Wild About Math! Making Math fun and accessible

Review: The Big Questions: Mathematics

What motivates the study of mathematics? Pure Math and recreational Math may not seem to have any connection to our physical world (although they sometimes do) but much of what we study was once motivated by the need to solve some practical problem. The longer I serve in the role of Math communicator the more important I feel it to be to connect people, mathematicians and non-mathematicians alike, with the stories behind the concepts and calculations. Storytelling is a powerful way to help people to relate to the experience of being a mathematician and thinking like a mathematician. Plus, most of us love stories, if they're well told and if they contain intriguing elements. In The Big Questions: Mathematics, Tony Crilly tells 20 compelling stories of the development of mathematical ideas.

The second chapter, Where do numbers come from?, takes us back to the earliest counting methods, some 30,000 years ago. Crilly tells us about the tally sticks and notched bones that our ancestors used to count things. We learn about the Babylonians and Egyptians and their counting system based on the number 60, from which we get 60 seconds in a minute, 60 seconds in an hour, and 360 degrees in a circle. And, there's a nice yet simple exploration of the merit of a number system based on 60 -- think of how easily 60 divides into groups of equal number. The chapter on imaginary numbers not only gives a nice introduction to complex numbers, quaternions, octonions, and Clifford Algebras; it also (briefly) connects us to practical applications of complex analysis. More importantly, though, Crilly paints the picture of the people who pioneered the study of complex numbers. We can put ourselves in the shoes of these mathematical inventors and get a sense of their struggles and of their triumphs.

I like "The Big Questions: Mathematics." If you're looking for challenging Math problems to chew on this isn't the book for you. If you would enjoy a broad brush telling of 20 interesting stories then I'd encourage you to pull up a chair and get a copy of the book. The ideas are fantastic and Crilly's storytelling is superb.

Review: Mathematics Education for a New Era: Video games as a Medium for Learning

How can we rethink the current Math education paradigm to consider the wealth of available technology? Can video games teach basic Math skills or are they just a waste of time? Can video games help students to gain Math proficiency? What are the key elements of a game that promote mastery of mathematics? These are some of the "game changing" questions that Keith Devlin tackles in his new book "Mathematics Education for a New Era: Video Games as a Medium for Learning."

Keith Devlin is well qualified to explore these important questions. He is a researcher focused on using different media to teach mathematics. He is the author of 30 books; a number of them explore how we learn Math. Devlin has published over 80 research articles and he has won numerous prestigious prizes and awards. And, many of know Keith Devlin as "the Math Guy" on National Public Radio, the man who, since 1995, has been taking important mathematical ideas from current events and explaining them so that general audiences can understand them.

Review: The Number Sense

Oxford University Press sent me a review copy of The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition, by Stanislas Dehaene. The book is an update of the original edition, which was published in 1997.

The author writes in the preface of this new edition that the goal of the first edition of the book was

"to assemble all the available facts on how the brain does elementary arithmetic, and prove that a new and promising field of research, ripe with empirical findings, was dawning."

This new edition updates the reader on findings in the field of numerical cognition. Wikipedia has a nice introduction to the subject, including a list of questions at the heart of the field.

• How do non-human animals process numerosity?
• How do infants acquire an understanding of numbers (and how much is inborn)?
• How do humans associate linguistic symbols with numerical quantities?
• How do these capacities underlie our ability to perform complex calculations?
• What are the neural bases of these abilities, both in humans and in non-humans?
• What metaphorical capacities and processes allow us to extend our numerical understanding into complex domains such as the concept of infinity, the infinitesimal or the concept of the limit in calculus?

Review: The Mystery of the Prime Numbers

Matthew Watkins contacted me out of the blue a while ago, offering me a review copy of his new book, "The Mystery of the Prime Numbers." Not really having a sense of what the book was about but knowing that I like mysteries and prime numbers I happily accepted. When the book arrived I opened it to a few random pages to get a feel for the material. I was immediately hooked. Bear with me while I tell a bit of a story and then I'll get back to what hooked me.

When I was in high school I attended the summer Ross program at the Ohio State University. Professor Arnold Ross taught us number theory. The course was hard, really hard. The problem sets were brutal. But, there was something exhilarating about the program. Part of the thrill was Professor Ross' way of conveying difficult concepts. An equal part of the thrill was the subject itself. Number theory is the kind of subject that lends itself to very rich exploration. It was thrilling that, as a high school student, without a background in advanced mathematics, I could dive into such a rich subject matter that so many consider to be out of reach. I vividly remember Professor Ross telling us to "think deeply of simple things." The message stuck. Much of what we consider to be "advanced" mathematics -- calculus, number theory, and other branches -- are accessible to us if we think deeply of simple things.

Back to Matthew's book. It's about prime numbers. The concepts are simple. There are no equations to scare readers off. There are fun illustrations, by Matt Tweed. The concepts are deep. Matthew dives into the Prime Number Theorem, harmonic decomposition, spiral waves, and much more. The book reads like a fairy tale - a journey for children of all ages into the depths of truly simple mathematics. The book, in my judgment, lives up to its promise of being accessible. It is very entertaining yet remarkably rigorous. It renews my pleasure of finding joy in deep and simple things.

Review: Here’s Looking at Euclid

I have a confession. Book reviews are hard for me to write. When I open an exceptional book, like Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math by Alex Bellos, I get writer's block. I get lost in the awe of the material. I respond to Math books with a feeling rather than with a bunch of words. The feeling is often awe, or joy, or wow, or some combination of them. This book triggers all of the above.

Alex Bellos is a journalist. This is his first popular Math book and it is a big hit, particular in the UK. Fifteen Amazon reviewers have given the book an average rating of 4 1/2 stars. Bellos traveled around the world meeting with people who have interesting Math-related stories to tell. A few items from the table of contents will give you a feel for the book:

Chapter Three -- Something about nothing... In which the author travels to India for an audience with a Hindu seer. He discovers some very slow methods of arithmetic and some very fast ones.

Chapter Five -- The x-factor... In which the author explains why numbers are good but letters are better. He visits a man in the English countryside who collects slide rules and hears the tragic tale of their demise. Includes an exposition of logarithms and how to make a superegg.

Chapter Six -- Playtime... In which the author is on a mathematical puzzle quest. He investigates the legacy of two Chinese men -- one was a dim-witted recluse and the other fell off the earth -- and then flies to Oklahoma to meet a magician.

Review: 101 Things Everyone Should Know About Math

A friend, who later started a home organization business, once told me that she believed everything we own should be beautiful or useful. That pretty well sums up my feelings about Math. 101 Things Everyone Should Know About Math provides a compilation of problems in the realm of "useful."

"101 Things" has questions in eight areas:

1. Facts, Just Math Facts
2. Health, Food and Nutrition
3. Travel
4. Recreation and Sports
5. Economics
6. Nature, Music and Art
7. Miscellaneous
8. Bonus Questions

Here's one problem from the "Health, Food & Nutrition" section:

A cake recipe says to put batter into two 8" round pans, but you don't have any. Of the following, which combination of pans will work best?
   A. Two 8" square pans
   B. One 9" square pan
   C. One 9" x 13" rectangular pan
   D. Three 8" x 4" rectangular pans

Review: How to Read Historical Mathematics

Princeton University Press sent me a review copy of Benjamin Wardhaugh's "How to Read Historical Mathematics." I was excited to receive this book because I don't know of any other books that provide a basic introduction to the subject.

From Wardhaugh's web site:

Benjamin Wardhaugh is a historian; he does research and teaches at the University of Oxford, where since October 2007 he has been a Post-Doctoral Research Fellow at All Souls College. He is a graduate of Cambridge, Oxford, and the Guildhall School of Music and Drama in London, and holds degrees in mathematics, music, and history. ... He teaches the history of mathematics in various periods, in both the Mathematical Institute and the History Faculty at Oxford. A selection of the many things he has learned from his students will appear in his forthcoming textbook, How to Read Historical Mathematics.

How to Read Historical Mathematics is a quick read at 116 pages. Will you become an expert at reading historical Math after you read the book? Of course not. That will take years. What Wardhaugh does exceptionally well is to break the ice for readers interested in the subject. He does this largely by training readers to ask insightful questions when they read a historical text. Here's a set of questions from the book:

How they thought: What notation does the text use? What words? What concepts? How are these different from what you would use in the same situation? Does it use words or concepts you don't recognize? Can you work out what they mean, or find out what they mean from the author's definitions? Does it use familiar words or notation, but with different meanings from what you would expect?