In

*Journey through Genius*, William Dunham introduced some of the most influential mathematicians in history alongside explanations for one or two of their most profound discoveries in math.*Journey through Genius*gives a historical context for the mathematicians and their discoveries, and tries to convince the reader of the greatness of the discovery—the worthiness, as it may be, for why that piece of mathematical history has made it into this book. While the content provided in*Journey through Genius*is accessible to those with only a high-school level mathematics education, the means to coming to the results (via the proofs included in the book) are still so genius that one with a more in-depth understanding can appreciate the proofs given. If the purpose of the book was to inform the reader of some of the great mathematical theorems and those who discovered them, then this book mostly achieved its goal—its main fault is the short-sighted nature of its scope.
There
are twelve chapters in

*Journey through Genius*, each one (more or less) dedicated to a main theorem and to the life of the man who discovered it. Each chapter introduced context of that area of math at the time of the discovery, gave a proof outlining the main theorem, and concluded with an explanation of how the theorem influenced math and sometimes summarized the rest of the discoverer’s life. Not only was each of the twelve chapters focused on someone (or, in Chapter 11’s case, some people) from the Western world, but even introductions and conclusion rarely mention anyone outside of the Western culture. Dunham tries to explain this obvious exclusion in one of his chapters, stating, amongst other things, that “Because the Islamic mathematicians put less emphasis on proving their results in complete generality, no great theorem appears here” (131). This weak excuse for omitting some of the great thinkers of the Islamic world is more consolation than the void of an excuse for why discoveries from China, India, and other realms of the world aren’t explored.
Even if the excuse
Dunham supplies is true, it doesn’t explain why more of the Islamic
mathematicians’ work isn’t explored in the introduction or conclusion of the
chapters. Throughout the introductions and conclusions of the chapters, Dunham
does thorough exploration of other theorems that aren’t the chapter’s central
topic. He does this time and time again, and in a few of the chapters he goes
so far as to mention that there was some progress made in the area by
non-Western mathematicians, yet no short proof was supplied, no exploration of
any non-Western “discovered” mathematics was ever explained by Dunham. In
total, there are less than five pages dedicated to non-Western mathematical
discoveries (out of 283), which, in my opinion, is

*Journey through Genius*’s greatest downfall.
The information that
Dunham did include about the mathematicians and the discoveries that he did
highlight were both intellectually and emotionally satisfying. I appreciated
learning how each great mathematician’s discovery was proven and about the
background for each great mathematician; hearing how each embodied genius,
handled his achievements, and went about his life. The background given for
each mathematician increased the impact felt when being led through how each
mathematician proved his theorem, giving the already extraordinary proofs
another layer of meaning and understanding. I learned much about the state of
mathematics from

*Journey through Genius*—from the discipline’s history, to the construction of proofs of some truly great results, to the realities of the Western-centric mindset of some of the mathematical community that still pervade today.
This is an extremely fair critique of the book. I like that you acknowledge the book's strengths as well.

ReplyDeleteBiz,

ReplyDeleteThis book sounds like a great read. From your strengths you wrote about the book I gather that the book had some very interesting points. I was looking at possibly reading this book as my second book for the semester and a review like this helped. From class and your review I had my second book narrowed down to either this or e: The Story of a Number.

I do agree with your critics. It does make it hard to read a book (especially one called Journey through Genius) if it doesn't try to give an equal representation to all those that have contributed to the findings. Even having a small chapter about Eastern countries would have drawn me more to this book. Even without formal proofs on all of the math, it is worth mentioning those that helped along the way and those that proposed the problem, which were probably Eastern countries.

This review was very helpful. I still have considerable interest in reading the book, but will be reading it with some of your thoughts in mind.