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.
