Book Review: Called Too Soon by Flames Afar: Niels Henrik Abel and His Times, Volume 49, Number 7
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Book Review Called Too Soon by Flames Afar: Niels Henrik Abel and His Times Reviewed by Jesper Lützen Called Too Soon by Flames Afar: Niels Henrik ideas were analyzed. Abel and His Times One could have tried Arild Stubhaug, translated by Richard H. Daly to reconstruct how Springer-Verlag, 2000, Berlin, Heidelberg, Abel successively de- New York veloped his ingenious $44.95, x + 580 pages, with 51 figures algebraic theorems ISBN 3-540-66834-9 and his revolutionary new approach to el- August 5, 2002, marks the bicentennial of the liptic integrals and birth of the Norwegian mathematical genius Niels functions, in particu- Henrik Abel. Many mathematicians will celebrate lar his idea of dealing this occasion at a meeting in his native country.1 with the problems in a But one can also celebrate the occasion at home by complex rather than a reading the new biography by Arild Stubhaug. It is real setting and his an extremely well-written account of Abel’s short idea of considering life (1802–29). It compares favorably with Oystein the inverse functions Ore’s biography Niels Henrik Abel: Mathematician rather than the elliptic integrals themselves. One Extraordinary, translated in 1957 from the Nor- could have contrasted these ideas with those of Abel’s predecessors, such as Lagrange and Le- wegian original Niels Henrik Abel; Et geni og hans gendre, with those of his contemporaries, such as samtid (1954), which is highly recommendable and Gauss, Jacobi, and Galois, and one could have an- was until now the most complete source on Abel’s alyzed the importance of Abel’s work for the later life. development of mathematics. One could have tried Stubhaug’s book is almost twice as long as Ore’s. to analyze the unpublished drafts that Abel left un- Does this reflect that much new Abel material has finished at his untimely death, and one could have been uncovered since Ore wrote his book? Not tried to reconstruct the ideas about integration in really. To be sure, Stubhaug has found some new finite terms that he wrote down in a paper that was traces of Abel’s life, but the primary material later lost, as well as his ideas on different algebraic dealing directly with the mathematical genius is still subjects that he hinted at on various occasions rather scant: his published mathematical papers, but did not have the time to develop. a few unpublished drafts, letters (in particular from Such an internal mathematical analysis—which his travel abroad), some official records, his friends’ would, so to speak, take the mathematics as the letters and diaries, obituaries, and a few other rec- main actor—is, however, not what Stubhaug pre- ollections from people who knew him. How does sents. His book is a real biography, in which the per- this material support a biography of 580 pages? son Abel is the central object of study. The book It could have served as a basis for an even longer is so long because the author wants to reflect Abel’s “scientific biography” in which Abel’s mathematical life in the world in which he lived—not so much the mathematical world he was a part of, but rather Jesper Lützen is professor of the history of exact sciences, the Norwegian society he grew up in and inhabited Department of Mathematics, Copenhagen University, Den- for most of his short life. It is the rich description mark, and at the California Institute of Technology. His e-mail address is [email protected]. of this local and regional society and its interac- tion with Abel that is the main novelty of this bi- 1The Abel Bicentennial Conference took place June 3–8, ography and that makes it so interesting to read. 2002, at the University of Oslo. AUGUST 2002 NOTICES OF THE AMS 795 Stubhaug vividly de- Although mathematics is not the main issue in scribes Abel’s family Stubhaug’s book, it is also not marginalized com- background, the liv- pletely, as it has been in recent Hollywood pro- ing conditions in ductions about mathematicians and scientists. southern Norway, and Stubhaug clearly conveys the message that Abel’s the very exciting na- greatness is to be found in his mathematics. He tional Norwegian and briefly explains the mathematical problems Abel Scandinavian political addressed, the methods he used, and the results and cultural events he arrived at. These explanations will be sugges- that directly or indi- tive to people with some college knowledge of rectly influenced mathematics, and they are brief enough that they The church in Gjerstad, Norway. Abel’s life. will not put off a mathematically untrained reader. When I, as a Scan- Abel’s mathematics is also presented in its histor- dinavian reader, got hold of the 1996 Norwegian ical context. However, rather than describe the original of Stubhaug’s book, Et foranskutt lyn: Niels technical mathematical developments that pre- Henrik Abel og hans tid, I was extremely interested ceded Abel’s discoveries, Stubhaug tends to tell sto- to learn how the knowledge I had about Abel’s life ries about the mathematicians behind the devel- and work was connected in a meaningful way to the opments. For example, rather than try to explain cultural, social, and political history of the time, the problems concerning the solution of polyno- which I knew only superficially from school. The mial equations by radicals and the content of La- book is written in an elegant and captivating liter- grange’s papers that Abel read and used, Stubhaug ary style that made it almost impossible for me to tells stories about the person Lagrange (whom Abel put down. Stubhaug, who has studied mathemat- never met) and the exciting story, involving ics, history, and literature and has published poems Tartaglia and Cardano, about the discovery of the as well as papers on literary and cultural history, solution of the third- and fourth-degree equations. deservedly won the most prestigious Norwegian lit- And instead of trying to explain Galois theory, ex- erary prize (Brageprisen) for his biography of Abel. cept in the most general terms, Stubhaug tells the When I heard that the book had been translated dramatic story of Galois’s life. He also recounts the into English, I was a bit worried. Would it be pos- history of Fermat and his last (translated literally sible to render the captivating literary style in a as “great”) theorem and other good stories from the translation? It turned out that my worries were history of mathematics. Some of them have the unfounded. As far as I can tell, the translation by character of anecdotes, but generally the histori- Richard H. Daly is also a very good read. The style cal facts are accurate except for a few details, such of the translation is also literary and pleasant. as the claim that Pascal was the first to determine There are some, admittedly somewhat trivial, prob- the area under a cycloid. Stubhaug also succeeds lems with the translation. For example, on page 147 in conveying the importance and ingenuity of Abel’s the word Domkirke, meaning “cathedral”, is not mathematics by quoting contemporary and later translated, and this is unfortunate because the evaluations of it. connection to the Cathedral School being discussed But the main purpose of the biography is to at this point in the book becomes unclear. The place Abel in his local environment. The first third most glaring problem, however, is the translation of the book introduces Abel’s family and the early of mathematical terms and phrases. Here are some nineteenth-century southern Norway he grew up in. examples: solve algebraic equations with root in- At that time Norway and Denmark were ruled by dicators (page 204), equations of the fifth magni- the same king. Abel’s family had come to Norway tude (page 205), great and small infinities in the seventeenth century from Abild (whence the (page 210), Newton’s concept of marginal value name Abel) in Northern Schleswig, which also was (page 210), the Radon Transformer (page 285), the ruled by the Danish-Norwegian king. Abel’s grand- reverse function (page 301), Abelian theorem of lim- father was a parish vicar at Gjerstad near Risør in itation values (page 344), the Sylowian proposi- the coastal region of southern Norway. Abel’s father, tions (page 552). A mathematically trained reader Søren Georg, attended the Cathedral School in Hels- can easily interpret these somewhat peculiar ingør, Denmark, and studied theology at Copen- phrases, and since the mathematics is not the main hagen University before he married the daughter of issue in this book, the bad translations should not the richest merchant in Risør and became a vicar detract from its merits. It is remarkable, however, at Finnøy near Stavanger. Here the young couple had that such a highly respected mathematics pub- their first two sons in 1800 and 1802. They named lisher as Springer-Verlag did not ask a mathemat- the second son Niels Henrik after his maternal ically trained person to change these mistransla- grandfather. Two years later the family moved back tions, which lend an unintentionally comical flavor to Gjerstad, where Søren Georg took over as vicar to the mathematical passages. after the death of his father. Niels Henrik grew up 796 NOTICES OF THE AMS VOLUME 49, NUMBER 7 in Gjerstad with four siblings. He was taught by his In 1821 Abel entered the university in Christia- father and later by a hired teacher. Only few con- nia that his father had helped to establish in 1811. crete facts and anecdotes about Abel are preserved Here he read the masters of mathematics and after from this period of his life.