#ThanksEinstein: Jürgen Renn on popularizing Einstein

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Einstein: Missionary of Science

By Jürgen Renn

Jürgen Renn is a director at the Max Planck Institute for the History of Science in Berlin. This is the story of how he came to play such a major role in popularizing Einstein.

I encountered Albert Einstein at crucial turning points in my life, first studying his general theory of relativity while exploring quantum field theory on curved space-time backgrounds for my diploma thesis in physics at the Freie Universität in Berlin. I published my first papers on general relativity together with two postdocs I had the fortune to work with at the time: Tevian Dray and Don Salisbury. I would like to have pursued this topic for my PhD thesis as well but instead turned to quantum field theory and statistical physics. Meanwhile, I developed a passion for the history of science and began to prepare an edition of Galileo’s manuscripts. In 1985, working on my PhD in Rome, I was convinced that I could do physics and the history of science at the same time, and that I would stay in Italy for a long time to come. But things would soon change dramatically.

Kurt Sundermeyer, one of the people who taught me about general relativity, brought my attention to an advert looking for an assistant editor at the Collected Papers of Albert Einstein, then located at Boston University. I quickly applied and, after being interviewed by the founding editor, John Stachel, got the position. The work I did for the edition turned out to be a revelation and deeply shaped my future career. Arriving in Boston in 1986, the first volume was already underway and included the early letters between Albert and his fiancé Mileva Marić.

einstein old lettersThis newly discovered source gave key insights into Einstein’s early intellectual biography, leading up to his “miraculous year” 1905. Together with Robert Schulmann I published a special edition of these letters for Princeton University Press. Working on the scientific annotation of these letters, I was very fortunate to work with and learn from my senior colleagues John Stachel, Robert Schulmann, and David Cassidy. Later I also profited from encounters with other Einstein experts such as Fabio Bevilacqua, Diana Buchwald, Jean Eisenstaedt, Peter Galison, Hubert Goenner, Gerald Holton, Don Howard, David Kaiser, Martin Klein, Anne Kox, John Norton, Karin Reich, David Rowe, Robert Rynasiewicz, and many others, some of whom have meanwhile become close friends. John Stachel played a pivotal role in launching Einstein studies as a field of collaboration among physicists, historians, and philosophers of science and has always been my mentor in this field. He also pioneered broad-ranging studies in the history of general relativity, a field that I soon made my own, working in close collaboration with talented younger colleagues, in particular, Michel Janssen, Tilman Sauer, and Matthias Schemmel. Eventually, Michel, Tilman, the two Johns, several other younger colleagues, and I formed the team that would produce a four-volume study on The Genesis of General Relativity, published with Springer in 2007. But this is getting ahead of things.

In the late 1980s, commuting between Boston and Berlin, I also collaborated closely with the exceptional science historian and native Berliner Peter Damerow, who was always a great source of inspiration for my work. Together with an Italian colleague, Paolo Galluzzi, Peter and I developed a vision to create an electronic Galileo-Einstein Archive which would make all of Galileo’s and Einstein’s archival resources openly available in digital form. The idea was supported by the NSF and its program director Ron Overman, and we used the grant they subsequently awarded to explore our vision of an electronic archive in hypertext format. Like-minded colleagues all over the world were contacted, including the people who were just then creating the Web at CERN in Geneva. But our vision was evidently premature and the result was eventually limited to an electronic archive of Galileo’s manuscripts on mechanics. This was realized only after the foundation of the Max Planck Institute for the History of Science where I became a director in 1994. It took the persistence and courage of the current director of the Collected Papers of Albert Einstein, Diana Buchwald, supported by Prineinstein old letterceton University Press, to eventually realize over twenty years later the vision of a freely accessible Digital Einstein Archive.

The Genesis of General Relativity was the first major collaborative research project of the newly founded Max Planck Institute for the History of Science. Today, the collaboration endures as the new image to emerge from this study of Einstein’s most important achievement continues to be developed. The project has also been expanded by the work of younger colleagues at the institute such as Alex Blum and Roberto Lalli. Together with one of the founders of the project, Michel Janssen, another colleague, Christoph Lehner, recently published the Cambridge Companion to Einstein. The research undertaken in this field is not confined to the intellectual dimension of Einstein’s work, however, but also extends to the cultural and political contexts, as is illustrated by Milena Wazeck’s study Einstein’s Opponents, or by Giuseppe Castagnetti’s and Hubert Goenner’s studies on the institutional contexts. I plan to bring some of these perspectives together in my forthcoming book on Einstein, entitled On the Shoulders of Giants and Dwarfs.

Einstein’s engagement as a missionary and popularizer of science has made a deep impression on me and it is in this spirit that my collaborators and I became involved in the Einstein Year 2005, when the centenary of Einstein’s miraculous year was celebrated. The centerpiece of this celebration in Germany was the extensive exhibition “Albert Einstein — Chief Engineer of the Universe,” an online presentation of which can still be seen today.

relativity 100 yearsWorking with other scholars on Einstein’s life and work continues to be a great source of inspiration for me. I am particularly grateful for the friendships that have developed from my various collaborations. One striking example is my friendship with Hanoch Gutfreund, a great scholar, an interminable source of energy, and a wonderful human being. With Hanoch, I recently wrote two books for Princeton University Press, The Road to Relativity and Relativity: The Special and the General Theory. 100th Anniversary Edition. In preparing these books, we developed a common style of popularization without compromising on scientific rigor. Having met late in life, we are all the more determined to write many more books together.

Jürgen Renn is a director at the Max Planck Institute for the History of Science in Berlin. His books include The Road to Relativity.

Einstein graphic courtesy of the Albert Einstein Facebook page.

#ThanksEinstein: Katherine Freese on how relativity rejuvenated her career

Thanks Einstein Meme 3Under the Spell of Relativity

By Katherine Freese

Katherine Freese is director of Nordita, the Nordic Institute for Theoretical Physics, in Stockholm, and author of The Cosmic Cocktail, which tells of the epic quest to solve one of the most compelling enigmas of modern science—what is the universe made of? This is the story of how one of today’s foremost pioneers in the study of dark matter came back from the brink of burnout because of Relativity.

My career choice was hugely influenced by the work of Albert Einstein. I chose a career in physics precisely because I was inspired by his theories of relativity. My first exposure to physics was at Exeter Summer School in New Hampshire when I was fifteen years old. I went there after my junior year in high school because, frankly, I enjoyed learning and would otherwise have been bored over the long summer. I took an introductory course in physics and have to admit that, at first, I was a bit intimidated. But I got into it quickly and was gratified to discover that I did really well. The course was inspiring, and my teacher Mr. Dudley probably has no idea what an impact he had on me.

It was when the summer course turned to Special Relativity that I became really excited. What a bizarre and fascinating subject! To begin with, the idea that there is no absolute reference frame was an eye-opener. I later tried to explain this to friends, but they persisted in arguing that the Earth really does provide a special reference frame, world freeseat least for humans, so we should just compute everything from our own point of view.

Strange paradoxes arise when one makes one simple postulate, that the speed of light is the same in every reference frame. Two observers moving with relativistic speeds (relative to one another) measure completely different things. Clocks measure different times, and rulers measure different lengths. The shortest time is measured in the reference frame where the event takes place, and in every other frame time appears dilated. So an astronaut, who goes off into space and eventually returns, ages more slowly than the rest of us. There can be time travel! In the sense that the astronaut can come back to the Earth at an arbitrarily distant point in the future…if she can tolerate traveling at those speeds. Recently I met quite a few astronauts in Stockholm at the Congress of the Association of Space Explorers. They are amazing people. I was invited to give a 20 minute talk on “What we know about the Universe today.” A tall order in front of these folks. Can you guess what I talked about? Cosmology, beginning with Einstein’s relativity, of course.

These exciting things I learned when I was 15 made me determined to learn more physics, and I ended up majoring in physics in college. I went very young, at 16, and graduated with a bachelor’s degree in physics from Princeton University at the age of 20. It was really hard, I was burning out quickly, and at that point I wasn’t sure I wanted to continue. Chapter One of The Cosmic Cocktail, the book that was published by Princeton University Press just over a year ago, describes what happened next. I decided to take some time off from school. With my best friend, I went off to Tokyo to teach English and ended up serving drinks in bars for a giant salary. (I finally surpassed it a few years ago as a Full Professor.) A year and a half later, I went to Korea to renew my visa. While I was traveling around Pusang, my stomach, or so I thought, started to hurt. When I returned to Tokyo I was walking around doubled over with pain. Indeed it turned out to be appendicitis. I went to the Catholic Hospital, run by English nuns, and had my appendix removed.

While I was lying in the hospital bed, I read the only book I had brought with me, Spacetime Physics by Taylor and Wheeler. It is a book about Einstein’s special relativity. The book is beautifully written and only requires simple knowledge of forces, energy, and so on, and I loved it. The minute I got out of the hospital, I flew back to the US, reinvigorated by the desire to study physics. I contacted Columbia University, which had previously accepted me, and they let me in at a moment’s notice. I was lucky they did.

Einstein’s influence persisted. Two years into my graduate program at Columbia University, I went to Fermilab, the particle physics accelerator outside of Chicago, to work in experimental high energy physics. However, I also took a class in cosmology at the University of Chicago twice a week, out of curiosity. Plus, it took me into the city of Chicago. Fermilab is on a farm an hour west and has buffalo roaming around. The professor who taught the course, David Schramm, was a giant both physically and mentally, and one of the founders of the field of astroparticle physics, where the smallest particles explain the properties of the largest galaxies. We nicknamed him “Schrammbo.” (If you want to know more about him, you’ll have to read my book.) In that course, Einstein’s equations were applied to the Universe as a whole. Wow. I stopped showing up in the lab and instead sat in my housing at Fermilab and read about general relativity, this time at a graduate level framed by far deeper mathematics. Again, it was a turning point. I transferred to the University of Chicago to get my PhD with David Schramm in the field of cosmology.

In human history, every culture has had creation myths. In the past 100 years we have developed our own, the Big Bang. The difference is that the Hot Big Bang is right! The achievements over the past century in the field of cosmology are breakthroughs for all of mankind. We understand everything about our observable Universe all the way out to the farthest distant that light could have traveled to us in the age of the Universe (anything farther out could not have impacted us because the information could not travel in excess of the speed of light).

Now I’m a professional. I work with Einstein’s equations or their immediate consequences every day. I’m a theorist. I invent things and hope they turn out to match reality. All my work lies within the framework of modern cosmology, which began with Einstein’s work in relativity in 1915. What a brilliant man he was! Ever since I learned about relativity I’ve been under its spell, and I still am.

Katherine Freese is director of Nordita, the Nordic Institute for Theoretical Physics, in Stockholm, and professor of physics at the University of Michigan. She is the author of The Cosmic Cocktail.

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

#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.

#ThanksEinstein: Jimena Canales on the ideal figure of Einstein

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Me, Myself and Einstein

By Jimena Canales

Jimena Canales is the author of The Physicist and the Philosopher, which tells the remarkable story of how an explosive debate between two intellectual giants transformed our understanding of time and drove a rift between science and the humanities that persists today. This is the story of how she came to study the iconic physicist when she initially had no interest in “such a great man, or any great men.”

I arrived at Einstein after following a winding, circuitous road. Like so many others, I was acquainted with his life and works since my college years. I majored in Engineering Physics, taking the required relativity lessons as part of my Modern Physics courses. Like so many others, I struggled to understand the philosophical significance of the theory’s paradoxes (particularly those pertaining to simultaneity and time and length dilation). Comprehending that was a lot harder than the comparatively simple number-crunching that led me to the right answers in the final exam.

But as a historian of science, I was initially not interested in such a great man or in any great men, for that matter. In fact, early on in my career I was more interested in understanding broader social and historical transformations than those that could ever be brought about by single individuals, no matter how brilliant they were. No one person created modernity, and I was interested in understanding how it came about.

Yet once I came to know Einstein, my career and my views about the history of science changed dramatically. It all started when I found the transcript of a meeting at the Société française de philosophie that took place in April 6, 1922. I had been looking for that particular document because I was trying to find out everything I could about Henri Bergson, one of the most important philosophers of the century widely renowned for his insightful views about time. Bergson’s conception of time had been more famous than Einstein’s — it was only natural that I would focus on him. But what I found out upon reading the transcript shocked me beyond belief. I read about Henri Bergson debating, face-to-face, with Albert Einstein himself.

I tried to read as much as I could about this day, and—surprisingly—found almost nothing in the existing Einstein scholarship. But it seemed to me that everywhere else I looked I found references to that particular meeting. What is more, I found an astounding number of prominent intellectuals and scientists all discussing Einstein and Bergson together, and asking which of the two men was correct when it came to the prickly question of time.

Given my interest in Bergson, I was invariably led to study Einstein. I had thought that everything interesting about Einstein must have already been worked on to death by historians. I thought I would have nothing new to contribute. But the Einstein I was starting to get to know was quite different from the one I had read about.

I was at first a reluctant Einstein scholar, but as I read more and more I was hooked. My encounter with his work affected me in the most unexpected and wonderful ways imaginable. I was reminded how in even the most treaded upon topics there remain elements of surprise. Truth be told, the Einstein I got to know through my sources was not the mythical figure we all know—he is of this world. In my book, we find him saving a small piece of soap to give to his wife because he cannot afford to buy it; we find him desperately trying to combat the objections of Bergson to defend his theory; we see him speaking on the radio and reenacting for television some of the most important moments of his life; and, finally, we encounter him reflecting about Bergson in melancholic and personal letters written to his best friend in the years before his death. By reading his private correspondence, I got to know his sense of humor as much as his callousness; his sectarianism as much as his noble internationalist ideals; his pacifism as much as his uncompromising politics (I was surprised, for example, to see him take such a strong stance against the League of Nations). I was able to see his brilliance as well as his limitations (in almost everything that involved knowing the language and culture of France).

Einstein slowly appeared to me as much more than a great man—he became an ideal figure through which we could explore broader questions, such as the division between the science and the humanities, the role of expert knowledge versus lay wisdom, the relation of science to the media and to other areas of culture (including art). We could learn how cosmological and universal conceptions of time (in theory) are related to our use of time (in practice). We could explore processes that lead to the formation of our own subjectivities and psychological make-up and, most importantly, analyze our ever-changing place amongst things, machines and new technologies.

Years after my first scholarly encounter with Einstein, I cannot but be more than grateful to that great physicist, who a century after creating his General Theory of Relativity, continues to teach us so much.

Jimena Canales holds the Thomas M. Siebel Chair in the History of Science at the University of Illinois, Urbana-Champaign, and was previously associate professor of the history of science at Harvard University. She is the author of The Physicist and the Philosopher, and A Tenth of a Second: A History.

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

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.

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

Introducing the new video trailer for The Quotable Feynman

Nobel Prize-winning physicist Richard P. Feynman (1918–88) is widely known for his scientific genius. But during his life, he became as famous for the wit, wisdom, and lucidity of his popular lectures and writings as for his fundamental contributions to physics. We are pleased to present the new video trailer for The Quotable Feynman, including approximately 500 quotations carefully selected by his daughter, Michelle Feynman, from his spoken and written legacy:

Check out chapter one here.





An interview with Nicholas Higham on The Princeton Companion to Applied Mathematics

Higham jacket

We are excited to be running a series of posts on applied mathematics by Nicholas Higham over the next few weeks. Higham is editor of The Princeton Companion to Applied Mathematics, new this month. Recently he took the time to answer some questions about the book, and where the field is headed. Read his popular first post on color in mathematics here.

What is Applied Mathematics?

NH: There isn’t any generally agreed definition, but I rather like Lord Rayleigh’s comment that applied mathematics is about using mathematics to solve real-world problems “neither seeking nor avoiding mathematical difficulties”. This means that in applied mathematics we don’t go out of our way to consider special cases that will never arise in practice, but equally we do not sidestep genuine difficulties.

What is the purpose of The Companion?

NH: The Companion is intended to give an overview of the main areas of applied mathematics, to give examples of particular problems and connections with other areas, and to explain what applied mathematicians do—which includes writing, teaching, and promoting mathematics as well as studying the subject. The coverage of the book is not meant to be exhaustive, but it is certainly very broad and I hope that everyone from undergraduate students and mathematically interested lay readers to professionals in mathematics and related subjects will find it useful.

What is an example of something aspect of applied mathematics that you’ve learned while editing the book?

NH: Applied mathematics is a big subject and so there are many articles on topics outside my particular areas of expertise. A good example concerns applications of computational fluid dynamics in sport. An article by Nicola Parolini and Alfio Quarteroni describes the mathematical modeling of yachts for the America’s cup. The designer wishes to minimize water resistance on the hull and maximize the thrust produced by the sails. Numerical computations allow designs to be simulated without building and testing them. The article also describes mathematical modeling of the hi-tech swimsuits that are now banned from competition. The model enables the benefit of the suits on race times to be estimated.

The Companion is about 1000 pages. How would advise people to read the book.

NH: The book has a logical structure, with eight parts ranging from introductory material in Part I, the main areas of applied mathematics in Part IV (the longest part), through to broader essays in the final part. It is a good idea to start by reading some of the articles in Part I, especially if you are less familiar with the subject. But a perfectly sensible alternative approach is to select articles of interest from the table of contents, read them, and follow cross-references. Or, you can just choose a random article and start reading—or simply follow interesting index entries! We worked very hard on the cross-references and index so an unstructured approach to reading should lead you around the book and allow you to discover a lot of relevant material.

What was the hardest thing about editing The Companion?

NH: The hardest aspect of the project was ensuring that it was completed in a reasonable time-frame. With 165 authors it’s hard to keep track of everything and to to ensure that drafts, revisions, and corrected proofs are delivered on time.

How much of the book did you write?

NH: I wrote about 100 of the 1000 pages. This was great fun, but it was some of the hardest writing I’ve done. The reason is partly that I was sometimes writing about topics that I don’t normally write about. But it was also because Companion articles are quite different from the papers I’m used to writing: they should have a minimal number of equations and formal statements of theorems, lots of diagrams and illustrations, and no citations (just Further Reading at the end of the article).

How did you choose the cover?

NH: We considered many different ideas. But after a lot of thought we settled on the motor boat picture, which captures the important topics of fluid mechanics, waves, and ocean, all of which are covered in the book in a number of articles.

What is the most unexpected article?

NH: Perhaps the article Mediated Mathematics: Representations of Mathematics in Popular Culture and Why These Matter by sociologist of education Heather Mendick. She discusses the way mathematics is represented in numerous TV shows and films.

What would you be doing if you hadn’t become a mathematician?

NH: I’d be playing a Hammond B3 organ in a jazz or blues band. I’m a keen musician and played keyboards semi-professionally for many years, starting in my teens.

How did you go about organizing the book?

NH: I recruited five Associate Editors with expertise in different areas and we met and planned out the eight parts of the book and the articles, along with a list of authors to invite. We looked for authors who are leading international experts in their field and are at the same time excellent expositors. Signing up the 165 authors was quite a long process. We were able to find authors for almost every article, so just a very small number had to be dropped. In some cases the authors suggested changes of content or emphasis that we were happy to agree with.

What range of readers is The Companion aimed at?

NH: The target audience for The Companion is very broad. It includes mathematicians at undergraduate level or above, students, researchers, and professionals in other subjects who use mathematics, and mathematically interested lay readers. Some articles will also be accessible to students studying mathematics at pre-university level.

Why not just seek information online? Why is there a need for a book?

NH: When Princeton University Press asked me to edit The Companion they told me that reference books still have great value. Many people have trouble navigating the vast amount of information available online and so the need for carefully curated thematic reference works, written by high calibre authors, is as great as ever. So PUP’s experience is that print is definitely not dead, and indeed my own experience is that I have many books in PDF form on my computer, but if I want to read them seriously I use a hard copy.

How have you ensured that the book will not go out of date quickly?

NH: This was a major consideration. This was a five and a half year project and we wanted to make sure that the book will still be relevant 10, 20, or 50 years from now. To do that we were careful to choose articles on topics that have proven long-term value and are not likely to be of short-term interest. This is not to say that we don’t cover some relatively new, hot topics. For example, there are articles on compressed sensing (recovering sparse, high-dimensional data from a small number of indirect measurements) and on cloaking (hiding an object from an observer who is using electromagnetic, or other, forms of imaging, as in Harry Potter or Romulan space ships in Star Trek), both of which are areas that have grown tremendously in the last decade.

What sort of overview of applied mathematics does the book give?

NH: Applied mathematics is a huge subject, so we cannot cover everything in 1000 pages. We have tried to include the main areas of research as well as key underlying concepts, key equations, function and laws, as well as lots of example of applied mathematics problems. The examples range from the flight of a golf ball, to robotics, to ranking web pages. We also cover the use of applied mathematics in other disciplines such as engineering, biology, computer science, and physics. Indeed the book also has a significant mathematical physics component.

Where is the field going?

NH: Prior to the 20th century, applied mathematics was driven by problems in astronomy and mechanics. In the 20th century physics became the main driver, with other areas such as biology, chemistry, economics, engineering, and medicine also providing many challenging mathematical problems from the 1950s onwards. With the massive and still growing amounts of data available to us in today’s digital society information, in its many guises, will be an increasingly important influence on applied mathematics in the 21st century.

To what extent does The Companion discuss the history of applied mathematics?

NH: We have an excellent 25-page article in Part I titled The History of Applied Mathematics by historians of mathematics June Barrow-Green and Reinhard Siegmund-Schultze. Many articles contain historical information and anecdotes. So while The Companion looks to the future it also gives an appreciation of the history of the subject.

How do you see the connections between applied mathematics and other disciplines developing?

NH: Applied mathematics is becoming ever more interdisciplinary. Many articles in The Companion illustrate this. For example,

  • various facets of imaging feature in several articles, including those on compressed sensing, medical imaging, radar, and airport baggage screening,
  • the article on max-plus algebras shows how what may seem like an esoteric area of pure mathematics has applications to all kinds of scheduling processes,
  • the article on the spread of infectious diseases shows the value of mathematical models in epidemiology,
  • several articles show how mathematics can be used to help understand the earth’s weather and climate, focusing on topics such as weather prediction, tsunamis, and sea ice.

What are you thoughts on the role of computing in applied mathematics?

NH: Computation has been a growing aspect of applied mathematics ever since the first stored program computer was invented here in Manchester. More and more it is the case that numerical computations and simulations are used in tandem with, or even in place of, the classical analysis that relies just on pen and paper. What I find particularly interesting is that while the needs of mathematics and of science in general have, naturally, influenced the development of computers and programming languages, there have been influences in the other direction. For example, the notation for the ceiling and floor functions that map a real number to the next larger or smaller integer, respectively, was first introduced in the programming language APL.

Of course numerical computations are expressed in terms of algorithms, and algorithms are ubiquitous in applied mathematics, and strongly represented in the book.

Do you have any views on ensuring the correctness of work in applied mathematics?

NH: As the problems we solve become every more complicated, and the computations we perform run for longer and longer, questions about the correctness of our results become more important. Applied mathematicians have always been good at estimating answers, perhaps by an asymptotic analysis, so we usually know roughly what the answer should look like and we may be able to spot gross errors. Several particular aspects of treating correctness are covered in The Companion.

Uncertainty quantification is about understanding how uncertainties in the data of a problem affect the solution. It’s particularly important because often we don’t know the problem data exactly—for example, in analyzing groundwater flow we don’t know the exact structure of what lies under the ground and so have to make statistical assumptions, and we want to know how these impact the computed flows.

A different aspect of correctness concerns the reproducibility of our computations and treats issues such as whether another scientist can reproduce our results and whether a computation on a high-performance computer will produce exactly the same answer when the computation is repeated.

All of these issues are covered in multiple articles in the book.

Nicholas J. Higham is the Richardson Professor of Applied Mathematics at The University of Manchester. Mark R. Dennis is professor of theoretical physics at the University of Bristol. Paul Glendinning is professor of applied mathematics at The University of Manchester. Paul A. Martin is professor of applied mathematics at the Colorado School of Mines. Fadil Santosa is professor of mathematics at the University of Minnesota. Jared Tanner is professor of the mathematics of information at the University of Oxford.

Washington Post highlights historic clash between Einstein and Bergson on the nature of time

2015_Einstein_bannerWith the 100th anniversary of the general theory of relativity coming up in November, Einstein is popping up everywhere. Yesterday’s Washington Post ran a terrific feature on Einstein books, including three of our own: Hanoch Gutfreund and Jürgen Renn’s The Road to Relativity, Einstein’s Relativity: The Special and the General Theory, and Jimena Canales’s The Physicist and the Philosopher.

One of the most fascinating chapters of Einstein’s public life revolves around an encounter he had with Henri Bergson, the renowned philosopher, on April 6, 1922, in Paris. It was on this day that Einstein and Bergson publicly debated the nature of time, touching off a clash of worldviews between science and the humanities that persists today. The philosopher Bergson argued that time was not merely mechanical, and should be seen in terms of lived experience; Einstein dismissed Bergson’s psychological notions as irreconcilable with the realities of physics. The Physicist and the Philosopher tells the remarkable story of how this explosive debate between two famous thinkers created intellectual rifts and revolutionized an entire generation’s understanding of time.

Nancy Szokan’s piece in Washington Post recounts the dramatic collision:

In The Physicist and the Philosopher, Canales recounts how Bergson challenged Einstein’s theories, arguing that time is not a fourth dimension definable by scientists but a ‘vital impulse,’ the source of creativity. It was an incendiary topic at the time, and it shaped a split between science and humanities that persisted for decades—though Einstein was generally seen as the winner and Bergson is all but forgotten.

Bergson and Einstein, toward the end of their lives, each reflected on his rival’s legacy and dedication to the pursuit of truth: Bergson during the Nazi occupation of Paris and Einstein in the wake of the first hydrogen bomb. Referencing Einstein’s quest for scientific truth, Hanoch Gutfreund recently had an article in the Huffington Post on how Einstein helped shape the Hebrew University of Jerusalem (home of the Albert Einstein Archives online):

On the occasion of the opening of the university, Albert Einstein published a manifesto “The Mission of our University”, which generated interest and excitement in the entire Jewish and academic worlds.

It states: “The opening of our Hebrew University on Mount Scopus, at Jerusalem, is an event which should not only fill us with just pride, but should also inspire us to serious reflection. … A University is a place where the universality of human spirit manifests itself. Science and investigation recognize as their aim the truth only.”

Read the rest here.

November’s big anniversary serves as a reminder of the enduring commitment to scientific investigation that continues at The Hebrew University and centers of learning all over the world today.

Read sample chapters of The Physicist and the Philosopher here, The Road to Relativity here, and Relativity here.

You can find information on the Digital Einstein Papers, an open access site for The Collected Papers of Albert Einstein, comprising more than 30,000 unique documents here.

Win a copy of THE ROAD TO RELATIVITY over on the official Einstein Facebook page!

Head on over to the official Facebook page of Albert Einstein to enter to win a copy of The Road to Relativity.

The contest starts today and will run from July 22nd at 11 AM ET until Wednesday, August 5th at 10:59 AM ET.

Einstein Book Contest Flyer 2

To celebrate the 100th anniversary of Albert Einstein’s theory of general relativity, Princeton University Press launches books by Hanoch Gutfreund and Jürgen Renn

The Road to RelativityOn July 15th, Princeton University Press proudly launched two books by Professor Hanoch Gutfreund and Jürgen Renn, Relativity and The Road to Relativity, at the 14th Marcel Grossman meeting on relativistic physics in Rome.

The two books are being published to celebrate the 100th anniversary of Albert Einstein’s formulation of the theory of general relativity in 1915, and so it was fitting to launch them at a conference that demonstrates the ongoing influence of Einstein’s theory on cutting edge work on black holes, pulsars, quantum gravity, and other areas fundamental to our understanding of the universe.

The launch took place at the Besso Foundation, the family home of Albert Einstein’s friend and colleague, Michele Besso, during an exhibition, organized by Professor Gutfreund, of original Einstein letters and notebooks from the Albert Einstein Archives at the Hebrew University in Jerusalem.

relativity jacketMore than 150 distinguished physicists and invited guests, including the Chief Rabbi of Rome, Riccardo di Segni, and members of the Besso and Grossman families, listened to Professor Gutfreund and Professor Renn provide a compelling overview of their research and of the new insights it has brought to the history of the development of general relativity. Professor Gutfreund stressed the fundamental insights into Einstein’s work provided by the rich Archives in Jerusalem, while Renn dismissed the notion of Albert Einstein as an isolated and idiosyncratic genius, stressing his network of collaborators and colleagues, including Besso.


Renn and Gutfreund

Professor Hanoch Gutfreund and Jürgen Renn at the book launch in Rome

Photo from Renn and Gutfreund launch

Launch for Relativity and The Road to Relativity, at the 14th Marcel Grossman meeting on relativistic physics in Rome


History & Philosophy of Science 2015 Catalog

Our History & Philosophy of Science 2015 catalog is now available.

Be sure to check out The Quotable Feynman, a collection of about 500 quotations from Nobel Prize-winning physicist Richard P. Feynman (1918-88), compiled by his daughter, Michelle Feynman. Read it cover-to-cover or flip to a specific section, from childhood to religion, from family to politics.

Looking for a comprehensive and authoritative guide to everything Albert Einstein? An Einstein Encyclopedia is your indispensible resource. The book contains entries on a range of topics, including his romantic relationships, hobbies, educational affiliations, and friends. Written by three leading Einstein scholars, researchers and those with a casual curiosity alike will find much to interest them. And don’t forget to scroll to page 3 of the catalog for a wealth of additional Einstein-related titles, including Relativity: 100th Anniversary Edition and Einstein and the Quantum.

Finally, the richly illustrated Mathematics and Art is written by Lynn Gamwell, a cultural historian of both topics. Gamwell shows how mathematics and art have informed and influenced one another from antiquity to the present.

We invite you to look through our catalog and learn about many more new titles in History & Philosophy of Science.

If you’d like updates on new titles sent directly to your inbox, subscribe here.