New Books in Mathematics

Our guest today is Kartik Hosanagar, the author of A Human’s Guide to Machine Intelligence: How Algorithms Are Shaping Our Lives and How We Can Stay in Control(Viking, 2019). This is one of those rare books that I think everyone can read and I think everyone should read. In fact, knowledge of algorithms can in some sense be considered to be the literacy of the 21st century, and the author has written a book which can greatly held advance this type of literacy. If you want to become 21st-century literate, you should read this instructive and immensely enjoyable book. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Andrew C. A. Elliott‘s Is That a Big Number? (Oxford University Press, 2018) is a book that those of us who feast on numbers will absolutely adore, but will also tease the palates of those for whom numbers have previously been somewhat distasteful.  This book helps us not only to realize the relative magnitudes of many of the numbers which surround us, but also helps us understand precisely how and why our understanding of the universe often comes down to the numbers which describe it.  It’s just a shame that Pythagoras, who was reputed to say that “All is number,” isn’t around to appreciate it. By the way, the Elliot maintains a great website called “Is That a Big Number.” Well worth visiting! Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Eli Maor explains the math-music connection from Pythagoras to Schoenberg. Topics include parallel crises in physics and music, acoustic principles demonstrated with a slinky, comparison of ear and eye perception of vibrations, Stravinsky's revolutionary music, and the crucial role of reference systems in art and music.

Today I talked to Vicky Neale about her new book Closing the Gap: The Quest to Understand Prime Numbers (Oxford University Press, 2017). The book details one of the most exciting developments to happen in the last few years in mathematics, a new approach to the Twin Primes Conjecture. The story involves mathematicians from five different centuries and probably every continent except Antarctica. Vicky does a great job of telling not only what the problem is and how work on it has proceeded, but also how mathematical research has evolved given the resources available in the twenty first century. If you like numbers, you’ll love this book—and if you don’t like numbers, maybe this book can help you appreciate them. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book discussed here is the The Joy of Mathematics (Prometheus Books, 2017), whose lead author, Alfred Posamentier, is our guest today. The subtitle Marvels, Novelties, and Neglected Gems That Are Rarely Taught in Math Classdescribes the book nicely. Much of the book can be read by someone with only a couple of years of high school math, and the book does a terrific job of showing the reader why those of us who love math do so. We like arithmetic, algebra, geometry, infinity, and the counterintuitively surprising, and the book contains lovely examples of all of these. Enjoy! Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Big Data: How the Information Revolution Is Transforming Our Lives (Icon Books, 2017), by Brian Clegg, is a relatively short book about a subject that has emerged only recently, but is rapidly becoming a significant force in the evolution of society. Most of us have heard the term “big data,” but many of us erroneously assume that its just a lot of little data. It’s considerably more than that, and Big Data, which is an easy and fun read, serves as a terrific introduction to a topic which has an ever-increasing impact on many aspects of our lives. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Brian Clegg is one of England’s most prolific and popular writers on science. His latest work, The Reality Frame: Relativity and Our Place in the Universe (Icon Books, 2017), covers Einstein’s Theories of Relativity and a whole lot more. Simply as an exposition of Einstein’s theories, the book is excellent its beautifully organized and delivered, with Clegg’s usual clarity and insight. But what makes the book transcend the usual work on this subject is that Clegg looks at relativity as a concept that can help us understand what distinguishes humanity as a species, and where our species fits into the Universe. Einstein himself would have enjoyed participating in a discussion of this fascinating topic, and may well have shared some of Clegg’s points of view. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book discussed here is entitled The Calculus of Happiness: How a Mathematical Approach to Life Adds Up to Health, Wealth, and Love (Princeton University Press, 2017) by Oscar Fernandez. If the thought of calculus makes you nervous, don’t worry, you won’t need calculus to enjoy and appreciate this book. Its actually an intriguing way to introduce some of the precalculus topics that will later be needed in a calculus class, through the examination of some of the basic mathematical ideas that can be used to analyze the problems of how to attain relationship bliss, live long, and prosper and all without being a Vulcan. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

For many cognitive scientists, psychologists, and philosophers of mind, the best current theory of cognition holds that thinking is in some sense computation “in some sense,” because that core idea can and has been elaborated in a number of different ways that are or at least seem to be incompatible in at least some respects. In Unifying the Mind: Cognitive Representations as Graphical Models (MIT Press, 2014), David Danks proposes a version of this basic theory that links the mind closely with the computational framework used in machine learning: the idea that thinking involves manipulation of symbols encoded as graphical models. Danks, who is Professor of Philosophy and Psychology at Carnegie Mellon University, argues that graphical models provide a unifying explanation of why we are able to move smoothly between different cognitive processes and why we are able to focus on features of situations that are relevant to our goals. While the book includes the mathematics behind graphical models, Danks explains his proposal in accessible yet precise terms for the non-mathematically trained reader. He discusses how graphical models work in causal reasoning, categorization, and other processes, how his view is related to more familiar cognitive frameworks, and some implications of his view for modularity and other traditional debates. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

If ever there were a course that needs a book like Raffi Grinberg’s The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs (Princeton University Press, 20170, analysis is unquestionably it, and I only wish that Raffi had gotten into the wayback machine and delivered me a copy when I was taking this course more than half a century ago. I got a C+, and almost certainly would have done a lot better if I’d had this book, and so will present and future students who struggle with this course. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics