The Genius of Euler: Reflections on His Life and Work.The Genius of Euler: Reflections on His Life and Work
William Dunham (ed.) Published by the Mathematical Association of America The Mathematical Association of America (MAA) is a professional society that focuses on undergraduate mathematics education. Members include teachers at the college and high school level; graduate and undergraduate students; and mathematicians and scientists. (2007) 309 pp., ISBN ISBN
International Standard Book Number
ISBN International Standard Book Number
ISBN n abbr (= International Standard Book Number) → ISBN m 0-88385-558-5 US$47.95
Another in the wonderfully entertaining and informative MAA MAA
macroaggregated albumin Spectrum Series, this book is one of two in a series celebrating the 300th anniversary of the birth of Leonhard Euler (the other is The Early Mathematics of Leonhard Euler). It brings together 34 previously published papers, which were assembled from a core of papers first appearing in the special 1983 issue of Mathematics Magazine in recognition of the 200th anniversary of Euler's death. A number of the authors will be well known to readers of mathematical literature (Florian Cajori Florian Cajori (February 28 1859 in St Aignan (near Thusis), Graubünden, Switzerland—August 15, 1930, Berkeley, California) was one of the most celebrated historians of mathematics in his day. He emigrated to the United States at the age of sixteen. He received a Ph.D. , Morris Kline Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
Kline grew up in Brooklyn and in Jamaica, Queens. , Philip J. Davis Philip J. Davis (1923, Lawrence, Massachusetts - ) is an American applied mathematician. He is known for his work in numerical analysis and approximation theory, as well as his investigations in the history and philosophy of mathematics. , George Polya, Paul Erdos), and a pleasant surprise is to find included a poem co-written by Australia's Marta Sved.
The standard of writing is superb, and the editor (who is also a contributor, and a self-confessed Euler fan) is to be commended for the skill with which he has selected, organised and presented the individual papers into a coherent collection.
There are two parts. Part I highlights the life and times of Leonhard Euler, and includes several revealing biographies, some fascinating historical background material, and enthusiastic assessments of the brilliance and achievements of this remarkable mathematician. We learn that Euler was not only the most prodigious writer of seminal mathematics, but he also made significant contributions to physics and astronomy, wrote widely influential textbooks on calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value. , algebra and analysis, and achieved for analysis what Euclid did for geometry. No wonder he is considered by some mathematicians to be in the same league as Archimedes, Newton and Gauss, and therefore the fourth in a "mathematical" Mount Rushmore of mathematicians (a proposal illustrated humorously on pages 92 and 94).
Whereas Part I is accessible to most people, Part II places some real mathematical demands on its readers, and features "a heavy dose of formulas, series and integrals". Indeed, most papers require a broad background of advanced calculus and number theory. However, there are some papers which would be well within the grasp of enquiring and mathematically literate high school students, such as those exploring Euler's famous formula (E = F + V - 2), the Konigsberg Bridge problem and Graeco-Latin Squares.
As a tribute to Euler's work, this selection of papers is revelatory, and will be rewarding for any mathematics teachers willing to revisit mathematical ideas first explored in their undergraduate days. For myself, for instance, I now have a much better understanding of the problems involved in proving the Fundamental Theorem of Algebra fundamental theorem of algebra
Theorem of equations proved by Carl Friedrich Gauss in 1799. It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. and how it is possible to calculate factorials of rational and negative numbers.
To remind us of the extraordinary breadth of Euler's contributions to mathematics, there is a glossary of 11 pages giving a brief selection of terms, functions, formulas, equations, techniques and theorems This is a list of theorems, by Wikipedia page. See also
This is an elegant and well-illustrated volume, which is recommended for reading by anyone wishing to be inspired by one of the greats of the world of mathematics.
Peter C. Brinkworth