Tuesday, July 22, 2008

Review of ‘The Prince of Mathematics Carl Friedrich Gauss’ by M. Tent

This is a fantastic biography of Carl F Gauss (1777 to 1855). It is a well written book and the author, M Tent, will achieve her goal of inspiring readers to explore the world of mathematics with this book. This is a book for the layman but will be a real inspiration for a sixth former or undergraduate student of mathematics.
The author highlights some well known stories about the young Gauss such as:
By the age of 10 he knew the formula for the difference of two squares and had a smart technique of adding up the first 100 consecutive natural numbers.
The author also claims that Gauss tried to prove the parallel postulate using the first 4 postulates in Euclid’s Elements. Towards the end of the book Margaret Trent shows how this lead to Gauss develop non-Euclidean geometry 25 years before the Russian mathematician Lobachevsky published his work on this topic.
By the age of 11 Gauss could prove the irrationality of the square root of 2.
By the age of 18 Gauss had constructed a regular polygon of 17 sides using unmarked straight edge and compass only.
Some of the material in the book is from Gauss’s diary which has results in shorthand notation such as
This result says that any natural number N can be written as the sum of at most 3 triangular numbers. The author claims that this was Gauss’s Eureka moment and was a beautiful discovery.
For his PhD, Gauss proved the Fundamental Theorem of Algebra and also showed the mistakes made by Euler, Lagrange and Alembert in their proofs.
He also made a major contribution to number theory and proved the Fundamental Theorem of Arithmetic.
The author goes on to describe the political turmoil in Germany particularly in the Duchy of Braunschweig (Brunswick). The Duchy of Braunschweig had supported Gauss financially for 15 years but he was killed by Napoleon’s forces in 1806.
After the Duke’s death, Gauss was offered a post at the prestigious University of Gottingen which he took up. He remained there for the rest of his life. At Gottingen he had to teach as well as do research but in the beginning he did not enjoy teaching. He suggested to his wife “I would prefer simply to give my students a text and if they encounter any problems they can see me.” Amongst his students at Gottingen were Richard Dedekind and Mobius. At the University of Gottingen he had become the director of the observatory and published papers on infinite series, astronomy, optics, number theory and algebra.
Additionally between 1833 and 1855 Gauss worked very closely with Weber at Gottingen in the field of magnetism. They also produced the first telegraph system.
Whilst at Gottingen Gauss produced a map of entire kingdom of Hanover by using his triangulation and least squares methods.
Gauss had become an important figure in mathematics throughout Europe and beyond. Even the Universities of Berlin and Petersburg tried to lure Gauss to work for them but he refused each time.
The book is a biography of Gauss with his family and friends at the centre of his life. The only matter of concern is we don’t really know which of the stories are factual.
However this is a smashing book and definitely worth buying.