Feliksiak’s first nonfiction publication tackles one of the great unsolved problems of mathematics.
Riemann’s hypothesis, which, among other things, posits the distribution of all prime numbers, represents such a complex problem that even modern mathematical computing software can only perform the calculations to a limited point. As a result, Feliksiak’s work is, of necessity, intended for those with a solid understanding of advanced mathematics. However, the author eschews a mathematician’s dry tone and instead opts for conversational, direct language, even slipping the occasional colloquialism into his prose—such as an explanation of why an estimation error doesn’t “blow up.” The language is technically perfect, to lessen the risk of inaccurately communicating the mathematical steps involved in proving the “very complex problem at hand.” At every step, he explains cogently, if briefly, how each theorem represents another small advance toward a better estimate of the prime counting function and, ultimately, an elementary proof of one of the great unsolved problems of mathematics. However, readers without a solid background in number theory will, unfortunately, be lost. As it is, Feliksiak’s proposed two-page proof requires more than 100 pages of buildup, even in the compressed language of mathematics. But the author has, at least, managed to make his advanced computations and reasoning accessible to anyone who understands the mathematical terms he employs. Along the way, he offers tidbits of history about the development of number theory and prior attempts to prove Riemann’s hypothesis, establishing a context of other mathematicians’ past contributions.
For readers with a grounding in number theory, the interlocking parts of this mathematical proof come together to create a surprisingly harmonious whole.