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.