Peter Dougherty & Al Bertrand: On Being Einstein’s Publisher

by Peter Dougherty and Al Bertrand

So many people today—and even professional scientists—seem to me like somebody who has seen thousands of trees but has never seen a forest. (Albert Einstein to Robert A Thornton, 7 December 1944, EA 61-574)

For all of the scholarly influences that have defined Princeton University Press over its 111-year history, no single personality has shaped the Press’s identity as powerfully, both directly and indirectly, as Albert Einstein. The 2015 centenary of the publication of Einstein’s “Theory of General Relativity” as well as the affirmation this past February and again in June of the discovery of gravitational waves has encouraged us to reflect on this legacy and how it has informed our identity as a publisher.

The bright light cast by Einstein the scientist and by Einstein the humanist has shaped Princeton University Press in profound and far-reaching ways. It expresses itself in the Press’s standard of scholarly excellence, its emphasis on the breadth and connectedness of liberal learning across all fields, and in our mission of framing scholarly arguments to shape contemporary knowledge. All the while, Einstein’s role as a citizen of the world inspires our vision to be a truly global university press.


Albert Einstein is not only Princeton University Press’s most illustrious author; he was our first best-selling author. Following his public lectures in Princeton in 1921, the Press—itself less than 20 years old at the time—published the text of those lectures, titled “The Meaning of Relativity”, in 1922. Publication followed the agitated exhortation of the Press’s then-manager, Frank Tomlinson, urging Professor Einstein to get his manuscript finished. Tomlinson wrote:

My dear Professor Einstein—

On July 6 I wrote you inquiring when we might expect to receive the manuscript of your lectures. I have had no reply to this letter. A number of people have been inquiring when the book will be ready, and we are considerably alarmed at the long delay in the receipt of your manuscript, which we were led to believe would be in our hands within a month after the lectures were delivered. The importance of the book will undoubtedly be seriously affected unless we are able to publish it within a reasonable time and I strongly urge upon you the necessity of sending us the copy at your earliest convenience. I should appreciate also the favor of a reply from you stating when we may expect to receive it.

the meaning of relativity jacketMr. Tomlinson’s letter marks something of a high point in the history of publishers’ anxiety, but far from failing, The Meaning of Relativity was a hit. It would go on to numerous successive editions, and remains very much alive today as both a print and digital book, as well as in numerous translated editions.

For all its glorious publishing history, The Meaning of Relativity can be thought of as a mere appetizer to the bounteous publishing banquet embodied in THE COLLECTED PAPERS OF ALBERT EINSTEIN, surely PUP’s most ambitious continuing publication and one of the most important editorial projects in all of scholarly publishing.

The Collected Papers of Albert Einstein

Authorized by the Einstein Estate and the PUP Board of Trustees in 1970, and supported by a generous grant from the late Harold W. McGraw, Jr., chairman of the McGraw-Hill Book Company, THE EINSTEIN PAPERS, as it evolves, is providing the first complete and authoritative account of a written legacy that ranges from Einstein’s work on the special and general theories of relativity and the origins of quantum theory, to expressions of his profound concern with civil liberties, education, Zionism, pacifism, and disarmament.

einstein old letterAn old saying has it that “good things come to those to wait,” words that ring resoundingly true regarding the EINSTEIN PAPERS. Having survived multiple obstacles in the long journey from its inception through the publication of its first volume in 1987, the Einstein Papers Project hit its stride in 2000 when Princeton University Press engaged Professor Diana Buchwald as its sixth editor, and moved the Project to Pasadena with the generous support of its new host institution, the California Institute of Technology.

Since then, Professor Buchwald and her Caltech-based editorial team, along with their international network of scholarly editors, have produced successive documentary and English translation volumes at the rate of one every eighteen months. To give you an idea of just how impressive a pace this is, the Galileo papers are still a work in progress, nearly four centuries after his death.

The EINSTEIN PAPERS, having reached and documented Einstein’s writings up to 1925, has fundamentally altered our understanding of the history of physics and of the development of general relativity, for example by destroying the myth of Einstein as a lone genius and revealing the extent to which this man, with his great gift for friendship and collegiality, was embedded in a network of extraordinary scientists in Zurich, Prague, and Berlin.

Along with the EINSTEIN PAPERS, the Press has grown a lively publishing program of books drawn from his work and about Einstein. Satellite projects include The Ultimate Quotable Einstein, as well as volumes on Einstein’s politics, his love letters, and the “miraculous year” of 1905.

Last year the Press published two new books drawn from Einstein’s writings, The Road to Relativity, and the 100th anniversary edition of Relativity: The Special and General Theory, both volumes edited by Jürgen Renn of the Max Planck Institute in Berlin, and Hanoch Gutfreund of the Hebrew University in Jerusalem.   These volumes celebrate the centenary of Einstein’s publication of the theory of general relativity in November 1915.

In this same centenary year, PUP published several other Einstein titles, including:

— Volume 14 of the Collected Papers, The Berlin Years, 1923-1925.

An Einstein Encyclopedia, edited by Alice Calaprice, Daniel Kennefick, and Robert Schulman;

Einstein: A Hundred Years of Relativity, by Andrew Robinson

Especially notable, in January 2015 the Press released THE DIGITAL EDITION OF THE COLLECTED PAPERS OF ALBERT EINSTEIN, a publishing event that has attracted extraordinary worldwide attention, scientific as well as public. This online edition is freely available to readers and researchers around the world, and represents the historic collaboration between the Press and its partners, the Einstein Papers Project at Caltech and the Albert Einstein Archive in the Hebrew University in Jerusalem.

Moreover, works by and about Einstein sit at the crossroads of two major components of the Princeton list: our science publishing program which comprises a host of fields from physics through mathematics, biology, earth science, computer science, and natural history, and our history of science program which connects PUP’s Einstein output to our humanities publishing, helping to bridge the intellectual gap between two major dimensions of our list.

Einstein’s dual legacy at Princeton University Press thus serves to bookend the conversation defined by the Press’s unusually wide-ranging array of works across and throughout the arts and sciences, from mathematics to poetry. C.P. Snow famously described the sciences and the humanities as “two cultures.” Einstein’s legacy informs our effort as a publisher to create an ongoing correspondence between those two cultures in the form of books, which uniquely serve to synthesize, connect, and nurture cross-disciplinary discourse.


Much as the living legacy of the EINSTEIN PAPERS and its related publications means to Princeton University Press as a publisher, it holds a broader meaning for us both as editors and as leaders of the institution with which we’ve long been affiliated.

Like most of our colleagues, we arrived at the Press as editors previously employed by other publishers, and having little professional interest in physics. Each of us specialized in different editorial fields, economics and classics, respectively.

Our initial disposition towards the field of physics, while full of awe, was perhaps best summed up by Woody Allen when he said: “I’m astounded by people who want to ‘know’ the universe when it’s hard enough to find your way around Chinatown.”  

But we soon discovered, as newcomers to PUP inevitably do, that the Princeton publishing legacy of Albert Einstein carried with it a set of implications beyond his specific scientific bounty that would help to shape our publishing activity, as well as that of our colleagues. We see the Einstein legacy operating in three distinct ways on PUP’s culture:

First, it reinforces the centrality of excellence as a standard: simply put, we strive to publish the core scholarly books by leading authors, senior as well as first-time. Einstein’s legacy stands as a giant-sized symbol of excellence, an invisible but constant reminder that our challenge as publishers at Princeton is not merely to be good, but to be great. As we seek greatness by publishing those books that help to define and unite the frontiers of modern scholarship, and connect our authors’ ideas with minds everywhere, we are upholding a standard embodied in the work of Albert Einstein.

The second implication of the bounty Albert Einstein is a commitment to seeing liberal knowledge defined broadly, encompassing its scientific articulation as well as its expression in the humanities and social sciences. PUP purposefully publishes an unusually wide portfolio of subject areas, encompassing not only standard university press fields such as literary criticism, art history, politics, sociology, and philosophy, but a full complement of technical fields, including biology, physics, neuroscience, mathematics, economics, and computer science. A rival publisher once half-jokingly described PUP as “the empirical knowledge capital of the world.” She was referring to our capacious cultivation of scientific and humanistic publishing, an ambitious menu for a publisher producing only around 250 books a year, but one we think gives the Press its distinctive identity.

It is no coincidence that Albert Einstein, PUP’s most celebrated author, cast his influence across many of these fields both as a scientist and as a humanist, engaged fully in the life of the mind and of the world. His legacy thus inspires us to concentrate our editorial energies on building a list that focuses on knowledge in its broadest and deepest sense—that puts into play the sometimes contentious, and even seemingly incongruous, methodologies of science and the humanities and articulates a broad yet rigorous, intellectual vision, elevating knowledge for its own sake, even as the issues change from decade to decade.

A third implication appears in Einstein’s challenge to us to be a great global publisher. Einstein, a self-professed “citizen of the world” was in many ways the first global citizen, a scholar whose scientific achievement and fame played out on a truly global scale in an age of parochial and often violent nationalist thinking.

Einstein’s cosmopolitanism has inspired the Press to pursue a path of becoming a truly global university Press. To do this, PUP has built lists in fields that are cosmopolitan in their readership, opened offices in Europe and China, expanded its author and reviewer base all over the world, and has licensed its content for translation in many languages. As we go forward, we intend to continue to build a network that allows us to connect many local publishing and academic cultures with the global scholarly conversation. This vision of the Press’s future echoes Einstein’s call for a science that transcends national boundaries.


It has been nearly a century since publication of The Meaning of Relativity and half that since the original agreement for the EINSTEIN PAPERS was authorized. We can only imagine that the originators of the latter project would be proud of what our collective effort has produced, grateful to the principals for the job they have done in bringing the PAPERS to their current status, and maybe above all, awed by the global exposure the PAPERS have achieved in their print and now digital formats.

As we continue our work with our colleagues at Caltech and the Hebrew University to extend the EINSTEIN PAPERS into the future, we are reminded of the significance of the great scientist’s legacy, especially as it bears on our identity as a global publisher, framing the pursuit of knowledge imaginatively across the arts and sciences.

The eminent Italian publisher Roberto Calasso, in his recent book, The Art of the Publisher, encourages readers to imagine a publishing house as,

“a single text formed not just by the totality of books that have been published there, but also by its other constituent elements, such as the front covers, cover flaps, publicity, the quantity of copies printed and sold, or the different editions in which the same text has been presented. Imagine a publishing house in this way and you will find yourself immersed in a very strange landscape, something that you might regard as a literary work in itself, belonging to a genre all its own.”

Now, at a time when the very definition of publishing is being undermined by technological and economic forces, it is striking to see each publisher as a “literary work unto itself.” So it is with Princeton University Press. In so far as PUP can claim a list having a diversified but well-integrated publishing vision, one that constantly strives for excellence and that stresses the forest for the trees, it is inescapably about the spirit and substance reflected in the legacy of Albert Einstein, and it is inseparable from it.

Einstein_blog (small)



Peter J. Dougherty is Director of Princeton University Press. This essay is based in part on comments he delivered at the Space-Time Theories conference at the Hebrew University in Jerusalem in January, 2015. Al Bertrand is Associate Publishing Director of Princeton University Press and Executive Editor of the Press’s history of science publishing program, including Einstein-related publications.

Happy Birthday, Alan Turing

Hodges_AlanTuring movie tie inThursday, June 23rd marks the birthday of Alan Turing, widely credited with being the father of the modern computer and artificial intelligence, as well as with leading the Bletchley Park codebreakers in cracking an encryption method used by the Nazi’s. PUP is proud to have published Alan Turing: The Enigma, a scientific biography of the famous cryptologist that went on to become a New York Times Bestseller, and was adapted in the 2014 historical drama/thriller The Imitation Game. The film was a commercial and critical success, grossing over $233 million worldwide. Turing is, for many, a modern day mathematical hero in the spirit of Albert Einstein or John Nash.

Yet despite his genius and groundbreaking accomplishments, Turing was hounded to his early death about his sexuality. After facing a 1952 charge of indecency over his relationship with another man, a criminal act in the UK at the time, he endured chemical castration and took his own life only two years later at age 41.

Archaic attitudes and inhumane treatment of LGBT people continued by the agency (and more broadly in society) for decades after Turing’s death. But in a historic move this past April, the GCHQ (UK Government Communications Headquarters) issued a formal apology, acknowledging that the treatment of Turing was “horrifying”.

You can read more about the apology here.

A man who changed the modern world while anticipating gay liberation by decades, Turing’s tragically brief four decades of life were unarguably well spent. Happy birthday, Alan Turing.

An interview with John Stillwell on Elements of Mathematics

elements of mathematics jacketNot all topics that are part of today’s elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become “elementary.” Elements of Mathematics: From Euclid to Gödel, by John Stillwell gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.

You’ve been writing math books for a long time now. What do you think is special about this one?

JS: In some ways it is a synthesis of ideas that occur fleetingly in some of my previous books: the interplay between numbers, geometry, algebra, infinity, and logic. In all my books I try to show the interaction between different fields of mathematics, but this is one more unified than any of the others. It covers some fields I have not covered before, such as probability, but also makes many connections I have not made before. I would say that it is also more reflective and philosophical—it really sums up all my experience in mathematics.

Who do you expect will enjoy reading this book?

JS: Well I hope my previous readers will still be interested! But for anyone who has not read my previous work, this might be the best place to start. It should suit anyone who is broadly interested in math, from high school to professional level. For the high school students, the book is a guide to the math they will meet in the future—they may understand only parts of it, but I think it will plant seeds for their future mathematical development. For the professors—I believe there will be many parts that are new and enlightening, judging from the number of times I have often heard “I never knew that!” when speaking on parts of the book to academic audiences.

Does the “Elements” in the title indicate that this book is elementary?

JS: I have tried to make it as simple as possible but, as Einstein is supposed to have said, “not simpler”. So, even though it is mainly about elementary mathematics it is not entirely elementary. It can’t be, because I also want to describe the limits of elementary mathematics—where and why mathematics becomes difficult. To get a realistic appreciation of math, it helps to know that some difficulties are unavoidable. Of course, for mathematicians, the difficulty of math is a big attraction.

What is novel about your approach?

JS: It tries to say something precise and rigorous about the boundaries of elementary math. There is now a field called “reverse mathematics” which aims to find exactly the right axioms to prove important theorems. For example, it has been known for a long time—possibly since Euclid—that the parallel axiom is the “right” axiom to prove the Pythagorean theorem. Much more recently, reverse mathematics has found that certain assumptions about infinity are the right axioms to prove basic theorems of analysis. This research, which has only appeared in specialist publications until now, helps explain why infinity appears so often at the boundaries of elementary math.

Does your book have real world applications?

JS: Someone always asks that question. I would say that if even one person understands mathematics better because of my book, then that is a net benefit to the world. The modern world runs on mathematics, so understanding math is necessary for anyone who wants to understand the world.

John Stillwell is professor of mathematics at the University of San Francisco. His many books include Mathematics and Its History and Roads to Infinity. His most recent book is Elements of Mathematics: From Euclid to Gödel.

Nicholas J. Higham: The Top 10 Algorithms in Applied Mathematics


From “Computational Science” by David E. Keyes in Princeton Companion to Applied Mathematics

In the January/February 2000 issue of Computing in Science and Engineering, Jack Dongarra and Francis Sullivan chose the “10
algorithms with the greatest influence on the development and practice of science and engineering in the 20th century” and presented a group of articles on them that they had commissioned and edited. (A SIAM News article by Barry Cipra gives a summary for anyone who does not have access to the original articles). This top ten list has attracted a lot of interest.

Sixteen years later, I though it would be interesting to produce such a list in a different way and see how it compares with the original top ten. My unscientific—but well defined— way of doing so is to determine which algorithms have the most page locators in the index of The Princeton Companion to Applied Mathematics (PCAM). This is a flawed measure for several reasons. First, the book focuses on applied mathematics, so some algorithms included in the original list may be outside its scope, though the book takes a broad view of the subject and includes many articles about applications and about topics on the interface with other areas. Second, the content is selective and the book does not attempt to cover all of applied mathematics. Third, the number of page locators is not necessarily a good measure of importance. However, the index was prepared by a professional indexer, so it should reflect the content of the book fairly objectively.

A problem facing anyone who compiles such a list is to define what is meant by “algorithm”. Where does one draw the line between an algorithm and a technique? For a simple example, is putting a rational function in partial fraction form an algorithm? In compiling the following list I have erred on the side of inclusion. This top ten list is in decreasing order of the number of page locators.

  1. Newton and quasi-Newton methods
  2. Matrix factorizations (LU, Cholesky, QR)
  3. Singular value decomposition, QR and QZ algorithms
  4. Monte-Carlo methods
  5. Fast Fourier transform
  6. Krylov subspace methods (conjugate gradients, Lanczos, GMRES,
  7. JPEG
  8. PageRank
  9. Simplex algorithm
  10. Kalman filter

Note that JPEG (1992) and PageRank (1998) were youngsters in 2000, but all the other algorithms date back at least to the 1960s.

By comparison, the 2000 list is, in chronological order (no other ordering was given)

  • Metropolis algorithm for Monte Carlo
  • Simplex method for linear programming
  • Krylov subspace iteration methods
  • The decompositional approach to matrix computations
  • The Fortran optimizing compiler
  • QR algorithm for computing eigenvalues
  • Quicksort algorithm for sorting
  • Fast Fourier transform
  • Integer relation detection
  • Fast multipole method

The two lists agree in 7 of their entries. The differences are:

PCAM list 2000 list
Newton and quasi-Newton methods The Fortran Optimizing Compiler
Jpeg Quicksort algorithm for sorting
PageRank Integer relation detection
Kalman filter Fast multipole method

Of those in the right-hand column, Fortran is in the index of PCAM and would have made the list, but so would C, MATLAB, etc., and I draw the line at including languages and compilers; the fast multipole method nearly made the PCAM table; and quicksort and integer relation detection both have one page locator in the PCAM index.

There is a remarkable agreement between the two lists! Dongarra and Sullivan say they knew that “whatever we came up with in the end, it would be controversial”. Their top ten has certainly stimulated some debate, but I don’t think it has been too controversial. This comparison suggests that Dongarra and Sullivan did a pretty good job, and one that has stood the test of time well.

Finally, I point readers to a talk Who invented the great numerical algorithms? by Nick Trefethen for a historical perspective on algorithms, including most of those mentioned above.

This post originally appeared on Higham’s popular website.

Higham jacketNicholas J. Higham is the Richardson Professor of Applied Mathematics at The University of Manchester. He most recently edited The Princeton Companion to Applied Mathematics.

Happy Birthday, Albert Einstein!

What a year. Einstein may have famously called his own birthday a natural disaster, but between the discovery of gravitational waves in February and the 100th anniversary of the general theory of relativity this past November, it’s been a big year for the renowned physicist and former Princeton resident. Throughout the day, PUP’s design blog will be celebrating with featured posts on our Einstein books and the stories behind them.

HappyBirthdayEinstein Graphic 3

Here are some of our favorite Einstein blog posts from the past year:

Was Einstein the First to Discover General Relativity? by Daniel Kennefick

Under the Spell of Relativity by Katherine Freese

Einstein: A Missionary of Science by Jürgen Renn

Me, Myself and Einstein by Jimena Canales

The Revelation of Relativity by Hanoch Gutfreund

A Mere Philosopher by Eoghan Barry

The Final Days of Albert Einstein by Debra Liese


Praeteritio and the quiet importance of Pi

pidayby James D. Stein

Somewhere along my somewhat convoluted educational journey I encountered Latin rhetorical devices. At least one has become part of common usage–oxymoron, the apparent paradox created by juxtaposed words which seem to contradict each other; a classic example being ‘awfully good’. For some reason, one of the devices that has stuck with me over the years is praeteritio, in which emphasis is placed on a topic by saying that one is omitting it. For instance, you could say that when one forgets about 9/11, the Iraq War, Hurricane Katrina, and the Meltdown, George W. Bush’s presidency was smooth sailing.

I’ve always wanted to invent a word, like John Allen Paulos did with ‘innumeracy’, and πraeteritio is my leading candidate–it’s the fact that we call attention to the overwhelming importance of the number π by deliberately excluding it from the conversation. We do that in one of the most important formulas encountered by intermediate algebra and trigonometry students; s = rθ, the formula for the arc length s subtended by a central angle θ in a circle of radius r.

You don’t see π in this formula because π is so important, so natural, that mathematicians use radians as a measure of angle, and π is naturally incorporated into radian measure. Most angle measurement that we see in the real world is described in terms of degrees. A full circle is 360 degrees, a straight angle 180 degrees, a right angle 90 degrees, and so on. But the circumference of a circle of radius 1 is 2π, and so it occurred to Roger Cotes (who is he? I’d never heard of him) that using an angular measure in which there were 2π angle units in a full circle would eliminate the need for a ‘fudge factor’ in the formula for the arc length of a circle subtended by a central angle. For instance, if one measured the angle D in degrees, the formula for the arc length of a circle of radius r subtended by a central angle would be s = (π/180)rD, and who wants to memorize that? The word ‘radian’ first appeared in an examination at Queen’s College in Belfast, Ireland, given by James Thomson, whose better-known brother William would later be known as Lord Kelvin.

The wisdom of this choice can be seen in its far-reaching consequences in the calculus of the trigonometric functions, and undoubtedly elsewhere. First semester calculus students learn that as long as one uses radian measure for angles, the derivative of sin x is cos x, and the derivative of cos x is – sin x. A standard problem in first-semester calculus, here left to the reader, is to compute what the derivative of sin x would be if the angle were measured in degrees rather than radians. Of course, the fudge factor π/180 would raise its ugly head, its square would appear in the formula for the second derivative of sin x, and instead of the elegant repeating pattern of the derivatives of sin x and cos x that are a highlight of the calculus of trigonometric functions, the ensuing formulas would be beyond ugly.

One of the simplest known formulas for the computation of π is via the infinite series 𝜋4=1−13+15−17+⋯

This deliciously elegant formula arises from integrating the geometric series with ratio -x^2 in the equation 1/(1+𝑥^2)=1−𝑥2+𝑥4−𝑥6+⋯

The integral of the left side is the inverse tangent function tan-1 x, but only because we have been fortunate enough to emphasize the importance of π by utilizing an angle measurement system which is the essence of πraeteritio; the recognition of the importance of π by excluding it from the discussion.

So on π Day, let us take a moment to recognize not only the beauty of π when it makes all the memorable appearances which we know and love, but to acknowledge its supreme importance and value in those critical situations where, like a great character in a play, it exerts a profound dramatic influence even when offstage.

LA MathJames D. Stein is emeritus professor in the Department of Mathematics at California State University, Long Beach. His books include Cosmic Numbers (Basic) and How Math Explains the World (Smithsonian). His most recent book is L.A. Math: Romance, Crime, and Mathematics in the City of Angels.

Where would we be without Pi?

Pi Day, the annual celebration of the mathematical constant π (pi), is always an excuse for mathematical and culinary revelry in Princeton. Since 3, 1, and 4 are the first three significant digits of π, the day is typically celebrated on 3/14, which in a stroke of serendipity, also happens to be Albert Einstein’s birthday. Pi Day falls on Monday this year, but Princeton has been celebrating all weekend with many more festivities still to come, from a Nerd Herd smart phone pub crawl, to an Einstein inspired running event sponsored by the Princeton Running Company, to a cocktail making class inside Einstein’s first residence. We imagine the former Princeton resident would be duly impressed.

Einstein enjoying a birthday/ Pi Day cupcake

Einstein enjoying a birthday/ Pi Day cupcake

Pi Day in Princeton always includes plenty of activities for children, and tends to be heavy on, you guessed it, actual pie (throwing it, eating it, and everything in between). To author Paul Nahin, this is fitting. At age 10, his first “scientific” revelation was,  If pi wasn’t around, there would be no round pies! Which it turns out, is all too true. Nahin explains:

Everybody “knows’’ that pi is a number a bit larger than 3 (pretty close to 22/7, as Archimedes showed more than 2,000 years ago) and, more accurately, is 3.14159265… But how do we know the value of pi? It’s the ratio of the circumference of a circle to a diameter, yes, but how does that explain how we know pi to hundreds of millions, even trillions, of decimal digits? We can’t measure lengths with that precision. Well then, just how do we calculate the value of pi? The symbol π (for pi) occurs in countless formulas used by physicists and other scientists and engineers, and so this is an important question. The short answer is, through the use of an infinite series expansion.

NahinIn his book In Praise of Simple Physics, Nahin shows you how to derive such a series that converges very quickly; the sum of just the first 10 terms correctly gives the first five digits. The English astronomer Abraham Sharp (1651–1699) used the first 150 terms of the series (in 1699) to calculate the first 72 digits of pi. That’s more than enough for physicists (and for anybody making round pies)!

While celebrating Pi Day has become popular—some would even say fashionable in nerdy circles— PUP author Marc Chamberland points out that it’s good to remember Pi, the number. With a basic scientific calculator, Chamberland’s recent video “The Easiest Way to Calculate Pi” details a straightforward approach to getting accurate approximations for Pi without tables or a prodigious digital memory. Want even more Pi? Marc’s book Single Digits has more than enough Pi to gorge on.

Now that’s a sweet dessert.

If you’re looking for more information on the origin of Pi, this post gives an explanation extracted from Joseph Mazur’s fascinating history of mathematical notation, Enlightening Symbols.

You can find a complete list of Pi Day activities from the Princeton Tour Company here.

Solving last week’s L.A. Math challenge

LA MathWe’re back with the conclusion to last week’s LA Math challenge, The Case of the Vanishing Greenbacks, (taken from chapter 2 of the book). After the conclusion of the story, we’ll talk a little more with the author, Jim Stein. Don’t forget to check out the fantastic trailer for LA Math here.

Forty‑eight hours later I was bleary‑eyed from lack of sleep. I had made no discernible progress. As far as I could tell, both Stevens and Blaisdell were completely on the up‑and‑up.   Either I was losing my touch, or one (or both) of them were wasting their talents, doctoring books for penny‑ante amounts.   Then I remembered the envelope Pete had sealed. Maybe he’d actually seen something that I hadn’t.

I went over to the main house, to find Pete hunkered down happily watching a baseball game. I waited for a commercial break, and then managed to get his attention.

“I’m ready to take a look in the envelope, Pete.”

“Have you figured out who the guilty party is?”

“Frankly, no. To be honest, it’s got me stumped.” I moved to the mantel and unsealed the envelope. The writing was on the other side of the piece of paper. I turned it over. The name Pete had written on it was “Garrett Ryan and the City Council”!

I nearly dropped the piece of paper. Whatever I had been expecting, it certainly wasn’t this. “What in heaven’s name makes you think Ryan and the City Council embezzled the money, Pete?”

“I didn’t say I thought they did. I just think they’re responsible for the missing funds.”

I shook my head. “I don’t get it. How can they be responsible for the missing funds if they didn’t embezzle them?”

“They’re probably just guilty of innumeracy. It’s pretty common.”

“I give up. What’s innumeracy?”

“Innumeracy is the arithmetical equivalent of illiteracy. In this instance, it consists of failing to realize how percentages behave.” A pitching change was taking place, so Pete turned back to me. “An increase in 20% of the tax base will not compensate for a reduction of 20% in each individual’s taxes.   Percentages involve multiplication and division, not addition and subtraction. A gain of 20 dollars will compensate for a loss of 20 dollars, but that’s because you’re dealing with adding and subtracting. It’s not the same with percentages, because the base upon which you figure the percentages varies from calculation to calculation.”

“You may be right, Pete, but how can we tell?”

Pete grabbed a calculator. “Didn’t you say that each faction was out $198,000?”

I checked my figures. “Yeah, that’s the amount.”

Pete punched a few numbers into the calculator. “Call Ryan and see if there were 99,000 taxpayers in the last census. If there were, I’ll show you where the money went.”

I got on the phone to Ryan the next morning. He confirmed that the tax base in the previous census was indeed 99,000. I told Pete that it looked like he had been right, but I wanted to see the numbers to prove it.

Pete got out a piece of paper. “I think you can see where the money went if you simply do a little multiplication. The taxes collected in the previous census were $100 for each of 99,000 individuals, or $9,900,000. An increase of 20% in the population results in 118,800 individuals. If each pays $80 (that’s the 20% reduction from $100), the total taxes collected will be $9,504,000, or $396,000 less than was collected after the previous census. Half of $396,000 is $198,000.”

I was convinced. “There are going to be some awfully red faces down in Linda Vista. I’d like to see the press conference when they finally announce it.” I went back to the guesthouse, called Allen, and filled him in. He was delighted, and said that the check would be in the mail.   As I’ve said before, when Allen says it, he means it. Another advantage of having Allen make the arrangements is that I didn’t have to worry about collecting the fee, which is something I’ve never been very good at.

I wondered exactly how they were going to break the news to the citizens of Linda Vista that they had to pony up another $396,000, but as it was only about $3.34 per taxpayer I didn’t think they’d have too much trouble. Thanks to a combination of Ryan’s frugality and population increase, the tax assessment would still be lower than it was after the previous census, and how many government agencies do you know that actually reduce taxes? I quickly calculated that if they assessed everyone $3.42 they could not only cover the shortage, but Allen’s fee as well. I considered suggesting it to Ryan, but then I thought that Ryan probably wasn’t real interested in hearing from someone who had made him look like a bungler.

My conscience was bothering me, and I don’t like that. I thought about it, and finally came up with a compromise I found acceptable. I went back to the main house.

Pete was watching another baseball game. The Dodgers fouled up an attempted squeeze into an inning‑ending double play. Pete groaned. “It could be a long season,” he sighed.

“It’s early in the year.” I handed him a piece of paper. “Maybe this will console you.”

“What’s this?” He was examining my check for $1,750. “Your rent’s paid up.”

“It’s not for the rent, Pete. It’s your share of my fee.”

“Fee? What fee?”

“That embezzling case in Orange County. It was worth $3,500 to me to come up with the correct answer. I feel you’re entitled to half of it. You crunched the numbers, but I had the contacts and did the legwork.”

Pete looked at the check. “It seems like a lot of money for very little work. Tell you what. I’ll take $250, and credit the rest towards your rent.”

A landlord with a conscience! Maybe I should notify the Guinness Book of Records. “Seems more than fair to me.”

Pete tucked the check in the pocket of his shirt. “Tell me, Freddy, is it always this easy, doing investigations?”

I summoned up a wry laugh. “You’ve got to be kidding. So far, I’ve asked you two questions that just turned out to be right down your alley. I’ve sometimes spent months on a case, and come up dry. That can make the bottom line look pretty sick. What’s it like in your line of work?”

“I don’t really have a line of work. I have this house and some money in the bank. I can rent out the guesthouse and make enough to live on. People know I’m pretty good at certain problems, and sometimes they hire me. If it looks like it might be interesting, I’ll work on it.” He paused. “Of course, if they offer me a ridiculous amount of money, I’ll work on it even if it’s not interesting. Hey, we’re in a recession.”

“I’ll keep that in mind.”   I turned to leave the room. Pete’s voice stopped me.

“Haven’t you forgotten something?”

I turned around. “I give up. What?”

“We had a bet. You owe me five bucks.”

I fished a five out of my wallet and handed it over. He nodded with satisfaction as he stuffed it in the same pocket as the check, and then turned his attention back to the game.

What made you include this particular idea in the book?

JS: The story features one of the most common misunderstandings about percentages.  There are innumerable mistakes made because people assume that percentages work the same way as regular quantities.  But they don’t — if a store lowers the cost of an item by 30% and then by another 20%, the cost of the item hasn’t been lowered by 50% — although many people make the mistake of assuming that it has.  I’m hoping that the story is sufficiently memorable that if a reader is confronted by a 30% discount followed by a 20% discount, they’ll think “Wasn’t there something like that in The Case of the Vanishing Greenbacks?

There are 14 stories in the book, and each features a mathematical point, injected into the story in a similar fashion as the one above.  I think the stories are fun to read, and if someone reads the book and remembers just a few of the points, well, I’ve done a whole lot better than when I was teaching liberal arts math the way it is usually done.

James D. Stein is emeritus professor in the Department of Mathematics at California State University, Long Beach. His books include LA Math, Cosmic Numbers (Basic) and How Math Explains the World (Smithsonian).

Try your hand at solving an L.A. Math mystery

If you caught the rather incredible trailer for L.A. Math, you know it’s not your typical scholarly math book. Romance, crime, and mathematics don’t often go hand in hand, but emeritus professor in the Department of Mathematics at California State University Jim Stein cooked up the idea for an unconventional literary math book that would speak to students in his liberal arts math class. The end result is an entertaining, backdoor approach to practical mathematics knowledge, ranging from percentages and probability to set theory, statistics, and the mathematics of elections. Recently, Stein spoke to us about writing L.A. Math. Not only that, he left us with a mathematical mystery to solve.

L.A. Math is definitely an unusual book.  Brian Clegg described it by saying “It’s as if Ellery Queen, with the help of P. G. Wodehouse, spiced up a collection of detective tales with a generous handful of practical mathematics.”  How did you happen to write it?

JS: I absolutely loved it when he described it that way, because I was brought up on Ellery Queen.  For younger readers, Ellery Queen was one of the greatest literary detectives of the first half of the twentieth century, specializing in classic Sherlock Holmes type cases.  The Ellery Queen stories were written by the team of Manfred Dannay and Frederick Lee — and my mother actually dated one of them!

LA MathThe two other mystery writers who influenced me were Agatha Christie and Rex Stout.  Rex Stout wrote a series featuring Nero Wolfe and Archie Goodwin; the books are presumably written by Archie Goodwin describing their cases, so I used that as the model for Freddy Carmichael.  The relationship between Archie and Nero also served, somewhat, as a parallel for the relationship between Freddy and Pete.  Nero and Pete both have addictions — Nero wants to spend his time eating elaborate cuisine and raising orchids, and Pete wants to spend his time watching and betting on sports.  It’s up to Archie and Freddy to prod them into taking cases.

How does Agatha Christie enter the picture?

JS: I’d taught liberal arts mathematics — math for poets — maybe ten times with temporary success but no retention.  Students would learn what was necessary to pass the course, and a year later they’d forgotten all of it.  That’s not surprising, because the typical liberal arts math course has no context that’s relevant for them.  They’re not math-oriented.  I know I had several history courses discussing the Battle of Azincourt, but I don’t remember anything about it because it has no context for me.

Agatha Christie’s best-known detective is Hercule Poirot, and one day I was in a library reading a collection of short stories she had written entitled The Labors of Hercules.  Christie had a background in the classics, and did something absolutely brilliant — she constructed a series of twelve detective stories featuring Hercule Poirot, each of which was modeled, in one way or another, around the Twelve Labors of Hercules in classical mythology.  I thought to myself — why don’t I do something like that for topics in liberal arts math?  Maybe the students would remember a few of the ideas because they’d have the context of a story from which to remember it.

Could you give an example?

JS: How about this?  Why don’t we take a story from the book, and present it the way Ellery Queen would have.  Ellery Queen always played fair with the reader, giving him or her all the clues, and after all the clues had been presented, EQ would write a paragraph entitled “Challenge to the Reader”.  EQ would tell the reader “Now you have all the clues.  Can you figure out whodunit?” — or words to that effect.

OK, here’s what we’ll do.  We’ll take The Case of the Vanishing Greenbacks, Chapter 2 in L.A. Math, and present the story up to the crucial point.  Then we’ll let the reader try to figure out whodunit, and finish the story next week.

Chapter 2 – The Case of the Vanishing Greenbacks

   The phone rang just as I stepped out of the shower. It was Allen.

“Freddy, are you available for an embezzlement case?”

My biggest success had been in an embezzlement case involving a Wall Street firm specializing in bond trading. Allen had given me a whopping bonus for that one, which was one of the reasons I could afford to take it easy in L.A. I had done well in a couple of other similar cases, and had gotten the reputation of being the go-to guy in embezzlement cases. It never hurts to have a reputation for being good at something. Besides, you don’t see many guys in my line of work who can read balance sheets.

I’ve always felt it’s important to keep the cash flow positive, and the truth was that I was available for a jaywalking case if it would help the aforementioned cash flow. But it never hurts to play a little hard-to-get.

“I can probably clear my calendar if it looks interesting.”

Allen paused for a moment, either to collect his thoughts or to take a bite of one of those big greasy pastrami sandwiches he loves. “I’m pretty sure you’ll find it interesting. It’s stumped some people in L.A., and I told them I had a good man out there. BTW, that’s you.”

It’s nice to be well thought of – especially by someone in a position to send you business. I knew that Allen’s firm, though headquartered in New York, had arrangements with other firms in other cities. I didn’t really care about the details as long as the check cleared – which it always had.

“I’m certainly willing to listen. What’s the arrangement?”

“Consulting and contingency fee. Fifty‑fifty split.”

That was our usual arrangement. Burkitt Investigations got a guaranteed fee, plus a bonus for solving the case. Allen and I split it down the middle.

“OK, Allen, fill me in.”

“Ever heard of Linda Vista, Freddy?”

Temporary blank. Movie star? Socialite? Then I had it. Linda Vista was a town somewhere in Orange County with a big art community.

For those of you not up on California politics, Orange County is a bastion of conservatism. You have Orange County to thank, or blame, for Richard Nixon and Ronald Reagan. But Linda Vista, which my fragmentary Spanish translates as “pretty view”, was different from your basic Orange County bastion.

The vista in Linda Vista was sufficiently linda that it had attracted a thriving artistic community.   There were plenty of artists in Linda Vista, and most of them were liberals.

As a result, Linda Vista was highly polarized. The moderates were few and far between. On the left, you had the artists, with their funky bungalows and workshops. On the right, you had the stockbrokers and real-estate moguls, living in gated communities so they wouldn’t have to have any contact with the riff-raff, except for the tradesmen delivering or repairing stuff. However, there were enough artists and hangers-on to acquire political clout – after all, it’s still one man-one vote in a democracy, rather than one dollar-one vote. Pitched battles had raged over practically every issue from A (abortion) to Z (zoning), and many of these battles had made state and even national news.

That’s all I knew about Linda Vista, other than not to try to drive down there at rush hour, which turned one hour on the 405 to more than twice that. The obvious question was: what kind of a contingency case had they got? So I asked it.

Allen filled me in. “The city is out a bunch of bucks, and each side is accusing the other of fraud and embezzlement. Because of the split in the political situation, the City Manager gave half the budget to the conservatives, and the other half to the liberals, letting each determine how to spend its half. Both sides claim to have been shortchanged.”

Allen paused to catch his breath. “I’ve got a friend who works in the City Manager’s office. I told him I had a good man out there who’d done a lot of first‑class work in embezzlement cases. Want to take a look at it?”

“Sure. How much time should I put in before I throw in the towel?” In other words, how much is the consulting fee?

“As much as you like.” In other words, since Allen’s meter wasn’t running, feel free to burn some midnight oil. “The consulting fee is $3,000, upped to ten if you figure it out and get proof.” You don’t have to be an expert at division to realize that I was guaranteed a minimum of $1,500 for the time I put in, and $5,000 if I doped it out. You also don’t have to be an expert at division to realize that Allen was getting the same amount for making a phone call. I decided to be reincarnated as an employer rather than an employee.

Allen gave me a brief description of the protagonists, and I spent a good portion of the evening with a pot of coffee and my computer, getting some background information on them. I’ll say one thing for the Information Age; it’s a lot easier to run a background check on people than it used to be. What with search engines and social networks, you save a lot on gas money and shoe leather.

The next morning I waited until after rush hour, and made the trek to Linda Vista. The City Hall was located in a section of town where the vista was a long way from linda, unless strip malls filled with 7‑11s and fast-food stores constitute your idea of attractive scenery. I found a place to park, straightened my coat and tie, and prepared for the interviews.

I was scheduled to have three of them. I had been hoping to arrange for longer interviews, but everyone’s in a rush nowadays, and I was getting a quarter-hour with each, tops. They’d all been interviewed previously – Allen had mentioned that this case had stumped others – and people are generally less than enthusiastic about being asked the same questions again. And again. The first interview was with Everett Blaisdell, conservative city councilman, who would explain why the conservatives happened to be short. The next was with Melanie Stevens, liberal city councilwoman, ditto. The last interview would be with Garrett Ryan, City Manager.

I have a bad habit. My opinion of members of groups tends to be formed by the members of those groups that I have seen before. Consequently, I was expecting the conservative Everett Blaisdell to look like a typical paunchy southern senator with big jowls. So I was a little surprised to discover that Everett Blaisdell was a forty-ish African-American who looked like he had spent years twenty through thirty as an NBA point guard.

He got right down to business. “I want you to know,” he barked, “that everything that we have done with our budget allocation has been strictly by the book. Our expenses have been completely documented.” He handed me a folder full of ledger sheets and photos of checks, which I glanced at and stashed in my briefcase.

Blaisdell was clearly angry. “The business community is the heart of Linda Vista, and it is ridiculous to suggest that it would act in a manner detrimental to its citizens. We are $198,000 short in our budget.”

You don’t expect NBA point guards to get out of breath too easily, considering the time they have to go up and down the court, but maybe Blaisdell wasn’t in shape. He paused, giving me a chance to get a question in edgewise. “Just what do you think has happened, Mr. Blaisdell?” I inquired mildly.

“I know what has happened. Melanie Stevens and her radical crowd have managed to get hold of that money. They want $200,000 to fund a work of so‑called art which I, and every right‑thinking citizen of Linda Vista, find totally offensive. It’s mighty suspicious that the missing funds, $198,000, almost precisely cover the projected cost of the statue.”

I was curious. “If you don’t mind my asking, exactly what is this statue?”

Blaisdell’s blood pressure was going up. “They are going to build a scale replica of the Statue of Liberty and submerge it in Coca‑Cola. You may know that Coca‑Cola is acidic, and it will eventually dissolve metal. They say that this so‑called dynamic representational art represents the destruction of our civil liberties by over‑commercialization. Well, let me tell you, we’ll fight it.”

He looked at his watch. “Sorry, I’ve got another appointment. When you find out what those scum have done with the money, let me know.” He walked me to his door.

It took a few minutes to locate Melanie Stevens’ office, as it was in a different wing of the building, possibly to minimize confrontations between her and Blaisdell. It was a bad day for stereotypes. My mental picture of Melanie Stevens, ultra‑liberal, was that of a long-haired hippie refugee from the ’60s. The real Melanie Stevens was a pert gray‑haired grandmother who looked like she had been interrupted while baking cookies for her grandchildren. She, too, was evidently on a tight schedule, for she said, “Sorry, I can only give you about ten minutes, but I’ve made copies of all our expenses.” More ledger sheets and photos of checks went into my briefcase.

“Let me tell you, Mr. Carmichael, that we could have used that $198,000. We planned to use it for a free clinic. I know exactly what has happened. Blaisdell has doctored the books. I’m sure glad that Ryan had the guts to ask you to look into it.”

“Blaisdell seems to think that your people are responsible for the missing funds,” I observed.

She snorted. “That’s just typical of what they do. Whenever they’re in the wrong, they lie and accuse the other side of lying. They rip off the community, and channel money into PACs. Political action committees. Or worse. Blaisdell knows he faces a stiff battle for re-election, and I wouldn’t be the least bit surprised to find that money turning up in his campaign fund.”

“He seems to think that you are going to use the funds for an art project, rather than a free clinic,” I remarked.

“He’s just blowing smoke. He knows quite well that the statue will be funded through private subscription.” She looked at her watch. “Let me know when you pin the loss on them.”

I left Stevens’ office for the last interview, with Garrett Ryan, whose anxious expression made it clear that he was not a happy camper. “Have you got any ideas yet?” he asked.

I shook my head. “I’ve just talked to Blaisdell and Stevens. They’ve each handed me files containing what they consider to be complete documentation. They’ve each given me a story asserting their own innocence, and blaming the other. I take it that the missing amount is $198,000?”

Now it was Ryan’s turn to shake his head. “No, each side says that it is missing $198,000. Quite a coincidence. And I’ll tell you, Mr. Carmichael, despite the animosity between them, I think that they are both honorable individuals. I find it difficult to believe that either would rip the city off.”

I focused on Ryan’s coincidence. “It’s funny that they are both short exactly the same amount. Perhaps you could tell me a little more about the budgetary process.”

“It’s really quite simple. Each resident of Linda Vista is taxed a fixed amount. Any complicated tax scheme would just result in a full employment act for accountants. The previous census resulted in a $100 assessment per individual. The population of Linda Vista increased by 20% since the last census. We didn’t need any increase in operating expenditures; under my guidance we’ve done a fiscally conservative and frugal job of running the city. As a result, the Council voted to reduce everybody’s taxes by 20%. Needless to say, this was a very popular move.”

“I’ll bet it was. Did everyone pay their taxes, Mr. Ryan?”

“Everybody. We’re very proud of that ‑‑ a 100% collection rate. Despite what you may have heard, the citizens of Linda Vista are very civic‑minded. Liberals and conservatives alike.”

I’ve spent enough time with balance sheets to know that accuracy is extremely important. “Was this population increase exactly 20%, or is that merely an approximate figure?”

Ryan consulted a sheet of paper. “Exactly 20%. I have a sheet of printout that gives information to four decimal places, so I can be quite sure of that.”

Just then a phone rang. Ryan picked it up, and engaged in some political doubletalk. After a few minutes he replaced the receiver. “Sorry, Mr. Carmichael. I’m behind schedule. Let me know if you make any progress.”   We shook hands, and I left.

A couple of hours later, I got home, having stopped for a bite but still avoiding rush-hour traffic. Pete noticed my presence, and asked, “So how’d things go in Linda Vista, Freddy?”

“I had a pretty interesting day. Want to hear about it?”

He nodded. I took about fifteen minutes to describe the problem and the cast of characters. “It looks like I’ll have to spend a day or so looking over the books.”

Pete shook his head. “It seems pretty clear to me.”

I’d seen it before — everybody’s a detective. Amateurs always think they know who the guilty party is, because it fits in with their preconceptions. I didn’t know whether Pete had cast Blaisdell in the role of a political fat-cat out to line his campaign war chest, or whether he was a conservative who saw Melanie Stevens as a radical troublemaker. Anyway, you’ve got to learn not to jump to conclusions in my line of work.

“You can’t do it like that, Pete. You’ve got to trace down the paper trails. I’ve done this lots of times.”

Pete grabbed a piece of paper, scribbled something on it, and sealed it in an envelope. “Five dollars will get you twenty that the name of the guilty party is inside this envelope.”

Pete needed taking down a peg. Maybe two pegs. Besides, I liked getting four‑to‑one odds on what was obviously an even‑ money proposition. “You’ve got a bet,” I said. We wrote our names on the envelope, and Pete put it on the table next to the HDTV.

“Whenever you’re ready, we’ll unseal the envelope.” I headed back to the guesthouse for a session with the books.

Challenge to the Reader: You have all the clues. Can you name the party responsible for the missing greenbacks? We’ll give you until the next blog to figure it out, when we’ll present the conclusion to the story.

New Physics & Astrophysics Catalog

We invite you to browse our Physics & Astrophysics 2016 catalog:


Interacademy Partnership Check out Doing Global Science, an introductory guide to responsible science in our globalized society. Written by a committee of leading scientists from all over the world, this text is required reading for anyone involved in scientific inquiry.
Thorne Modern Classical Physics is a graduate-level text and reference book for first-year students that covers statistical physics, optics, elastodynamics, fluid mechanics, plasma physics, and special and general relativity and cosmology.

A. Zee has contributed another new title to our In a Nutshell series entitled Group Theory in a Nutshell for Physicists. He takes all the nuts and bolts of a mathematical subject and makes it accessible for physicists. PUP is also publishing the second edition of Astrophysics in a Nutshell by Dan Maoz this season, a work that has become a standard text in courses on astrophysics.

If you would like updates of new titles emailed to you, subscribe to our newsletter.

Finally, PUP will be at the American Physical Society March Meeting in Baltimore from March 14 to March 18.

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: