**Spectrum**

Volume: 93;
2018;
385 pp;
Softcover

MSC: Primary 01; 05; 57; 58; 37; 97;

Print ISBN: 978-1-4704-4828-8

Product Code: SPEC/93

List Price: $60.00

AMS Member Price: $45.00

MAA Member Price: $45.00

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**Electronic ISBN: 978-1-4704-4911-7
Product Code: SPEC/93.E**

List Price: $60.00

AMS Member Price: $45.00

MAA Member Price: $45.00

#### Supplemental Materials

# Never a Dull Moment: Hassler Whitney, Mathematics Pioneer

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*Keith Kendig*

MAA Press: An Imprint of the American Mathematical Society

Hassler Whitney was a giant of twentieth-century mathematics. This
biography paints a picture of him and includes dozens of revealing
anecdotes. Mathematically, he had a rare detector that went off
whenever he spotted a piece of mathematical gold, and he would then
draw countless pictures, gradually forging a path from hunch to proof.
This geometric path is seldom reflected in the rigor of his formal
papers, but thanks to a close friendship and many conversations over
decades, author Kendig was able to see how he actually worked. This
book shows this through accessible accounts of his major mathematical
contributions, with figures copiously supplied.

Whitney is probably best known for introducing the grandfather of
today's innumerable embedding theorems—his strong embedding theorem
stating that any smooth manifold can be smoothly embedded in a
Euclidean space of twice the manifold's dimension. This in turn led
to several standard techniques used every day in algebraic topology.
Whitney also established the fundamentals of graph theory, the
four-color problem, matroids, extending smooth functions, and
singularities of smooth functions. He almost never used complicated
technical machinery, so most of his work is accessible to a general
reader with a modest mathematical background.

His math-music connection was intense: He played piano, violin, and
viola and won “best composition of the year” while earning
a Bachelor's degree in music at Yale. He was an accomplished mountain
climber, and as a tinkerer, at age fourteen he built the large-format
camera used to take this book's cover photograph. Whitney's family
generously provided dozens of photographs appearing here for the very
first time. This biography is a revealing portrait of a fascinating
personality and a titan of twentieth-century mathematics.

#### Readership

Undergraduate and graduate students and researchers interested in history, biography, and the history of topology.

#### Table of Contents

# Table of Contents

## Never a Dull Moment: Hassler Whitney, Mathematics Pioneer

- Cover Cover11
- Title page iii4
- Copyright iv5
- Contents vii8
- Preface xi12
- Permissions & Acknowledgments xv16
- Chapter 1. Some Snapshots 122
- Chapter 2. How Hassler Chose His Genes 930
- Chapter 3. Growing Up 2344
- Chapter 4. Hassler Goes to College 3758
- Chapter 5. Early Days at Harvard 4364
- Chapter 6. The Four-Color Problem: Some History and Whitney’s Contributions to It 4768
- Chapter 7. Whitney and the Four-Color Problem: A Closer Look 5576
- 7.1. Early results of Hassler 5576
- 7.2. How Hassler found Hamiltonian cycles 5980
- 7.3. Whitney’s planarity condition 6182
- 7.4. Chromatic polynomials 6990
- 7.5. Properties of the chromatic polynomial 7394
- 7.6. The “coefficients challenge” 7495
- 7.7. An illuminating strategy 7596
- 7.8. The siren, the stubborn beast! 79100

- Chapter 8. Whitney Discovers a Big Brother to the Matrix: The Matroid 83104
- Chapter 9. Topology: Its Beginnings 97118
- Chapter 10. Topology Grows Into a Branch of Mathematics 107128
- Chapter 11. Whitney Helped Revolutionize Algebraic Topology 133154
- Chapter 12. Whitney’s Extension Theorems 143164
- 12.1. Searching for that piece of gold 143164
- 12.2. First questions and examples 144165
- 12.3. Smooth versus just looking smooth 149170
- 12.4. Extending infinitely differentiable functions 151172
- 12.5. Exponential bridging functions in action 153174
- 12.6. Taming the clash of the titans 155176
- 12.7. Examples revisited 156177
- 12.8. Beyond the first dimension 158179

- Chapter 13. Whitney’s Weak Embedding Theorem 161182
- Chapter 14. Whitney’s Strong Embedding Theorem 175196
- Chapter 15. World War II 189210
- Chapter 16. From Harvard to the Institute; Insights on Smooth Mappings 197218
- Chapter 17. Are There Decomposition Theorems for Nonmanifolds? 217238
- Chapter 18. After Research 235256
- Chapter 19. Evolution or Revolution? 251272
- Chapter 20. Other Happenings at the Institute 267288
- Chapter 21. The Unspeakable Was About to Happen 281302
- Chapter 22. Sometimes You Get to Know People Through the Little Things 289310
- Chapter 23. Parting Shots: A Gallery of Photos 313334
- Notes 345366
- Chapter 1: Some Snapshots 345366
- Chapter 3: Growing Up 345366
- Chapter 4: Hass Goes to College 347368
- Chapter 6: The Four-Color Problem: Some History and Whitney’s Contributions to It 350371
- Chapter 7: Whitney and the Four-Color Problem: A Closer Look 351372
- Chapter 8: Whitney Discovers a Big Brother to the Matrix: The Matroid 353374
- Chapter 10: Topology Grows Into a Branch of Mathematics 353374
- Chapter 11: Whitney Helped Revolutionize Algebraic Topology 357378
- Chapter 12: Whitney’s Extension Theorems 359380
- Chapter 13: Whitney’s Weak Embedding Theorem 365386
- Chapter 16: From Harvard to the Institute; Insights on Smooth Mappings 365386
- Chapter 17: Are There Decomposition Theorems for Nonmanifolds? 370391
- Chapter 18: After Research 370391
- Chapter 20: Other Happenings at the Institute 370391
- Chapter 22: Sometimes You Get to Know People Through the Little Things 371392

- Bibliography 373394
- Index 381402
- Back Cover Back Cover1407