Lynn Gamwell on math and the visual arts’ shared cultural history

GamwellMathematicians and artists have historically shared a common interest: inquiry and comprehension of the intricacies of the world around them, whether through numerical or aesthetic design. Illustrating the relationship between math and art from antiquity to present day, Lynn Gamwells Mathematics and Art highlights the significant impact these two linked worlds have on one another. Gamwell recently took the time to answer some questions about her book. Examining the modern disciplines of art and math, she reveals the profound philosophy of self-reflection that these two cultural and intellectual pursuits share. Don’t forget to check out the stunning slideshow following the Q&A.

What’s the basic idea of your book?

LG: I started with the assumption that how people understand reality relates directly to the concepts of mathematics that develop in their culture. Mathematics is a search for patterns, and artists, in turn, create visualizations of the patterns discovered in their time. So I describe a general history of mathematics and the related artwork.

Since you begin in Stone Age times, your book covers over 5000 years. Is there a historical focus to the book?

LG: Yes, there are 13 chapters, and the first gives the background up to around 1800 AD. The other 12 chapters are on the modern and contemporary eras, although I occasionally dip back into pre-modern times to give the background of a topic. A central question that drove my exploration of the modern era was: where did abstract, non-objective art come from? Between around 1890 and 1915, many artists stopped depicting people and landscapes and start using pure color and form as the vocabulary of their art. Why? I argue that modern art is an expression of the scientific worldview. Beginning in the late nineteenth century and continuing today, researchers describe bacteria, cells, radiation, and pulsars that are invisible to the unaided eye, as well as mathematical patterns in nature.

Can you give a few examples of the relation of math and art?

LG: Italian Renaissance artists, such as Leonardo da Vinci, constructed the space in paintings such as The Last Supper using linear perspective, which is a geometric projection invented in the 1430s by the architect Filippo Brunelleschi. In the twentieth century, Swiss Constructivists such as Karl Gerstner created symmetrical patterns based on the mathematics of group theory, which measures the amount of symmetry in a system, such as atoms and sub-atomic particles. The contemporary America artist Jim Sanborn uses topology, which is the projection of geometric shapes onto surfaces that are stretched and distorted. For example in photographs of cliffs in Ireland, Jim first projected concentric circles onto the rocks and then took the photograph with a long exposure at moonrise. These artists are, of course, interested in many other things besides mathematics; aesthetic issues are their primary focus.

The examples you give are artists who are inspired by math; are mathematicians ever influenced by art?

LG: Mathematics are rarely inspired by a particular piece of art (since most artists use elementary arithmetic and geometry), but rather they aspire to include in their proofs general aesthetic qualities, such as purity, simplicity, and elegance.

You mention Leonardo da Vinci; didn’t he use the Golden Ration?

LG: No. It is a common misconception that a ratio described by Euclid as “mean and extreme ratio” has been used by artists throughout history because it holds the key to beautiful proportions. This myth was begun in the early nineteenth century by a German scholar who called Euclid’s ratio “golden.” The myth took a tenacious hold on Western intellectuals because, as science was beginning to take them off their privileged pedestal, it assured them that all beauty is based on a ratio embodied in human anatomy. There is no science supporting this claim.

Your book is a global history; did you find that there is a difference between math in the East and West?

LG: Yes, because a culture’s understanding of mathematics is based in its understanding of reality. In antiquity, Eastern mathematics in based in Taoism, the view that nature is composed of myriad parts that came together by self-assembly into a harmonious whole. Thus Chinese mathematicians discerned patterns in numbers, such as the Luoshu (magic square), in which numbers in the rows, columns, and diagonals have the same sum (the harmonious whole). On the other hand, Western cultures believed that a divine person (The Egyptian sun-god Ra, the God of Abraham, Plato’s carpenter) had imposed order on formless chaos. Thus Westerners went looking for this order, and they found it in the movement of the stars (the Babylonian zodiac), and the planets (Kepler’s Laws of Planetary Motion). Although there was a difference between Eastern and Western math when there was little contact, in today’s culture there is one global math.

The book includes the diverse fields of art, philosophy, mathematics, and physics; what is your educational background?

LG: I have a BA in philosophy and a PhD in art history. I’m self-taught in the history of science and math.

At 576 pages, this is a long book with extensive endnotes and 500+ illustrations; how long did it take you?

LG: 12 years of research and writing, plus one year in production.

Did you make any discoveries about art that especially surprised you?

LG: Yes. When I started my research I thought that artists during the modern era (the twentieth- and twenty-first centuries) would have only a vague knowledge of the math of their times, because of the famed “two cultures” divide. But I found specific historical evidence (an artist’s essay, manifesto, interview, or letter), which demonstrated that the artist had direct knowledge of a particular piece of mathematics and had embodied it in his or her art. Examples include: Aleksandr Rodchenko, Henry Moore, Piet Mondrian, Max Bill, Dorothea Rockburne, as well as musicians, such as Arnold Schoenberg, and poets, such as T. S. Eliot and James Joyce. Again, I would stress that for such artists mathematics is a secondary interest at best, and they are concerned with materials, expressive content, and purely aesthetic issues.

Any surprising discoveries about math and science?

LG: Yes, here are two. Much of what is taught as physics is really philosophy (interpretation) of physical data. An example is the Copenhagen interpretation of quantum physics, which was taught as THE gospel truth from its announcement in 1927 to around 1960. In fact, there are other ways to interpret the same laboratory data, which were largely ignored. I’m used to such dogmatism in the art world, where artists and critics are known to proclaim what art IS, but I expected to find a more cool-headed rationalism in the laboratory. Alas, we’re all human beings, driven by our passions. Another example is the strong resistance to Platonism (the view that abstract objects exist outside time and space) in modern culture, even though Platonism is the view held by most working mathematicians (i.e., they believe they are discovering patterns not creating them). While doing research, I found myself viewed with suspicion of being a religious missionary (disguised as a scholar) because I gave a sympathetic reading of historical religious documents (in other words, I tried to describe reality from their point of view). In fact, my outlook is completely secular. I came to realize that many secularists are unable to separate Platonism from its long association with religious doctrine, which touches a nerve in certain otherwise dispassionate academics.

Are you planning another project? What are you going to do next?

LG: I’m going to take some time off and regroup. I’ve started to think about writing something for children.

Check out the slideshow highlighting just a few of the book’s stunning images:

Lynn Gamwell is lecturer in the history of art, science, and mathematics at the School of Visual Arts in New York. She is the author of Exploring the Invisible: Art, Science, and the Spiritual (Princeton).

The Digital Einstein Papers: An Open Access Story

EinsteinA year ago in December, Princeton University Press rolled out an unprecedented open access initiative: the ongoing publication of Einstein’s massive written legacy comprising more than 30,000 unique documents. The Digital Einstein Papers, one of the most ambitious publishing projects ever undertaken, launched to widespread fanfare from the scientific, publishing, and tech communities, with enthusiastic coverage from The New York Times, (which hailed the papers as “the Dead Sea Scrolls of Physics”), to Inside Higher Ed, The Guardian, and far beyond. You can watch Diana Buchwald, editor of The Collected Papers of Albert Einstein, launch The Digital Einstein here.

A year out, what has the success looked like in terms of traffic? Ken Reed, Digital Production Manager at Princeton University Press takes us behind the scenes:

The Digital Einstein Papers site launched on 5 December 2014, and in the past year has had over 340,000 sessions, with over 3.2 million pageviews.

Site traffic has been worldwide, with the top five countries in order being the United States, Germany, India, Canada, and Brazil. The site is mobile optimized, especially for the iOS, which accounts for 50% of mobile traffic to the site. This is vital for global users, since by some accounts the mobile share of web traffic is now at 33% globally.

The Papers features advanced search technology and allows users to easily navigate between the original languages in which the texts were written and their English translation, as well as extensive supplementary material. But the Press is always looking to make technological improvements. In the past year, Princeton University Press has worked closely with the developer, Tizra, to monitor traffic and continually tweak display issues, especially around mobile devices. We have recently added a news tab, and the future will hold more enhancements to the site, including added functionality for the search results, and the addition of a chronological sort.

At present, the site presents 13 volumes published by the editors of the Einstein Papers Project, with a 14th slated to go online in 2016. Here is just a sampling of the included documents:

“My Projects for the Future” — In this high school French essay, a seventeen-year-old Einstein describes his future plans, writing that “young people especially like to contemplate bold projects.”

Einstein’s first job offer — Einstein graduated from university in 1900, but had great difficulty finding academic employment. He received this notice of his appointment as a technical clerk at the Swiss Patent Office in June 1902 and would later describe his time there as happy and productive.

“On the Electrodynamics of Moving Bodies” — Einstein’s 1905 paper on the special theory of relativity is a landmark in the development of modern physics.

Keep an eye on this exciting open access project as it evolves in 2016 and beyond. Explore for yourself here.

New Mathematics Catalog

We invite you to browse our Mathematics 2016 catalog:


Penrose In his forthcoming book, Roger Penrose makes the case that physicists are just as prone to be influenced by fashion, faith, and fantasy as anyone else. Sometimes, these forces can be positive, he argues, but they often lead researchers astray. Pick up a copy of Fashion, Faith, and Fantasy in the New Physics of the Universe to learn more.
AshGross Interested in numbers? Then Summing It Up by mathematicians Avner Ash and Robert Gross is for you! Ash and Gross have written an accessible book about current mathematical research that can be enjoyed by those with a casual interest and college math majors alike.
Nahin Paul J. Nahin explains how physics can be found in everyday situations in In Praise of Simple Physics. You’ll be surprised at how often you use it!

If you would like to be updated on new titles, subscribe to our newsletter.

Finally, if you’re going to be in Seattle for the Joint Mathematics Meeting from January 6 to January 9, visit PUP at booth #105 or follow it online using #JMM16.

Introducing the mesmerizing new trailer for Mathematics and Art

Looking for a unique coffee table book for someone mathematically or artistically inclined? Mathematics and art are surprisingly similar disciplines, given their distinctively introspective, expressive natures. Even before antiquity, artists have attempted to render mathematical concepts in visual form, and the results have often been spectacular. In a stunning illustrated cultural history that one truly has to see to appreciate, Lynn Gamwell of the School of Visual Arts in New York explores artistic representations from the Enlightenment—including Greek, Islamic, and Asian mathematics—to the modern era, including Aleksandr Rodchenko’s monochrome paintings. Check out her piece on the Guardian’s Adventures in Numberland blog, and the trailer for Mathematics and Art, here:


Romance, Crime, and… Mathematics? Presenting the new trailer for LA Math

LA Math by James D. Stein, emeritus professor in the Department of Mathematics at California State University, is full of A-listers and wannabes, lovers and lawyers, heroes and villains. And it’s also full of math—practical mathematics knowledge, ranging from percentages and probability to set theory, statistics, and the mathematics of elections. Check out the new trailer for this unconventional and highly readable book of mathematical short stories here:

Andrew Robinson to talk on “Einstein in Oxford” at Christ Church

In late 1915, in Berlin, Albert Einstein announced the general theory of relativity: his greatest achievement. In 1931-33, he lectured on relativity in Oxford, receiving an honorary degree from the university and staying in rooms in Christ Church, before fleeing his home in Nazi Germany and settling in Princeton. How much is known about Einstein’s time in the city of dreaming spires? For the centenary of general relativity, Einstein biographer Andrew Robinson will give a talk on “Einstein in Oxford” at Christ Church, Oxford on December 3. Robinson, the author of Einstein: A Hundred Years of Relativity, will reflect on relativity, Einstein’s intriguing relationship with Oxford and the puzzle of his universal fame. 

Ahead of his talk, Robinson shares some fascinating details about the historic visit:

Einstein in Oxford

By Andrew Robinson

My father was a physicist at Oxford’s Clarendon Laboratory for more than four decades, revered Einstein’s work and wrote a textbook on relativity. I was born, brought up and largely educated in Oxford. So I am naturally curious about Einstein’s relationship with the city.

When Einstein paid his first visit to England in 1921, The Times carried a two-sentence news item headlined “Professor Einstein at Oxford”. It read as follows: “Professor Einstein paid a private visit to Oxford University as the guest of Dr. Lindemann of Wadham College. A tour was made of the principal University buildings and the Professor returned to London in the evening.”

Einstein receiving an honorary degree at Oxford. Source:

Nothing further came of this Oxford visit for a decade. But the name of Einstein’s host in Oxford in 1921, the physicist Frederick Lindemann, proved to be very important. Though born in Germany in 1886, Lindemann was actually brought up in Britain and regarded himself as British. But he returned to Germany as a PhD student in Berlin. In 1911, when his Berlin supervisor, the future Nobel laureate Walther Nernst, organized a key scientific conference in Brussels—the first Solvay Congress—Nernst appointed his student Lindemann as one of the scientific secretaries of the conference. And it was at this historic conference—where the young Einstein lectured on quantum theory—that Lindemann first met him.

In 1919, Lindemann was elected Dr Lee’s professor of experimental philosophy (that is, physics) in Oxford, and began the much-needed rejuvenation of physics at the university, centred on the Clarendon Laboratory. The Dr Lee’s chair was attached to Wadham College, where Lindemann remained a fellow until his retirement. But in 1921 Lindemann was also elected, as was legally possible in those days, to a “studentship not on the governing body” at Christ Church, which had provided the endowment for the chair. This entitled Lindemann to rooms in Christ Church that were more spacious than Wadham could provide, and from 1922 for the rest of his life, until his death in 1957, ‘Prof’, as Lindemann was known, lived in Christ Church. He was living there when he became close to Winston Churchill in the mid-1920s and eventually acted as Churchill’s key scientific adviser during the Second World War.

In 1927, Lindemann made his first attempt to persuade Einstein to return to Oxford and give one or two lectures, on behalf of the newly established Rhodes Trust—without success. In 1930, he tried again. This time, Einstein agreed, then changed his mind. But Lindemann was determined. He saw Einstein in person in Berlin, and also worked on Mrs Einstein. Einstein agreed to give three lectures—one on relativity, the second on cosmological theory and the third on his much-discussed unified field theory—and to stay in Oxford for some weeks. A solicitous Lindemann assured Mrs. Einstein in a letter:

He can of course have as many meals as he likes alone in his rooms and I will endeavour to preserve him as much as possible from importunate invitations. I am taking steps to see that he can get some sailing, so that I hope he will not feel that he is wasting his time here altogether.

Einstein arrived in Oxford in early May 1931 and was given rooms in Christ Church on Tom Quad (now the Graduate Common Room) belonging to the classical scholar Robert Hamilton Dundas, who was away on a world tour in 1930-31. At a practical level, he was looked after by Lindemann’s indefatigable manservant and general factotum, James Harvey. Lindemann himself acted as Einstein’s mentor and guide, showing him the sights and introducing him to various friends and acquaintances. According to Lindemann, over the course of Einstein’s visit, he “threw himself into all the activities of Oxford science, attended the Colloquiums and meetings for discussion and proved so stimulating and thought-provoking that I am sure his visit will leave a permanent mark on the progress of our subject.”

His first Rhodes lecture was on 9 May. Entitled “The Theory of Relativity”, it drew a packed house in the Milner Hall of Rhodes House, with some people standing. But since the lecture included much mathematics and was also in German, it quickly went over the heads of most of the audience. Those whose maths was good enough to follow Einstein’s calculations, mostly lacked sufficient German to follow his words, while the German speakers certainly lacked sufficient maths.

By the time of the second lecture a week later, devoted to the recent notion of an expanding universe, there were somewhat fewer listeners. As The Times correspondent cautiously noted:

Once more he had an audience which, though not so large as for his first lecture, almost filled the hall. An analysis of the audience was interesting. Senior and junior members of the University were divided by a barrier. The senior members consisted chiefly of teachers in the faculties of Literae Humaniores, mathematics, natural science, and theology, all of whom are affected in some degree by the new theory. The junior members were drawn by considerations partly of science, partly of language, and partly of curiosity. The element of curiosity, however, was not so strong as for the previous lecture, and most of those present had a serious interest.… Two blackboards, plentifully sprinkled beforehand in the international language of mathematical symbol, served him for reference.

One of these Einstein blackboards was wiped by an over-zealous cleaner. Fortunately, the other one was rescued by one of the Oxford dons with a serious interest in relativity, who whisked it away to the Museum of the History of Science in Broad Street, where it today attracts much intrigued, if bemused, attention from visitors. (The wiped blackboard still exists, too, but lies ignominiously in the storeroom of the Museum.)

Just before the third lecture on 23 May, Einstein was awarded an honorary doctorate by the University at the Sheldonian Theatre. The Public Orator, presenting Einstein to the vice-chancellor in Latin, claimed that relativity, “which touched both science and philosophy, was specially acceptable to Oxonians … who had learnt from Heraclitus that you could not bathe in the same river twice”.

Then the audience in the Sheldonian—or at least those members strong enough to cope not only with Latin but also with Einstein’s German and his mathematics—proceeded to Rhodes House. After this lecture, Einstein remarked that the next time he had to lecture in Oxford, “the discourse should be in English delivered”. To which one of Lindemann’s friends was heard to murmur in German: “Bewahr!” But two years later, when Einstein gave the Herbert Spencer lecture in Oxford in 1933, “On the Method of Theoretical Physics”, he wisely spoke it in an excellent English version translated from his German by colleagues from Christ Church. This lecture included a piercing tribute to an Einstein hero, Galileo:

Conclusions obtained by purely rational processes are, so far as Reality is concerned, entirely empty. It was because he recognized this, and especially because he impressed it upon the scientific world, that Galileo became the father of modern physics and in fact of the whole of modern natural science.

However, Einstein also stated, controversially, his growing view—which would come to dominate his work in the United States—of the importance of mathematics over experiment in devising physical theories:

It is my conviction that purely mathematical construction enables us to discover the concepts and the laws connecting them which give us the key to the understanding of the phenomena of Nature. Experience can of course guide us in our choice of serviceable mathematical concepts; it cannot possibly be the source from which they are derived; experience of course remains the sole criterion of the serviceability of a mathematical construction for physics, but the truly creative principle resides in mathematics. In a certain sense, therefore, I hold it to be true that pure thought is competent to comprehend the real, as the ancients dreamed.

Undoubtedly, Einstein left a pleasant impression on the students (fellows) of Christ Church. The classicist Dundas—in whose rooms Einstein lived in 1931—was tickled to find a poem by Einstein written in German in his visitor’s book when he returned from his world tour, including the verse:

Grumble: Why’s this creature staying

With his pipe and piano playing?

Why should this barbarian roam?

Could he not have stopped at home?

While the economist Roy Harrod wrote in his biography of Lindemann that Einstein “was a charming person, and we entered into relations of easy intimacy with him.” Harrod recalled vividly that Einstein

divided his time between his mathematics and playing the violin; as one crossed the quad, one was privileged to hear the strains coming from his rooms. In our Governing Body I sat next to him; we had a green baize table-cloth; under cover of this he held a wad of paper on his knee, and I observed that all through our meetings his pencil was in incessant progress, covering sheet after sheet with equations.

On one occasion, Einstein turned up at the college’s entrance gate in a pony cart driven by a girl he had met over lunch at the house of some friends of Lindemann. Some of his admirers were waiting to help him out of the cart, but a big button from his Ulster had caught in the cart’s basket-work. His lady driver wanted to disentangle it and give it to Einstein, but the college porter said: ‘I wouldn’t worry, Miss. The gentleman will never miss it. He has one odd button on his coat already.” “Oh, in that case I shall keep it,” said the girl. “I shall probably never drive anyone so famous again!”

Robinson jacketAndrew Robinson will give a talk on “Einstein in Oxford” at Christ Church, Oxford on 3 December 2015. He is the author of Einstein: A Hundred Years of Relativity, published by Princeton University Press in 2015, and Genius: A Very Short Introduction, published by Oxford University Press in 2011.

#ThanksEinstein: J.P. Ostriker on Einstein and the wonder of pure thought

Einstein meme

Questions with No Reply

J. P. Ostriker

J.P. Ostriker is an astrophysicist and the co-author of Heart of Darkness, which tells the saga of humankind’s quest to unravel the deepest secrets of the universe: dark matter and dark energy. Here is his story about how an Einstein thought experiment he encountered as a teenager changed his life.

When I was a high school student I drove my teachers crazy with incessant and insatiable curiosity about the natural world. Next to our pictures in the yearbook, one of the teachers had added a line for each student and for me it was “I thought of questions that have no reply.”

And for the questions that I had that my teachers could not or would not answer, I went to books. Einstein wrote several of these that were accessible to high school students, and they fascinated me. I remember a “thought experiment” presented in one of them: A scientist sets up an exquisite laboratory on a train and tests both Newton’s laws of mechanics and Maxwell’s laws of electricity and magnetism. And, hypothetically, one finds that both are correct to arbitrary precision.

train image, copyright: phildaintThen the train begins to move and E shows that, since the laws transform differently with the velocity of the observer, they can no longer both be true! Therefore one (or both) theories must be false.

This amazed me. No experiment was necessary. Pure thought was all that was needed and any high school student who thought about it could have come to the same conclusion as Einstein, and could have invented special relativity to solve the problem! I thought that this was wonderful, truly wonderful. I resolved that I would pursue physics and think about simple and fundamental matters. It looked easy.

Well, needless to say it was not always easy, but it has always been fun. I’m thankful I had access to Einstein’s popular books when I was a teenager with more questions than answers.

Jeremiah P. Ostriker is professor of astrophysical sciences at Princeton University. He is author, with Simon Mitton, of Heart of Darkness: Unraveling the Mysteries of the Invisible Universe. His books include Formation of Structure in the Universe and Unsolved Problems in Astrophysics (Princeton).


Train tracks image from Shutterstock, copyright: phildaint

PUP congratulates writers chosen for The Best Writing on Mathematics 2015

Highlighting the finest articles published throughout the entire year, The Best Writing on Mathematics 2015 shines the spotlight on math’s brightest, most creative minds. Edited by Mircea Pitici, the volume is inviting to experienced mathematicians and numbers novices alike.

The Best Writing on Mathematics, in its sixth edition, offers surprising and meaningful insights and perspectives into the highly influential world of mathematics. Colm Mulcahy and Dana Richards express their appreciation and reflections of the significant work of icon Martin Gardner, Toby Walsh creatively uses the popular game Candy Crush as a vehicle to analyze the hardships of solving computational problems, Benoît Rittaud and Albrecht Heeffer investigate and question the true derivation of the pigeonhole principle, Carlo Cellucci considers and defines beauty in mathematics — and that’s just the beginning.

Best Writing on Math 2015

Congratulations to those chosen to be included in The Best Writing in Mathematics 2015!

Interpreting mathematics is not about mathematical truth (or any other truth); it is a personal take on mathematical facts, and in that it can be true or untrue, or it can even be fiction; it is vision, or it is rigorous reasoning, or it is pure speculation, all occasioned by mathematics; it is imagination on a mathematical theme; it goes back several millennia and it is flourishing today, as I hope this series of books lays clear, (xiii)

— Mircea Pitici, Editor


Articles and authors selected in The Best Writing on Mathematics 2015

Articles Authors
A Dusty Discipline Michael J. Barany and Donald MacKenzie
How Puzzles Made Us Human Pradeep Mutalik
Let the Games Continue Colm Mulcahy and Dana Richards
Challenging Magic Squares for Magicians Arthur T. Benjamin and Ethan J. Brown
Candy Crush’s Puzzling Mathematics Toby Walsh
Chaos on the Billiard Table Marianne Freiberger
Juggling with Numbers Erik R. Tou
The Quest for Randomness Scott Aaronson
Synthetic Biology, Real Mathematics Dana Mackenzie
At the Far Ends of a New Universal Law Natalie Wolchover
Twisted Math and Beautiful Geometry Eli Maor and Eugen Jost
Kenichi Miura’s Water Wheel, or The Dance of the Shapes of Constant Width Burkard Polster
Dürer: Disguise, Distance, Disagreements, and Diagonals! Annalisa Crannell, Marc Frantz, and Fumiko Futamura
The Quaternion Group as a Symmetry Group Vi Hart and Henry Segerman
The Steiner-Lehmus Angle Bisector Theorem John Conway and Alex Ryba
Key Ideas and Memorability in Proof Gila Hanna and John Mason
The Future of High School Mathematics Jim Fey, Sol Garfunkel, Diane Briars, Andy Isaacs, Henry Pollak, Eric Robinson, Richard Scheaffer, Alan Schoenfeld, Cathy Seeley, Dan Teague, and Zalman Usiskin
Demystifying the Math Myth: Analyzing the Contributing Factors for the Achievement Gap between Chinese and U.S. Students Guili Zhang and Miguel A. Padilla
The Pigeonhole Principle, Two Centuries before Dirichlet Benoît Rittaud and Albrecht Heeffer
A Prehistory of Nim Lisa Rougetet
Gödel, Gentzen, Goodstein: The Magic Sound of a G-String Jan von Plato
Global and Local James Franklin
Mathematical Beauty, Understanding, and Discovery Carlo Cellucci
A Guide for the Perplexed: What Mathematicians Need to Know to Understand Philosophers of Mathematics Mark Balaguer
Writing about Math for the Perplexed and the Traumatized Steven Strogatz
Is Big Data Enough? A Reflection on the Changing Role of Mathematics in Applications Domenico Napoletani, Marco Panza, and Daniele C. Struppa
The Statistical Crisis in Science Andrew Gelman and Eric Loken
Statistics and the Ontario Lottery Retailer Scandal Jeffrey S. Rosenthal
Never Say Never David J. Hand

Mircea Pitici holds a PhD in mathematics education from Cornell University, where he teaches math and writing. He has edited The Best Writing on Mathematics since 2010.

Children’s Literature for Grownups #ReadUp

Have you ever found yourself returning to a book considered “children’s literature?” There’s just something about our favorite children’s books that can draw us in. What’s with the magnetism? Children’s books are a part of our literary foundation, and some of the best ones hold a special place in our hearts. Or is it something more?

k10538Remember reading Alice’s Adventures in Wonderland? First published in 1865, PUP is publishing a new edition in honor of the 150th anniversary, illustrated by none other than the famous surrealist, Salvador Dalí.

The whimsical world of Wonderland holds a special charm for both children and adults. You can bet more adults will be purchasing this item for themselves than for their children, both for the sense of nostalgia and for the promise of new things that children’s books inevitably hold. This promise is much more prominent in children’s books than it is in adult books because children’s books are written differently. They are written with the idea that they will likely be revisited, often including multiple layers and facets. Just ask Neil Gaiman. In a recent article, Gaiman notes that “When I’m writing for kids, I’m always assuming that a story, if it is loved, is going to be re-read. So I try and be much more conscious of it than I am with adults.”

Re-reading a children’s book as an adult brings the gift of new perspective. Would you read A Wrinkle in Time or The Hobbit the same way now as you did when you were 10? We might find and identify common themes, or develop sympathies for characters we formerly loved to hate. When we revisit these stories later in life, we read them with a new lens, one altered by experience and time, often picking up on new and interesting tidbits that we never knew existed. This is particularly true of fairy tales. If these Disney-esque stories are meant for children, why do we, as adults, enjoy them so much? The answer probably lies in their adult origins. One of PUP’s most popular recent books is The Original Folk and Fairy Tales of the Brothers Grimm: The Complete First Edition. The first edition. Take note.k10300

AndreaDezso_BrothersGrimm3As David Barnett states in The Guardian in a piece titled, Adult content warning: beware fairy stories, “Wilhelm and Jacob Grimm . . . did not set out to collect the stories that bear their name in order to entertain children. They were primarily collectors and philologists, who assembled their tales as part of a life’s work. . . . And they were surprised when the adults who bought their collections of fairy tales to read to their children began to complain about the adult nature of the content.”

These stories were not polished and sanitized until much later. Originally, they were filled with violence and other adult content. (As evidenced by the picture on the above left, by Andrea Dezsö, featured in PUP’s The Original Folk and Fairy Tales of the Brothers Grimm). This image is from a tale entitled Herr Fix-It-Up. Herr Fix-It-Up must complete tasks denoted by a lord and king in order to win the lord his princess bride. One of the tasks is to kill a unicorn that’s been “causing a great deal of damage.” By today’s standards, beheading of unicorns is hardly the stuff of children’s tales, but these tales are more sociological accounts than children’s stories, reflecting the sensibilities of the time period and place in which they were written.

UntitledOthk10312er “children’s” books expand on this very aspect of fairy tales, including The Fourth Pig by Naomi Mitchison. Mitchison takes many of the classic tales of our childhood including Hansel and Gretel and The Little Mermaid and re-imagines them for an older audience.

As a fairly new member of the press, it never occurred to me that some titles on our list would include some of my old favorites. What children’s books do you love more as an adult?


You can take a tour of the gorgeous interior of Alice’s Adventures in Wonderland here:



Feature image by Steve Czajka –

Frontispiece designed by Gertrude Hermes


Feynman on the historic debate between Einstein & Bohr

The golden age of quantum theory put many of the greatest minds of the 20th century in contact with some of the most significant scientific and philosophical questions of their era. But it also put these minds in contact with one another in ways that have themselves been a source of curiosity and ongoing scientific debate.

Richard Feynman and Albert Einstein, two towering geniuses of their time, were both as revered for their scientific contributions as they were beloved for their bursts of wisdom on a wide range of subjects. It’s hard not to wonder just what these men thought of one another. Princeton University Press, which published The Ultimate Quotable Einstein in 2010 publishes The Quotable Feynman this fall. The book includes reflections by Feynman on Einstein, from his memorable mannerisms to his contributions to some of the most heated debates in 20th century science.Feynman quote

Perhaps because of the gap between their career high points, (Einstein died in 1955; Feynman didn’t receive his Nobel Prize until 1965), there are no verified quotes where Einstein alludes to Feynman or his expansive body of work. But Feynman had made observations on the older physicist, several of which revolve around Einstein’s famous 1927 public debate with Niels Bohr on the correctness of  quantum mechanics. Central to the debate was this question: Were electrons, light, and similar entities waves or particles? In some experiments they behaved like the former, and in others, the latter.

In an attempt to resolve the contradictory observations, Einstein proposed a series of “thought experiments”, which Bohr responded to. Bohr essentially took the stance that the very act of measuring alters reality, whereas Einstein insisted that reality exists, independent of the act of measurement. Key to the philosophy of science, the dispute between the two giants is detailed by Bohr in “Discussions with Einstein on Epistemological Problems in Atomic Physics”. Richard Feynman is quoted as commenting on the debate:Feynman quote 2

An Einstein Encyclopedia contains a section on the Einstein-Bohr debates, as well as a wealth of other information on Einstein’s career, family, friends. There is an entire section dedicated to righting the various misconceptions that swirl around the man, and another on his romantic interests (actual, probable, and possible).

In spite of their differences, Bohr and Einstein were friends and shared great respect for each others’ work. Until Einstein’s death 3 decades later, they continued their debates, which became, in essence, a debate about the nature of reality itself.  feynman quote 3

Check out other new Einstein publications this fall, including:

An Einstein Encyclopedia
The Road to Relativity

Why Calculus Will Save You from the Zombie Apocalypse

To survive a zombie apocalypse, one will need more than instinct and short term solutions – one will need logic and, most importantly, math. A thought-out plan comprised of sophisticated calculus equations will ensure long-term safety objectives. Thankfully, Zombies and Calculus by Colin Adams colorfully illustrates the critical implementation of calculus components when going head-to-head with zombies. Adams demonstrates how a professor and his students successfully exercise calculus to survive the attacks of zombies who not only disrupt their calculus class (the horror!), but are also out for human flesh.

Here are a few need-to-knows:

Zombies travel approximately at one yard per second – a constant derivative.

A derivative of a function is its rate of change. If a function is changing quickly, its derivate will be high, while if a function is changing slowly, its derivate will be low. Adams explains that we can measure the function’s rate of change through the steepness of the tangent line. zombies and calculus rate of change
Since speed is defined as distance divided by time, one can calculate the speed required to get from Point A to Point B in a specific time, while being able to evade any unwanted visitors (zombies). Keep in mind — speed tends to vary (not for zombies, remember, they travel in a constant derivative!), so the derivate of the function has the potential to increase or decrease. Using these simple formulas, one is able to plan out the distance, time, and speed needed to outrun these deadly predators.

It’s hard to crack a zombie’s skull. It’s easier to knock a zombie unconscious.

As detailed in Zombies and Calculus, the amount of force necessary to crack a human skull is 10,000 newtons (a newton is a measurement for force that equals 1 kilogram meter per second squared). Adams offers an example: if a baseball is going 90 miles per hour (40.2 meters/second), weighs 5 ounces (0.145 kilograms), and comes into contact with a head for .007 seconds, its force can be calculated through:Screen Shot 2015-10-29 at 4.44.31 PMSo since a baseball, with said specifications, can only create approximately 800 newtons, imagine how much force is needed to produce 10,000 newtons! When attacking a zombie with force, do not try to go for the easy kill — rather play strategically by knocking the zombie unconscious with a sudden sharp blow to the head. This will create a dramatic head jerk, causing the brain to get knocked around in the cranial cavity, thus causing a short circuit. The benefit of knocking a zombie unconscious, of course, is additional planning and escape time!

Zombies pursue in a radiodrome path.

Like a dog pursues a rabbit, a zombie pursues its human prey. A zombie will follow its prey’s path at the prey’s given location at that specific instant. In a scene from Zombies and Calculus, (pause to imagine it), a Dean is running towards the safe haven of an academic building in a straight line. However, a zombie is present and begins to pursue the Dean, always having its tangent vector pointing at the Dean. The zombie is going to travel to wherever the Dean is in that current moment. Screen Shot 2015-10-29 at 4.39.23 PM

Since zombies are incapable of developing an efficient plan, the zombie does not run at a diagonal towards the academic building, which would cut-off the dean’s path. Instead of recognizing the Dean’s travel pattern or destination, the zombie is chasing the dean like a dog chasing a bunny’s tail to the rabbit hole. If only the dog knew that its radiodrome procedure was flawed, the dog would be able (with a speed higher than the rabbit) to cut-off the rabbit at its hole and claim victory. If dogs were to catch on, there would probably be fewer bunnies hopping around.

Cold-blooded creatures are unable to regulate their body heat.

Like other cold-blooded creatures, zombies hibernate. A zombie’s body temperature will decrease according to the differential equation that guides the temperature change of an object placed in a space with a different temperature (so for instance, if a zombie with a temperature of 60 degrees is placed a room of 30 degrees.) According to Newton’s Law of Cooling (remember Newton from discussing the measurement ‘newton’ for force?), the temperature of a body’s rate of change is proportional to the difference between the present temperature of that body and the ambient temperature (basically, the temperature of its surroundings). Given as a function of time, the zombie’s temperature (where Tg is the specific location):Screen Shot 2015-10-29 at 4.42.31 PMThe larger the contrast of temperatures, the faster the body temperature will drop. As the characters in the book discover, if there is a zombie apocalypse, it might be time to consider a move to our friendly neighbor to the north, Canada.


Zombies and CalculusTo discover more lifesaving tips, fun and entertaining mathematical applications, and learn the fate of the brave calculus professor and his students, read Colin Adam’s  Zombies and Calculus. Just in case the zombie apocalypse does occurs (maybe tomorrow?) it should be comforting to know there’s a mathematical guide to survival on your bookshelf.

An exclusive trailer for Alice’s Adventures in Wonderland, featuring illustrations by Salvador Dalí

ALICE WAS BEGINNING TO get very tired of sitting by her sister on the bank, and of having nothing to do: once or twice she had peeped into the book her sister was reading, but it had no pictures or conversations in it, “and what is the use of a book,” thought Alice, “without pictures or conversations?”

Thus begins Alice’s Adventures in Wonderland, one of the most beloved classics of children’s literature. Commemorating the 150th anniversary of its publication, this illustrated edition of Alice’s Adventures in Wonderland, edited by Lewis Carroll expert Mark Burstein, features rarely seen illustrations by Salvador Dalí. In the introduction, Burstein discusses Dalí’s connections with Carroll, the nature of wonderland, and his treatment of the towering (though sometimes shrinking) figure of Alice.

Take an exclusive peek inside the curiously mathematical world into which Alice famously falls, here: