LOVE AND MATH (EDWARD FRENKEL)
TURING'S CATHEDRAL (GEORGE DYSON)
VISIONS OF INFINITY (IAN STEWART)
STALKING THE RIEMANN HYPOTHESIS (DANIEL ROCKMORE)
Love and Math: The Heart of Hidden Reality was crucial to not only the mathematics of this project, but the philosophy and narrative as well. Apart from detailing various mathematical topics like braiding and Fermat's Last Theorem, Edward Frenkel provides an auotobiography. As we learn increasingly complex mathematics, we in turn learn how Frenkel forged his love of math in the unforgiving setting of the USSR. The most poignant moment for me is how Frenkel describes learning math, comparing the structure of learning to paint a fence (stereotypical math class) to what it could be (starry night).
Turing's Cathedral: The Origins of the Digital Universe details not only Alan Turing's contributions to the creation of the computer, but the work of others who came before and after Turing. Once again, a compelling narrative is intertwined with detailed and helpful explanations of both the math and science that resulted in computer science. This book, especially its later chapters, not only helped me gain a handle on the vernacular of the mathematics, but provided the entire foundation of my understanding that I later built on with specific papers.
Ian Stewart is not only my favorite math author to read for fun, but his book Visions of Infinity supplemented two of my moves: P/NP and the Riemann hypothesis. The astounding truth about Visions of Infinity is that Stewart manages to briefly but deeply explain complex mathematics; what other books do in hundreds of pages, he does in tens. Not only does he explain the complex extremely well, but he does so with a sense of humor. Though his other books proved helpful over the course of this project, this one was a launching point from which I could begin my exploration of complex, unsolved problems. The insight he gives is coupled with funny ancedotes and vivid images. Additionally, this book details much more than P/NP and Riemann, but multiple other "great" mathematical problems.
Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers proved to be almost as pivotal to me as Love and Math. Of all of the problems I have come to love, the Riemann hypothesis is my favorite. Not only does this book explain the problem with tangible enthusiasm, but it goes beyond laying out the calculus and the zeta function. This book details the valiant, but futile, efforts of many to provide a proof. Every abstraction of the problem (even some more ridiculus than that which proved Fermat's Last Theorem) was fascinating, and it made me excited to see which future one would click. Will it be an application to chemistry? Chaos theory? Someday, hopefully soon, we will know and there will be books written about it, but until then, this one is brilliant.
