Dr Pickover, congratulations on being awarded the 2011 Neumann Prize from the British Society for the History of Mathematics for your book The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics. Over the last 20 years you have published a huge number of books on mathematics and science. When did you first get the urge to write?
I’ve had the urge to write as far back as the ninth grade. I recall that throughout high school, I would write strange short stories, using our family’s electronic typewriter. My interest in science writing, in particular, also started in high school, after receiving a copy of Martin Gardner’s The Unexpected Hanging and Other Mathematical Diversions, an early collection of some of his columns from Scientific American. The book’s tales of the fourth dimension, and matchbox computers for playing tic-tac-toe, energized my imagination. Gardner (1914-2010), an American mathematics and science writer, was one of my heroes, and I was so happy that he lived to see The Math Book, which is dedicated to him. Jasia Reichardt’s Cybernetic Serendipity, another book from my teenage days, kindled my early interest in mathematically driven computer art.
A remarkable fact about you is that you are not a full time author! Your ‘day job’ is at IBM’s Thomas J. Watson Research Center. How do you fit being an author in with a career as a research scientist? At a simple level – where do you find the time?
When people ask me how I find time to write books, I often reply, "Some people play golf on the weekends. Instead, I prefer to write." As an aside, writing is exactly like painting for me, adding a spot of color here, a detail there, a twig on this tree, a bit of foam on that ocean wave... No painter starts at the top of the painting and finishes at the bottom. Similarly, I often do not write books in a linear fashion, from beginning to end. Thank goodness for word processors! Of course, my book output pales in comparison to American novelist, lawyer, and workaholic Erle Stanley Gardner (1889-1970), who once worked on seven novels simultaneously and dictated 66,000 words a week. Erle Gardner did not start to dictate until he had formulated the entire plot of his novel. He actually hired six secretaries to handle his dictation, which he found more efficient than typing. His best-known works focus on the lawyer-detective Perry Mason.
Clearly you are passionate about communicating mathematics and science as a writer, but as a reader what are your favourite books?
My favourite novel is Robert Heinlein's The Number of the Beast, first published in 1980. The book not only provides a sense of adventure and mystic transport, but also ignites creative thinking with respect to multiple-universe theories. In the novel, the protagonists can access 10,314,424,798,490,535,546,171,949,056 universes. Heinlein goes further and promotes the creative theory called pantheistic multiple-ego solipsism, or world-as-myth, which posits that universes are created by the act of imagining them. Thus, his characters can access fictional worlds such as the Land of Oz and perhaps even the Martian landscapes of Edgar Rice Burroughs.
If we focus on mathematics and science, I often enjoy the “Introducing” series of graphic guides covering topics in philosophy, mathematics, and science. Books in this series are written by an expert in the field and illustrated, almost like comic books, by an imaginative artist. For mathematically curious readers, I would suggest Introducing Mathematics by Ziauddin Sardar, Van Loon, and Jerry Ravetz.
Do you have a favourite book amongst the ones you have written?
Because I personally learn most easily using visual representations, along with art to stimulate creative thinking, my two favourite books that I’ve written are The Math Book and The Physics Book, and these have also been my most successful. These books are actually the first two in a series of illustrated books I plan to write on various areas of human achievement and knowledge. My goal in writing The Math Book was to provide a wide audience with a brief guide to important mathematical ideas and thinkers, with entries short enough to digest in a few minutes. Most entries are ones that interested me personally. Some entries are eminently practical, involving topics that range from slide rules and other calculating devices to geodesic domes and the invention of zero. Occasionally, I include several lighter moments, which were nonetheless significant, such as the rise of the Rubik’s Cube puzzle or the solving of the Bed-Sheet Problem.
One of the features of The Math Book which I particularly like is that the format of single page entries on each topic allows it to be opened anywhere, giving the reader the chance to (if they wish!) randomly select episodes in mathematical history. From all those episodes, is there one which stands out for you as more remarkable than the others?
As you mentioned, each entry in this book is short, at most only a few paragraphs in length. This format allows readers to jump right in to ponder a subject, without having to sort through a lot of verbiage. If one topic bores the reader, leap to another! One of my favourites is the entry titled “Ant Odometer,” which describes research on desert ants that suggests that ant brains have the ability to count steps to help ants travel back to their tiny holes in the hot sands. The researchers actually glued stilts to the ants’ legs as part of their studies. Another favourite is titled “Curta Calculator,” which describes how the first commercially successful portable mechanical calculator was developed by Curt Herzstark (1902 -1988) while a prisoner in a German concentration camp.
On the page facing each entry there are full page, full colour, illustrations relating to the topic under discussion. Some of these are, quite literally, works of art (e.g. the Hilbert cube sculpture at Berkeley) and some more straightforwardly factual (e.g. pictures of mathematicians), and you comment in the photo credits on your love for the ‘diversity of mathematics, art, and history’. Was choosing the images to compliment the text an integral part of the book for you?
Creating The Math Book was quite a challenge. Not only did I have to perform the historical and mathematical research prior to writing, but I also needed to identify and obtain all the colour illustrations. I found the task to be very exciting as I reached out to various contemporary mathematical artists, searched through patent archives and old literature, or even created a few illustrations myself. The various illustrations should help coax even the math-phobic to become intrigued by many of the historical and mathematical topics.
In the introduction to The Math Book you comment on the use of computers in mathematics to help visualise, test and run simulations in mathematics. However, some mathematicians can be quite negative about the use of computers in mathematics. If I could ask you to gaze into your mathematical crystal ball for a moment, how do you see the role of computers in mathematics, both in education and research, evolving over the next 50 years?
American educator David Berlinski once wrote, “The computer has… changed the very nature of mathematical experience, suggesting for the first time that mathematics, like physics, may yet become an empirical discipline, a place where things are discovered because they are seen.” Indeed, we are continuing to encounter mathematical results discovered with the aid of computer-based tools. Of course, there is a more general challenge here. Mathematical proofs have been offered that have been far too long and complicated for experts to be certain that they are correct. A physics analogy is relevant here. When Werner Heisenberg worried that human beings might never truly understand atoms, Niels Bohr was a bit more optimistic. He replied in the early 1920s, “I think we may yet be able to do so, but in the process we may have to learn what the word understanding really means.”
Nevertheless, today, we use computers to help us reason beyond the limitations of our own intuition. In fact, experiments with computers are leading mathematicians to discoveries and insights never dreamed of before the ubiquity of computers. Computers and computer graphics allow mathematicians to discover results long before they can prove them formally, and open entirely new fields of mathematics. As Erica Klarreich reported in Science News, once the computer had produced a particular formula, proving that it was correct was extremely easy. Often, simply knowing the answer is the largest hurdle to overcome when formulating a proof.
When it comes to writing about mathematics, do you think that there are particular advantages of placing the subject matter in its historical context?
I believe that studying science and mathematics through the telescope of history has profound value for students and anyone curious about the evolution of thought and the limits of mind. Let’s take this question beyond mathematics and into physics and philosophy. Knowledge moves in an ever-expanding, upward-pointing funnel. From the rim, we look down and see previous knowledge from a new perspective as new theories are formed. Today's conjectures mutate, new theories evolve, and yesterday's impossibilities become part of everyday life.
When we study mathematics through the telescope of history, we see the challenges of both amateur and genius mathematicians who persevered; we see abacuses morphing into slide rules, and into calculators and computers. Our brains, which evolved to make us run from lions on the African savannah, may not be constructed to penetrate the infinite veil of reality. We may need mathematics, science, computers, brain augmentation, and even literature, art, and poetry to help us tear away the veils. For those of you who are about to embark on reading the The Math Book, look for the connections, gaze in awe at the evolution of ideas, and sail on the shoreless sea of imagination
To write on the history of mathematics, you must have read some historians of mathematics. Which ones most engaged you?
Some of the most fascinating educational content -- for anyone interested in mathematics and the evolution of our concept of numbers -- is the set of three DVD sets by The Great Courses, a publisher of educational DVDs and CDs. My three favourites in mathematics are: “Zero to Infinity: A History of Numbers,” by Edward Burger of Williams College; “The Queen of Sciences: A History of Mathematics,” by David Bressoud of Macalester College; and “Chaos,” by Steven Strogatz of Cornell. No set of math books can be more enlightening and inspiring than these three magnificent multimedia works.
Unusually, your book could work either as a printed book or as a website. Was this intended? How do you view the future of books when they are no longer printed on dead trees? Will the book form survive on devices such as the Kindle, or will it evolve into a new form?
Books such as The Math Book can be challenging to convert to a Web book or an e-book because the beauty of the two-page spread and the careful, artistic formatting may be lost. Certainly, such a book would be less compelling on a small, monochrome device. On the other hand, the “See Also” section at the bottom of each entry helps weave entries together in a web of interconnectedness and may help the reader traverse the book in a playful quest for discovery. This can be made easier on the Web or in an e-book.
You asked about the future of books, when they are increasingly available in electronic formats. Perhaps the greatest challenge will arise when all new books become available upon or before publication through unauthorized downloads. When ebook readers become even more pervasive, and it is very easy to get all books for free, I am a little unsure about the effect this will have on authors and publishers.
Some history of mathematics is easy to communicate, like Pythagoras’ triangle. But other mathematics is much more difficult, such as Bessel functions. Were there any topics that gave you particular difficulty or ones where you simply gave up?
By far the most challenging for me was trying to explain and illustrate the Langlands program that links two different branches of mathematics and involves conjectures that are said to be “like a cathedral” because they exhibit such an elegant fit. The Langlands program may be considered a grand unified theory of mathematics, which may take centuries to completely elucidate. But let us discuss, more generally, the art of communicating mathematics. Mathematicians like Keith Devlin have admitted in The New York Times that “the story of mathematics has reached a stage of such abstraction that many of its frontier problems cannot even be understood by the experts.” If experts have such trouble, one can easily see the challenge of conveying this kind of information to a general audience. We do the best we can. Mathematicians can construct theories and perform computations, but they may not be sufficiently wise to fully comprehend, explain, or communicate these ideas.