Mathematics without apologies. Portrait of a problematic vocation. (English) Zbl 1386.00008

Princeton, NJ: Princeton University Press (ISBN 978-0-691-15423-7/hbk; 978-1-400-85202-4/ebook). xxii, 438 p. (2015).
Mathematics without Apologies is an unusual book. Its title is an allusion to G. H. Hardy’s influential book [Zbl 0025.19301; Zbl 1242.01040]. Harris addresses the question what pure mathematicians do, and the reasons why they are doing it. Chances are, however, that readers without a very good background in mathematics are none the wiser after having read the book. Marina von Neumann, daughter of John von Neumann, confesses that she is “puzzled at a much higher level than before” after having read the book.
The book consists of sections that are mainly autobiographical and sketch the development of Michael Harris into a mathematician, several sections on “How to explain number theory at a dinner party”, and a chapter on Harris’s view on financial mathematics. The other parts of this book are not easily classified; they form a web of topics involving art, beauty, charisma, literature (Goethe’s Faust figures prominently), love, morals, music, the Langlands conjecture, and a lot more.
Although the book contains almost 70 pages of notes and a bibliography that is 25 pages long, I regard it as a work of art rather than a scientific work, and I recommend it as an entertaining book and a source of inspiration to every educated reader.


00A09 Popularization of mathematics
00A30 Philosophy of mathematics