#ThanksEinstein: Hanoch Gutfreund on the revelation of relativity

Einstein meme 2The Revelation of Relativity

By Hanoch Gutfreund

Hanoch Gutfreund is professor emeritus of theoretical physics at the Hebrew University of Jerusalem, where he is also the academic director of the Albert Einstein Archives. This is the story about how Einstein’s General Theory of Relativity revolutionized his teaching, understanding, and career.

My present day interest in Einstein evolved late in my academic life. It started when as Rector and then President of the Hebrew University, in the 1990’s, I became aware of the unique cultural asset possessed by the university – the Albert Einstein Archives. When I stepped down from the presidency, with einstein lightthe encouragement of my successor, I began to devote more and more time to promote the Einstein – H.U. connection, through public lectures on various Einstein topics and by organizing and helping to organize Einstein exhibitions in different places in the world.

As professor of theoretical physics, for many years I taught everything that Einstein did in his miraculous year – 1905. However, only in the late nineties did I read the original papers with commentaries by John Stachel. For me this was a revelation. Einstein’s way of thinking, his motivations, his introductions and conclusions – all this was very different from the way these topics were treated in ordinary textbooks. I believe that if I had known and understood what I know and understand today, my students would have appreciated and benefited from my lectures even more. Motivated by this revelation, I decided to fill a gap in my own physics education. As a student, I never had a course in general relativity. In the learning process, the historical context and Einstein’s intellectual struggle were for me at least as important as the scientific results.

Teinstein speed of lighto mark the 50th anniversary of the Israeli Academy of Science, we displayed the most important manuscript in the Einstein Archives, the manuscript of Einstein’s seminal paper on general relativity. Each one of the 46 pages of this manuscript was enclosed in a dimly illuminated box. People visited this exhibit as if they were entering a shrine.

Following this experience, I met with Jurgen Renn, director of the Max Planck Institute for the History of Science. We discussed an option to publish this manuscript as part of a comprehensive account of Einstein’s intellectual odyssey to general relativity.

Gutfreund_RoadtoRelativityThis meeting led to a fruitful collaboration, which has now produced The Road to Relativity: The History and Meaning of Einstein’s The Foundation of General Relativity. It attempts to make the essence of general relativity accessible to broader audiences. We have also initiated the recently published, 100th anniversary edition of Einstein’s popular booklet on the special and general theory of relativity, with extensive background material and a reading companion, intended to resent Einstein’s text in a historical and modern context. We are already considering other Einsteinian projects in the future. This year, as the world marks the 100th anniversary of general relativity, there are many requests addressed to the Albert Einstein Archives and to myself for assistance in organizing special exhibitions, for participation in scientific conferences and in public events, for interviews in the media and for help and advice in various other initiatives. It’s an exciting time, and I remain very grateful for this inspiring phase in my life.

Hanoch Gutfreund is professor emeritus of theoretical physics at the Hebrew University of Jerusalem, where he is also the academic director of the Albert Einstein Archives.

Check out the earlier post in this series by Jimena Canales.

#ThanksEinstein image courtesy of the official Albert Einstein Facebook page.

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:

Five places you didn’t expect to encounter applied math

You don’t need to step into a classroom to have a run-in with mathematics. Professionals from a range of backgrounds — engineering, economics, physics, biology, computer science — use mathematics every day. To celebrate the publication of the much-anticipated Princeton Companion to Applied Mathematics, edited by Nicholas J. Higham, we’re thinking about all of the unique places and situations where applied mathematics is at work. Here is a list of just a few, compiled with a little help from our numerically inclined friends.

On the Golf Course


Golf involves mathematics, and not just when keeping score. The flight of your golf ball is affected by how air interacts with the surface of the ball. Did you know that the dimples in golf balls have a purpose, one with a mathematical explanation? Douglas N. Arnold, professor of Mathematics at the University of Minnesota, tells us more:

In the middle of the nineteenth century, when rubber golf balls were introduced, golfers noticed that old scuffed golf balls traveled farther than new smooth balls, although no one could explain this unintuitive behavior. This eventually gave rise to the modern dimpled golf ball. Along the way a great deal was learned about aerodynamics and its mathematical modeling. Hundreds of different dimple patterns have been devised, marketed, and patented. However, even today the optimal dimple pattern lies beyond our reach, and its discovery remains a tough challenge for applied mathematics and computational science.

Check out Dr. Arnold’s entry, “The Flight of a Golf Ball,” where he explains why golf ball dimples are an important part of your Saturday morning tee time.

On Wall Street


Wall Street is all about the numbers. Whether modeling the risk of a single stock or mapping the complex interactions that make up the world’s financial structure, mathematics helps the financial sector to study and evaluate systemic risk.

“The complexity, unpredictability, and evolving nature of financial markets continues to provide an enormous challenge to mathematicians, engineers, and economists in identifying, analyzing, and quantifying the issues and risks they pose,” write Dr. René A. Carmona and Dr. Ronnie Sircar of Princeton University.

In their entry, “Financial Mathematics,” Dr. Carmona and Dr. Sircar discuss how the finance industry uses mathematics. They also examine the role of mathematics in understanding and regulating financial markets in light of the financial crisis of 2008.

On Your Phone’s Weather App

Do you check the 10-day forecast during the weekend before a big outdoor event, fingers crossed for clear skies and no rain? There’s math behind that “chance of thunderstorms” prediction. NWP [numerical weather prediction] helps meteorologists to predict weather patterns for more than a week ahead. Better numerical schemes are partially responsible for moving us forward from the weather prediction methods of fifty years ago.

In his article “Numerical Weather Prediction,” Peter Lynch presents the mathematical principles of NWP and illustrates the process by considering some specific models and their application to practical forecasting. Dr. Lynch describes the many conditions that can be better predicted using NWP:

NWP models are used to generate special guidance for the marine community. Predicted winds are used to drive wave models, which predict sea and swell heights and periods. Prediction of road ice is performed by specially designed models that use forecasts of temperature, humidity, precipitation, cloudiness, and other parameters to estimate the conditions on the road surface. Trajectories are easily derived from limited-area models. These are vital for modeling pollution drift, for nuclear fallout, smoke from forest fires, and so on. Aviation benefits significantly from NWP guidance, which provides warnings of hazards such as lightning, icing, and clear-air turbulence.

In the Airport Security Line

baggage claim

On your next trip through airport security, take a look at the x-ray machine. Once an object, like your suitcase, is scanned, the image can be viewed from multiple angles by a security officer. Threat detection software can also be used to locate problematic items. There is math at work here too.

W. R. B. Lionheart, professor of Applied Mathematics at the University of Manchester, explains this technology in his entry “Airport Baggage Screening with X-Ray Tomography.”

While Researching Your Next Vacation


Getting ready for your first vacation of the fall? Buying tickets, making dinner reservations, researching tourist attractions — what did we do without the internet? Or rather, what did we do before the organized internet?

When the internet was still in its early stages, search engines were not as advanced as they are today, and webpage results were ranked by simple rules. Searching for “New York sightseeing” may have led you to the page where the search term appears the most, instead of a page with the most useful information. Today, search engines use a more advanced method for ranking web pages: grouping pages into authority pages, which have many links to them, and hub pages, which point to many authorities. The catch is that these terms depend on one another. How does this work? In the Princeton Companion to Applied Mathematics, editor Nicholas Higham explains the mathematics behind webpage ranking.

Looking for more examples of math in the world? Check out this video from SIAM, where SIAM conference attendees are asked how they use math in their work. Math really is all around us.

Tipping Point Math Tuesdays With Marc Chamberland: What’s the Best Paper Size?

Tipping Point Tuesday takes on a global debate!

The United States and Canada use paper that is 8.5 inches by 11 inches, called US letter. However, the rest of the world officially uses A4 paper, which has a different aspect ratio. Which paper size is better, US letter or A4? Find the mathematical answer with the help of Marc Chamberland in a video from his YouTube channel Tipping Point Math.


Marc Chamberland takes on more mathematical scenarios in his book Single Digits: In Praise of Small Numbers. Read the first chapter here.

Tipping Point Math Tuesdays with Marc Chamberland: What’s the Pizza Theorem?

For the inaugural Tipping Point Math Tuesday, let’s find the math in something everyone loves, Pizza!

Have you ever opened your takeout pizza box and found that the slices were not cut evenly? What’s a party host to do? Marc Chamberland, author of Single Digits: In Praise of Small Numbers shows how mathematics can help you use the pizza theorem to evenly divide a pizza among yourself and your hungry friends:


Craving more math? Preview the first chapter of Chamberland’s book here.

Mathematics Awareness Month 2015: Math Drives Careers

Internet search, pharmaceuticals, insurance, finance, national security, medicine, ecology. What is the link between these diverse career fields? Students graduating with a mathematical sciences degree can find a professional future in all of these fields, and a wide range of others as well. This year’s Mathematics Awareness Month takes a step out of the classroom to show just where mathematics can lead after graduation.

Mathematics Awareness Month is an annual celebration dedicated to increasing public understanding of and appreciation for mathematics. The event, which started in 1986 as Mathematics Awareness Week, adopts a different theme each year. This year’s theme is “Math Drives Careers,” and PUP is excited to bring you a series of guest posts from our authors. Check back all this month for posts about using math to raise revenues, to understand sports and economics, and to solve complex problems.

The organizers of Mathematics Awareness Month explain the importance of mathematics in today’s workforce:

“Innovation is an increasingly important factor in the growth of world economies. It is especially important in key economic sectors like manufacturing, materials, energy, biotechnology, healthcare, networks, and professional and business services. The advances in and applications of the mathematical sciences have become drivers of innovation as new systems and methodologies have become more complex. As mathematics drives innovation, it also drives careers.”
Check out this official Mathematics Awareness Month poster, which includes career descriptions for 10 individuals who used their love for math to find rewarding careers:



Follow along with @MathAware and take a look at Math Awareness Month on Facebook.

Tim Chartier and the Mega Menger

math bytesHow many business cards are needed to complete a level 3 Menger Sponge? What is a level 3 Menger Sponge? Tim Chartier, author of Math Bytes: Google Bombs, Chocolate Covered Pi, and Other Cool Bits in Computing, explains.

In a Huffington Post article, A Million Business Cards Presents a Math Challenge, Chartier asks readers to go in their wallet and check for  business cards. If there aren’t any, “they may be part of a worldwide math challenge. Over the past month, people around the world have been building a mathematical structure out of more than a million business cards.” That mathematical structure is a Mega Menger, but before we get there, let’s discuss what a level 1 Menger Sponge is.

A level 1 Menger Sponge is a fractal consisting of twenty cubes. Each cube is made up of 6 business cards, so a level 1 Menger needs 120 business cards. A level 2 Menger is created using 20 level 1 Mengers, a level 3 Menger is made with 20 level 2 Mengers, so on and so on.

Here at the Press, we don’t have a million business cards to complete a Mega Menger, but we do have a lot of books. Using Chartier’s code (which you can play with here: http://lifeislinear.davidson.edu/sierpinski.html), we were able to create 2-D versions of a Menger Sponge called a Sierpinski Carpet using our jacket images. Below, see if you can figure out which books are featured in the fractal images below! Click the images to see the related title.






Invisible in the Storm wins the 2015 Louis J. Battan Author’s Award, American Meteorological Society

Congratulations to Ian Roulstone & John Norbury, co-authors of Invisible in the Storm: The Role of Mathematics in Understanding Weather, on winning the 2015 Louis J. Battan Author’s Award given by the American Meteorological Society.

The prize is “presented to the author(s) of an outstanding, newly published book on the atmospheric and related sciences of a technical or non-technical nature, with consideration to those books that foster public understanding of meteorology in adult audiences.” In the announcement of the prize, the committee said Invisible in the Storm “illuminates the mathematical foundation of weather prediction with lucid prose that provides a bridge between meteorologists and the public.”

For more information about the 2015 AMS awards: http://www.ametsoc.org/awards/2015awardrecipients.pdf


Invisible in the Storm
The Role of Mathematics in Understanding Weather
Ian Roulstone & John Norbury

This is how you survive the zombie apocalypse

Williams College math professor Colin Adams risks life and limb to record these survival guide videos. Ready your gear–armor, baseball bat, calculus textbook–and prepare for the onslaught.

Part 1: Why we can’t quite finish the zombies off.

Part 2: Escaping zombies in hot pursuit.

Credit: PBS’s NOVA and director Ari Daniel.

bookjacket Zombies and Calculus
Colin Adams

Grab your M&Ms and ace math this year with Math Bytes

In this segment from WCCB in Charlotte, NC, Tim Chartier shows how math can be both educational and delicious! This experiment is taken directly from his recent book Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing. There are lots of other hands-on experiments that are suitable for aspirational mathematicians of all ages in the book.

bookjacket Math Bytes:
Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing
Tim Chartier

Paying It Forward, Using Math: Oscar Fernandez’s ‘Everyday Calculus’ Donated to Libraries in Franklin County, PA

Everyday Calculus, O. FernandezWhat a week!

It was recently announced that one of our books, Everyday Calculus by Oscar Fernandez, is to be donated by the United Way of Franklin County, in partnership with the Franklin County Library System, to public libraries all throughout Franklin County. The decision recognizes the 2013 Campaign Chair, Jim Zeger, who has demonstrated a dedication to service and a “willingness to teach others” during the course of his four-year tenure on the board of directors.

But the choice of text was far from random; Everyday Calculus was selected “because of the need for materials that support financial and mathematical literacy within our library systems,” says Mr. Zeger. He’s one to know; before coming to United Way, Zeger studied math at Juniata College and taught mathematics at the Maryland Correctional Institute. He also served for a number of years as part of the Tuscarora School District school board, and “is very supportive and understanding of the value of relating and connecting applied math to students.”

Bernice Crouse, executive director of the Franklin County Library System, accepted the books and has found them a place in each County library, including the bookmobile, in order to make them more accessible to readers. According to Crouse, this book fits perfectly with Pennsylvania Library Association’s PA Forward initiative, which “highlights Financial Literacy as a key to economic vitality in Pennsylvania.”

Mr. Fernandez is reportedly “delighted” and “honored” by the decision, and looks forward to further collaborating with United Way.

Cue up The Bangles and join us as we Count Like an Egyptian with Fox News

Interested in learning more about how to do math like an ancient Egyptian, check out David Reimer’s book Count Like an Egyptian.