This book is an accomplished biography of a great mathematician of the XXth century: Hassler Whitney. A biography written from the vantage point of a close friend, also a mathematician. The book mixes with balance life events and mathematical achievements, as well as suitable digressions to contextualize the information given. All in a progressive chronological order cleverly organized, which catches the reader's fancy. We have the accounts of Whithey’s familiar and social circumstances, scientific motivations, academic events, mathematical achievements, various cultural interests... In the face of such an offer, it is advisable a quick global glimpse to all tresors hidden in the 385 pages to find afterwards a personal path to dwell morosely on them. For sure there will be rereadings, but this is only good. This book has many books inside ! Now, this spot is where one quits reading this review and starts reading the book: comments that follow could spoil surprises and enjoyement. The warning made, we proceed.
In non-academic matters, the book tells us about Whitney’s love of mountains, photography and music. And a fully proactive love indeed: he was an expert climber, constructed his own cameras and played violin in his own string quattor. Of all of this we get a vivid and appealing record. Each anecdote, each episode, each quotation is juicy and brought into life by Kending with ease and ability. The picture on the cover is a must!
But Whitney is a mathematical figure of his century, and his mathematical achievements are the main theme: graph theory and matroids (in connection with the four color problem), cup product and ring cohomology, embedding theorems, week (?) and strong, singularities of smooth mappings, stratifications… even some "after research" dealings with didactics. Here we find the minute rapport of Whitney discoverings: the triggering questions, the illuminating examples, the key ideas, including technical details and references to study closely. And the illustrations are so, so good! Furthermore the author provides the historical background prior to the moment Whitney plunges to a question and the contemporary atmosphere. An occasion to learn some history of Mathematics! There are also some rich phylosophical explanations, see those on the concept of decomposition. Compulsory to mention now the Notes collected at the end of the book.
Another remarkable feature are the discussions of Whithey’s ways to approach problems, turn around them, find crucial examples, make guesses to new insights and tackle the difficulties towards a happy solution. It is not a coincidence that Whitney’s umbrella is the archetypical counterexample all of us exhibit so often. Also, impossible not to mention the theatric accounter with Bezout "quite a" theorem as staged by Kending. And the adjective happy is not casual: it is distilled from Whitney’s attitude in research and learning.
Also, the author recollects more personal remembrances of the Institute, his experiences there, both academic and social. Seemingly collateral, they take us in emotionally and give a hint of more intimate issues. The way Kending meets A. Weil is a jewel! There is also a chapter on "little things" that mean a lot: a most gracious respite. Special mention deserves too the wealth of graphic stuff: pictures of Whitney, family, friends, other mathematicians, a stereo camera, social events… the picture on the cover, of course.
Thus we end back to the essential: forget this review and start reading the book.