932, he earned a PhD in mathematics at Harvard University. His doctoral dissertation was The Coloring of Graphs, written under the supervision of George David Birkhoff. At Harvard, Birkhoff also got him a job as instructor of Mathematics for the years 1930–31, and an Assistant Professorship for the years 1934–35. 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, Institute for Advanced Study, Princeton University, 1952–77; professor emeritus, 1977–89; Chairman of the Mathematics Panel, National Science Foundation, 1953–56; Exchange Professor, Collège de France, 1957; Memorial Committee, Support of Research in Mathematical Sciences, National Research Council, 1966–67; President, International Commission of Mathematical Instruction, 1979–82; Research Mathematician, National Defense Research Committee, 1943–45; Construction of the School of Mathematics. He was a member of the National Academy of Sciences; 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.

Honors In 1947 he was elected member of the American Philosophical Society. In 1969 he was awarded the Lester R. Ford Award for the paper in two parts "The mathematics of Physical quantities" (1968a, 1968b). In 1976 he was awarded the National Medal of Science. In 1980 he was elected honorary member of the London Mathematical Society. In 1982, he received the Wolf Prize from the Wolf Foundation, and finally, in 1985, he was awarded the Steele Prize from the American Mathematical Society.

Work

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Illustrations

Hassler Whitney illustration
Hassler Whitney: The Whitney–Gilman ridge on Cannon Mountain
The Whitney–Gilman ridge on Cannon Mountain

Worked examples

Example 1 — a first encounter with Hassler Whitney

Start with the simplest possible case. Write down what Hassler Whitney claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hassler Whitney before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hassler Whitney ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hassler Whitney

In research
Hassler Whitney appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Hassler Whitney in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Hassler Whitney is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1907 births, 1989 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Hassler Whitney outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Hassler Whitney in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Hassler Whitney means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Hassler Whitney out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hassler Whitney in simple terms?

Hassler Whitney (March 23, 1907 – May 10, 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.

Why does Hassler Whitney matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hassler Whitney?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hassler Whitney.

Tags

  • 1907 births
  • 1989 deaths
  • 20th-century American mathematicians
  • American geometers
  • American topologists
  • Graph theorists
  • Harvard Graduate School of Arts and Sciences alumni
  • Harvard University Department of Mathematics faculty
  • Institute for Advanced Study faculty
  • Mathematicians from New York (state)
  • Members of the American Philosophical Society
  • Members of the United States National Academy of Sciences

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