The most recommended math books

We absorb this tale, like Peter Pan's, from childhood, and it provides us all with a leaning to light-hearted fantasy and a story pattern of leaving the real world and returning to it. An adventure may begin by going through a wardrobe as in the first Narnia novel, or into and out of Tom Bombadil's Old Forest in Tolkien. Alice goes down a rabbit hole. There are rabbit holes, wardrobes, forests, sailboats.... The world Alice gets to is full of strangeness appealed to me for Orpheus Rising whose characters have a similar variety.

More than any other, this book influenced me most about wanting to study mathematics. Of course, I was young at the time and strongly partial to Einstein’s remark, “This is beyond doubt the most interesting book on the evolution of mathematics which has ever fallen into my hands.” Many years later, when I exhaustively tried to find the book in any bookstore I passed, it was out of print. So I suggested it to my publisher, who immediately acquired the rights and republished it under my editing guidelines. It is the quintessential lure into mathematics for readers of any age.   

When I was researching my own book I had a bit of difficulty finding more detailed information on the Asklepions (Asklepiea)—healing sanctuaries named after Asklepios, Greek god of medicine. So I was overjoyed to come across this book, which satisfactorily fleshed out the information I already had. The practice I was interested in was known as dream incubation, or temple sleep. The patients slept in the temple with the specific intention of experiencing a healing dream, the cure effected by awakening a healing instinct in the sleepers themselves. Dogs and serpents roamed the temple floor where the sleepers lay, the dogs even licking the patients’ wounds. I’ve included this book for anyone interested in this practice which is still discussed today, especially in the field of Hypnotherapy.

I find this book on the history of zero intriguing, and the contradiction embodied in its opening title captures a concept that is at once attractive and problematic.

This book, atypically opening with a chapter titled "Zero," and delightfully creative in other ways, presents historical concepts of zero not only as refreshingly non-linear, being termed anywhere from afterthoughts to casual alterations, rather than natural or logical progressions, but also as cross-cultural, involving Eastern Sumerians and Indian traditions and Western Greeks and European traditions, significantly in parallel, not as temporal or geographical extensions of each other.

I loved this book because it offers a refreshing view of what neuroscience can and should be. Unlike different, highly credentialed neuroscientists who routinely offer vastly incompatible views of consciousness and who we ultimately are, this book instead focuses on the extraordinary theme of how the brain organizes the engineering of consciousness rather than on the more elusive and controversial deeper questions. 

As an illustration of the many mind-broadening themes broached in this superb book, instinct is often used as the be-all and end-all explanation of certain animal and human behaviors. Of the two hundred or so books I have read on the subject of consciousness and the brain, I have never before come across a more cogent explanation of how instinct arises and sets over many generations. 

I always find myself applying algorithmic thinking in my everyday life—it affects the way I put away dishes, navigate to the store, and organize my to-do lists. And I think others could benefit from that mindset.

So, when I read this book, my reaction was "Yes! That's what I want people to know. I just wish I could have said it that well!" The authors (who I know, but didn't know they wrote a book together), did a fantastic job of selecting algorithms with deep human connections. Really! And they explain them just right, without getting too mathematical but while still hitting the key ideas with clarity and accuracy. Fantastic!

It's amazing how our thinking is influenced by a biased statement. This book shows that there is still hope when you look at the real facts.

The author asks a number of questions that require basic knowledge of everyday data that we read a lot about in the press. Questions such as: "How many people in the world are illiterate?" or "How many women are not educated?" are answered incorrectly by politicians, bankers, and scientists, those who determine our policy.

It is confronting to realize that more questions could have been answered correctly by simply guessing.

This book picks up where Evening in the Palace of Reason leaves off, with Bach composing the Musical Offering on a horrible theme from King Frederick.

It explains canons and fugues, and thus helps you understand Bach’s work better, but it then goes on a safari through the intellectual landscape of ideas related to fugues–strange loops, self-similarity, recursion, and of course the guys in the title. It’s not for everyone, but if you like any two of logic, philosophy, or music, give this a try.

I find Carlo Rovelli’s explanations of the sort of brain-mangling physics that usually seems beyond us non-mathematicians completely compelling.

In Anaximander, Rovelli tells the story of his hero, a man who figured out in 600 BCE that the earth was a physical body somehow floating in space. But it’s really the story of *how* Anaximander thought, not what he thought: he invented the scientific method – accretive, patient and skeptical.

Rovelli’s discussion of what that has meant since Anaximander, and what it means now, is just thrilling; and rather than being dry and abstract it’s full of historical curiosities that I found myself interrupting my wife to share with her. 

This is another book about the new research into how babies think. I am excited about this research because of its implications for how people learn mathematics and how researchers create math. This book taught me something important about how we all think. Gopnik distinguishes between what she calls flashlight consciousness and lantern consciousness. Flashlight is the way adults think. You focus on one thing at a time and give it your full attention. But babies, she claims, use their minds differently. Their lantern consciousness is unfocused and is aware of the big picture all at once.  

So what happens to lantern consciousness when you grow up? The answer is that creative individuals use it and alternate between lantern and flashlight consciousness. When we are creating or learning something new, we have to drop back to lantern consciousness. Logic comes from flashlight consciousness and, by itself, will never produce anything… show more.