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

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.

In 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.

For the love of books

What better way to celebrate Valentine’s Day than with a heartfelt declaration of our love of books? We offer up these quotes from our Quotable’s, as well as a special giveaway!

The Quotable Kierkegaard

“It is the most interesting time, the period of falling in love, where after the first touch of a wand’s sweeping sensation, from each encounter, every glance…one brings something home, just like a bird busily fetching one stick after the other to her nest, yet always feels overwhelmed by the great wealth.”

“What is it, namely, that connect the temporal and eternity, what else but love, which for that very reason is before everything and remains after everything is gone.”

The Quotable Feynman

“It’s necessary to fall in love with a theory, and like falling in love with a woman, it’s only possible if one does not completely understand her.”

The Quotable Thoreau

“How insufficient is all wisdom without love.”

“It is strange that men will talk of miracles, revelation, inspiration, and the like, as things past, while love remains.”

“What is the singing of birds, or any natural sound, compared with the voice of one we love?”

The Ultimate Quotable Einstein

“Love brings much happiness, much more so than pining for someone brings pain.”

The Quotable Jefferson

“If I love you more, it is because you deserve more.”

“We think last of those we love most.”

In Love’s Vision, Troy Jollimore puts forth a new way of thinking about love. For the most romantic holiday all year, we’re giving away three copies starting February 12. The entry period ends February 20. As you pay special attention to your loved ones let Troy Jollimore’s vision of love give you food for thought.

Gravitational waves making waves at Princeton

Today marks a new era in cosmology, astronomy, and astrophysics. The main page of the Einstein Papers Project website reports, “Gravitational waves do exist, as has been announced today with great joy by the scientists of the LIGO collaboration, after more than two decades of intensive experimental work.”

The cosmic breakthrough, which proves Einstein’s 100 year old prediction, has resulted in a tremendous response across the scientific community and social media. Scientific websites everywhere are already debating the meaning of the discovery, the #EinsteinWasRight hashtag has been bantered about on Twitter; You Tube featured a live announcement with over 80,000 people tuning in to watch (check it out at 27 minutes).

Princeton University Press authors Jeremiah Ostriker and Kip Thorne had a bet about gravitational wave detection in the 80s. Today when we contacted him, Ostriker, author of Heart of Darkness, was ebullient:

“The LIGO announcement today and the accompanying papers are totally persuasive. We all believed that Einstein had to be right in predicting gravitational waves, but to see them, so clean and so clear is marvelous. Two independent instruments saw the same signal from the same event, and it was just what had been predicted for the in-spiral and merger of two massive black holes.

A quarter of a century ago I had a bet with Kip Thorne that we would not see gravitational waves before the year 2000 – and I won that bet and a case of wine. But I did not doubt that, when the sensitivity of the instruments improved enough, gravitational waves would be found.  Now the skill and perseverance of the experimentalists and the support of NSF has paid off.

Hats off to all!!!”

But was Einstein always a believer in gravitational waves? Daniel Kennefick, co-author of The Einstein Encyclopedia says no:

“One hundred years ago in February 1916, Einstein mentioned gravitational waves for the first time in writing. Ironically it was to say that they did not exist. He said this in a letter to his colleague Karl Schwarzschild, who had just discovered the solution to Einstein’s equations which we now know describe black holes. Today brings a major confirmation of the existence both of gravitational waves and black holes. Yet Einstein was repeatedly skeptical about whether either of these ideas were really predictions of his theory. In the case of gravitational waves he soon changed his mind in 1916 and by 1918 had presented the first theory of these waves which still underpins our understanding of how the LIGO detectors work. But in 1936 he changed his mind again, submitting a paper to the Physical Review called “Do Gravitational Waves Exist?” in which he answered his own question in the negative. The editor of the journal responded by sending Einstein a critical referee’s report and Einstein angrily withdrew the paper and resubmitted it elsewhere. But by early the next year he had changed his mind again, completely revising the paper to present one of the first exact solutions for gravitational waves in his theory. So his relationship with gravitational waves was very far from the image of the cocksure, self-confident theorist which dominates so many stories about Einstein. Because of this, he would have been thrilled today, if he were still alive, to have this major confirmation of some of the most esoteric predictions of his theory.”

Here at Princeton University Press where we recently celebrated the 100th anniversary of Einstein’s theory of general relativity, the mood has been celebratory to say the least. If you’d like to read the Einstein Papers volumes that refer to his theory of gravitational waves, check out Document 32 in Volume 6, and Volume 7, which focuses on the theory. Or, kick off your own #EinsteinWasRight celebration by checking out some of our other relevant titles.

Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves
by Daniel Kennefick

Relativity: The Special and the General Theory, 100th Anniversary Edition
by Albert Einstein

The Meaning of Relativity: Including the Relativistic Theory of the Non-Symmetric Field
by Albert Einstein

Einstein Gravity in a Nutshell
by A. Zee

The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity” Featuring the Original Manuscript of Einstein’s Masterpiece
by Hanoch Gutfreund & Jürgen Renn.

The Curious History of Relativity: How Einstein’s Theory of Gravity Was Lost and Found Again
by Jean Eisenstaedt

An Einstein Encyclopedia
by Alice Calaprice, Daniel Kennfick, & Robert Sculmann

Gravitation and Inertia
by Ignazio Ciufolini & John Archibald Wheeler

Einstein’s Jury: The Race to Test Relativity
by Jeffrey Crelinsten

What Does a Black Hole Look Like?
by Charles D. Bailyn

Dynamics and Evolution of Galactic Nuclei
by David Merritt

The Global Nonlinear Stability of the Minkowski Space (PMS-41)
by Demetrios Christodoulou & Sergiu Klainerman

Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics
by Kip S. Thorne & Roger D. Blandford

The Collected Papers of Albert Einstein, Volume 7: The Berling Years: Writings, 1918-1921
by Albert Einstein

The Most Beautiful Equations in Applied Mathematics

By Nick Higham

The BBC Earth website has just published a selection of short articles on beautiful mathematical equations and is asking readers to vote for their favourite.

I wondered if we had included these equations in The Princeton Companion to
Applied Mathematics
(PCAM), specifically in Part III: Equations, Laws, and Functions of Applied Mathematics. We had indeed included the ones most
relevant to applied mathematics. Here are those equations, with links to the
BBC articles.

• The wave equation (which quotes PCAM author Ian Stewart). PCAM has a short
article by Paul Martin of the same title (III.31), and the wave equation
appears throughout the book.
• Einstein’s field equation. PCAM has a 2-page article Einstein’s Field
Equations
(note the plural), by Malcolm MacCallum (article III.10).
• The Euler-Lagrange equation. PCAM article III.12 by Paul Glendinning is about
these equations, and more appears in other articles, especially The
Calculus of Variations
(IV.6), by Irene Fonseca and Giovanni Leoni.
• The Dirac equation. A 3-page PCAM article by Mark Dennis (III.9) describes
this equation and its quantum mechanics roots.
• The logistic map. PCAM article The logistic equation (III.19), by Paul
Glendinning treats this equation, in both differential and difference forms.
It occurs in several places in the book.
• Bayes’ theorem. This theorem appears in the PCAM article Bayesian Inference in Applied Mathematics (V.11), by Des Higham, and in other articles employing
Bayesian methods.

A natural equation is: Are there other worthy equations that are the
subject of articles in Part III of PCAM that have not been included in the BBC
list? Yes! Here are some examples (assuming that only single equations are
allowed, which rules out the Cauchy-Riemann equations, for example).

• The Black-Scholes equation.
• The diffusion (or heat) equation.
• Laplace’s equation.
• The Riccati equation.
• Schrödinger’s equation.

Check out the Princeton Companion to Applied Math here.

The Digital Einstein Papers: An Open Access Story

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

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

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

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

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

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

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

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

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

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

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

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

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

Einstein in Oxford

By Andrew Robinson

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

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

Einstein receiving an honorary degree at Oxford. Source: http://www.einsteingalerie.de/zubehoer/grafiken/portraet/doctor1931.jpg

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Grumble: Why’s this creature staying

With his pipe and piano playing?

Why should this barbarian roam?

Could he not have stopped at home?

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

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

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

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

Happy 100th Anniversary to Einstein’s General Theory of Relativity!

Today is the final day of our popular #ThanksEinstein series, in which an array of prominent scholars and scientists have shared their insights and reflections on relativity, Einstein, and how his work inspired their own careers. Scroll through this week’s blog posts to read pieces by Daniel Kennefick, Katherine Freese, Hanoch Gutfreund, Jürgen Renn, Alice Calaprice, Jimena Canales, J.P. Ostriker, and many more special features, including this piece on Einstein’s final days.

Einstein’s General Theory of Relativity celebrates its 100 year anniversary today. November 25, 1915, during a particularly strenuous time in his life, is when Einstein submitted his final version of the general theory of relativity to the Prussian Royal Academy, complete with the field equations that define how the force of gravity arises from the curvature of space and time by matter and energy. The theory, which is the current theory of gravitation in modern physics, has implications for everything from black holes to the idea of universe expansion. It gained rapid popularity after its conception in 1915, and in the early 1920s alone, it was translated into ten languages. Fifteen editions in the original German appeared over the course of Einstein’s lifetime.

Princeton University Press has released a special edition of Relativity: The Special and the General Theory to commemorate the anniversary, including commentary from Hanoch Gutfreund and Jürgen Renn, Einstein experts, as well as additional content such as title pages from several language translations. You can browse through them in the slideshow below. Happy 100th to the general theory of relativity! Science wouldn’t be the same without you.

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Was Einstein the First to Discover General Relativity?

Today the world celebrates the day 100 years ago that Albert Einstein submitted his final version of the general theory of relativity to the Prussian Royal Academy. A theory of gravitation with critical consequences, it completely transformed the field of theoretical physics and astronomy. Einstein has long been celebrated and popularized for his contribution, but some have continued to ask whether he was, in fact, the first to discover general relativity. Daniel Kennefick, co-author of An Einstein Encyclopedia, looks at the debate:

Einstein’s Race

By Daniel Kennefick

On November 25, 1915 Einstein submitted one of the most remarkable scientific papers of the twentieth century to the Prussian Academy of Sciences in Berlin. The paper presented the final form of what are called the Einstein Equations, the field equations of gravity which underpin Einstein’s General Theory of Relativity. Thus this year marks the centenary of that theory. Within a few years this paper had supplanted Newton’s Universal Theory of Gravitation as our explanation of the phenomenon of gravitation, as well as overthrown Newton’s understanding of such fundamental concepts as space, time and motion. As a result Einstein became, and has remained, the most famous and celebrated scientist since Newton himself.

But what if Einstein was not the first scientist to publish these famous equations? Should they be called, not the Einstein equations, but the Einstein-Hilbert equations, honoring also the German mathematician David Hilbert? In 1915, Einstein visited Hilbert in Gottingen, and Hilbert convinced him that the goal of a fully general relativistic theory was achievable, something Einstein had nearly convinced himself could not be done. Einstein returned to work, and by November, he had found the field equations which give General Relativity its final form. However, Hilbert also worked on the ideas Einstein had discussed with him and published a paper discussing how Einstein’s theory fitted in with his own ideas on the role of mathematics in physics.

The argument for honoring Hilbert lies in a paper written by him which included the Einstein equations, derived from fundamental principles. This paper, while appearing several months after Einstein’s, was submitted on November 20, and Hilbert even sent Einstein a copy which probably reached Einstein before he submitted his own paper. In fact, a few people have even gone so far as to propose that Einstein might have stolen the final form of his equations from Hilbert.

Of course even if that were true, we are talking only about one final term in the equations (Einstein had published a close to correct version earlier in the month) and to Einstein would still belong sole credit for the enormous amount of work which went into the argument by which equations with these unique properties were singled out in the first place. We would still recognize Einstein for the critical physical thinking, while acknowledging Hilbert’s superior mathematical ability in more quickly finding the final correct form of the equations. Still, perhaps Hilbert would deserve a share of the credit for that final step. Why then do the centenary celebrations mention Einstein only and omit Hilbert almost completely?

One reason is that in the late 1990s a historian working on Hilbert named Leo Corry made a remarkable discovery. He found a copy of the proofs of Hilbert’s paper, with a printers stamp dating it to December 6, 1915. These proofs show that Hilbert made significant changes to the paper after this date. In addition, the proofs do not contain the Einstein equations. The proofs have been cut up here and there (probably by the printers themselves as they worked), so it is possible that the equations would be there if we had the missing pieces. But it is also quite possible that amidst the changes Hilbert made to the paper, he took the opportunity to include the final form of the equations from Einstein’s paper. Indeed some of the changes he made after December 6 were to update his argument from earlier versions of Einstein’s theory to the later version.

Certainly it was Einstein who felt himself to be the injured party in this short-lived priority dispute (arguably the only occasion in his life when Einstein found himself in such a dispute). He complained to a friend that Hilbert was trying to “nostrify” his theory, to claim a share of the credit. Einstein complained to Hilbert himself indeed, and some of the changes made in proofs by Hilbert included the addition of remarks giving credit for the basic ideas behind the theory to Einstein. At any rate, Einstein tried not to let proprietary feelings color his feelings of gratitude for Hilbert. He recalled well that Hilbert had played an important role in encouraging Einstein to return to his theory at a time when Einstein had, to some extent, given up on his original goals. On December 20, 1915, he wrote to Hilbert:

“There has been a certain resentment between us, the cause of which I do not want analyze any further. I have fought against the feeling of bitterness associated with it, and with complete success. I again think of you with undiminished kindness and I ask you to attempt the same with me. It is objectively a pity if two guys that have somewhat liberated themselves from this shabby world are not giving pleasure to each other.” (translated and quoted in Corry, Renn and Stachel, 1997).

So if Einstein was becoming the new Newton, as the man who solved the riddle of gravity, he was far from being a new Newton in another sense; of being the sort of man who carries on scientific grudges to the detriment of his friendship with the other great thinkers of his day.

Daniel Kennefick is associate professor of physics at the University of Arkansas, an editor of the Collected Papers of Albert Einstein, and the author of An Einstein Encyclopedia and Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves (Princeton).

For more on Einstein’s field equations, check out this article by Dennis Lehmkuhl at Caltech.

The Final Days of Albert Einstein

Albert Einstein’s time on earth ended on April 18, 1955, at the Princeton Hospital.

In April of 1955, shortly after Einstein’s death, a pathologist removed his brain without the permission of his family, and stored it in formaldehyde until around 2007, shortly before dying himself. In that time, the brain of the man who has been credited with the some of the most beautiful and imaginative ideas in all of science was photographed, fragmented —small sections parceled to various researchers. His eyes were given to his ophthalmologist.

These indignities in the name of science netted several so-called findings—that the inferior parietal lobe, the part said to be responsible for mathematical reasoning was wider, that the unique makeup of the Sulvian fissure could have allowed more neurons to make connections. And yet, there remains the sense that no differences can truly account for the cognitive abilities that made his genius so striking.

Along with an exhaustive amount of information on  the personal, scientific, and public spheres of Einstein’s life, An Einstein Encyclopedia includes this well-known if macabre “brain in a jar” story. But there is a quieter one that is far more revealing of the man himself: The story in which Helen Dukas, Einstein’s longtime secretary and companion, recounts his last days. Dukas, the encyclopedia notes, was “well known for being intelligent, modest, shy, and passionately loyal to Einstein.” Her account is at once unsensational and unadorned.

One might expect a story of encroaching death, however restrained, to chronicle confusion and fear. Medically supported death was a regular occurrence by the middle of the 20th century, and Einstein died in his local hospital. But what is immediately striking from the account is the simplicity and calmness with which Einstein met his own passing, which he regarded as a natural event. The telling of this chapter is matter of fact, from his collapse at home, to his diagnosis with a hemorrhage, to his reluctant trip to the hospital and refusal of a famous heart surgeon. Dukas writes that he endured the pain from an internal hemorrhage (“the worst pain one can have”) with a smile, occasionally taking morphine. On his final day, during a respite from pain, he read the paper and talked about politics and scientific matters.

“You’re really hysterical—I have to pass on sometime, and it doesn’t really matter when.” he tells Dukas, when she rises in the night to check on him.

As Mary Talbot  writes in Aeon, “Apprehending the truth that all things arise and pass away might be the ultimate groundwork for dying.” And certainly, it would be difficult to dispute Einstein’s wholehearted dedication to the truth throughout his life and work. His manifesto, referenced here by Hanoch Gutfreund on the occasion of the opening of the Hebrew University, asserts, “Science and investigation recognize as their aim the truth only.” From passionate debates on the nature of reality with Bohr, to his historic clash on the nature of time with Bergson, Einstein’s quest for the truth was a constant in his life.  It would seem that it was equally so at the time of his death. What, then, did he believe at the end? We can’t know, but An Einstein Encyclopedia opens with his own words,

Strange is our situation here upon earth. Each of us comes for a short visit, not knowing why, yet sometimes seeming to divine a purpose….To ponder interminably over the reason for one’s own existence or the meaning of life in general seems to me, from an objective point of view, to be sheer folly. And yet everyone holds certain ideals by which he guides his aspiration and his judgment. The ideals which have always shone before me and filled me with the joy of living are goodness, beauty, and truth. To make a goal of comfort or happiness has never appealed to me; a system of ethics built on this basis would be sufficient only for a herd of cattle.

Read a sample chapter of An Einstein Encyclopedia, by Alice Calaprice, Daniel Kennefick, & Robert Schulmann here.

Becoming an Einstein Author

By Alice Calaprice

Alice Calaprice is the editor of the hugely popular collection of Einstein quotations that has sold tens of thousands of copies worldwide and been translated into twenty-five languages. This is the story of how her knack for German and quest for full-time work in Princeton, New Jersey led her to a career she never imagined.

As a child I did not dream of someday becoming an author of books about Albert Einstein, nor did I contemplate the possibility even after graduating from UC Berkeley in the 1960s. Such an idea would not even have occurred to me. Along with my interest in science, languages, cultures, and history, it was eventually serendipity that took me there.

In the late 1970s, after my family had settled well into the routine of raising school-age children in Princeton, New Jersey, I assigned myself the task of finding full-time work. I had recently completed a course in the then relatively new field of computer technology, hoping it would help bolster a future career. One day in early 1978, a friend told me about a new venture being undertaken by Princeton University Press: the publication of the papers of Albert Einstein in a voluminous series that would span many years. An intriguing project, for sure, but I did not imagine myself being a part of it.

Calaprice at an Einstein statue in Washington DC (“worshipping at Einstein’s feet”).

Soon after, however, the founding editor of the project, physicist John Stachel, and I met after he had started some preliminary work on the papers. It interested him that I was a native German speaker, had spent time around computers, and wasn’t averse to physics jargon and working with physicists, being married to one at the time. He had been looking for someone for a specialized task: helping him prepare three electronic indexes of the contents of the Einstein archive. He explained that the archive contained about 10,000 documents, consisting of Einstein’s writings, correspondence, and third-party materials. The indexes would give him an overview of the archive’s size and contents–information crucial to the planning stages of the enormous undertaking.

Although the Collected Papers of Albert Einstein would be administered and published by the university press, the archive and his office were located at the nearby Institute for Advanced Study, in the same building where Einstein himself had worked during the last two decades of his life. Stachel asked if I was interested in helping to jump-start this initial phase of the project. The timing turned out to be perfect, and I agreed. I had no inkling that I was about to jump-start a lifelong career as well.

Hello, Einstein

This assignment, which required perusing and often carefully reading each document in the archive’s files, gave me the chance to familiarize myself with the details of Einstein’s legacy and life, with which I was not particularly familiar. It was also an opportunity to revive my long-neglected German-language aptitude, which had waned over the years. Einstein wrote almost exclusively in his native language, even after he came to America from Germany in 1933; his correspondence and papers were generally translated by his secretary or assistants. I was surprised by some of the particulars about his life. He was not so saintly, after all, and besides transforming scientific thinking he had also done ordinary things like play the violin and love animals.

My curiosity was piqued. I quickly became an autodidact, reading supplementary articles and books so I could put the archival material into context. Names of Einstein’s family, friends, and colleagues became familiar, as did the terms for concepts in physics used by him and his cohorts. The prewar and wartime venues and events in Germany became clearer, alive, and more personal. Berlin, the city of my wartime birth, took on new meaning: I discovered that the Einstein family had lived in the same neighborhood as my family, but, unlike them, we did not have to flee persecution. We did flee the city during the Allied bombings of 1945, long after the Einsteins had already departed for America. After short stints in various villages, we coincidentally ended up in Bad Cannstatt in southwestern Germany, which I later learned was also the ancestral home of Einstein’s mother. And, finally, both of us had found our way to Princeton, if at different times, by different routes, and for different reasons. After I had oriented myself to my new surroundings, I loved coming to work. I had found a stimulating job that suited me well. Not only was the timing of my employment in the archive ideal for me personally, but the times were exciting, too. The centennial of Einstein’s birth took place at the Institute—among other worldwide venues—in 1979. Some of Einstein’s assistants and collaborators were still alive and gave firsthand accounts of their recollections in a symposium on the campus. I was able to attend these talks.

Einstein’s Inner Circle

There and at other times, I met many people who had been associated with Einstein either directly or were now members of boards that were planning the eventual publication of his papers. Outstanding among these was Helen Dukas, Einstein’s longtime, modest, and intensely loyal secretary, who, after his death in 1955, had become the first archivist of his papers. Now in her early eighties, she still came to work almost daily. Her office was around the corner from mine on the third floor of Fuld Hall. She stopped by to chat every morning after exiting the elevator located across from my office, often inspecting the never-ending clutches of house finches nesting outside my window in spring and summer. She came to our house for dinner, and she invited my family to be her guests at the swimming pool in the Institute Woods.

At Helen’s crowded memorial service after her death in 1982, I heard her old friend Otto Nathan, the executor of Einstein’s estate, tearfully proclaim, “When Helen died, Einstein died a second time.” The Institute, a cosmopolitan place of world-renowned scholars, where foreign languages were heard more often than English, was a place where one could thrive professionally and personally.

We completed the indexes by the 1980 deadline. Because the 10,000 estimated documents had more than quadrupled to 42,000, we had hired a part-time assistant to help accomplish the task. I spent long hours working off-site in the evenings, when mainframe computers at the university’s Computer Center and, later, in my husband’s cyclotron laboratory in the physics department, were more readily available for use.

Herb Bailey, the well-regarded director of Princeton University Press who had long advocated for publication of the Collected Papers, was apparently pleased with my work. He now offered me a position in the editorial offices at the Press’s historic Scribner building on the university’s campus. My first day of work was on April Fool’s Day 1980, but I was assured my employment was not a joke. John Stachel continued his sole editorship of the papers at the Institute, and later at Scribner with a small staff. I was in touch with the group almost daily, grounding my interest in what came to be known as the Einstein Papers Project.

Fluent in Einstein

Five years later, after I had become a senior editor at PUP, I had the opportunity to again read the documents and letters that were about to be published in volume 1 of the Collected Papers. In 1985, the first manuscript in the series was turned over to the Press’s editorial office, and I was asked to take charge. I helped to set an editorial style for the series, copyedited the volumes as they arrived in-house, and became administrator and “principal investigator” of the concomitant National Science Foundation-funded English-translation project. Over a span of almost thirty years, I copyedited all fifteen of the volumes in the series—more recently as a freelancer—that have been published so far, including the translated volumes. Alas, so much reading, yet I never succeeded in understanding physics and relativity theory! Despite this shortfall, I became the liaison for nonscientific Einstein-related inquiries, book projects, film documentaries, and even the movie IQ in the early 1990s. I was a resource on matters dealing with Einstein, consistently learning something new in the process and having contact with an assortment of Einstein aficionados around the world. At the same time, I handled many other editing projects, mostly in the sciences. Surrounded by a group of wonderful, supportive, and good-humored colleagues and a continuously changing stream of engaging authors, I was having the time of my life. Those years set the stage for the twenty years ahead.

In 1995, I had an especially good year. First, it was the year I began mitigating my restlessness at home by taking annual trips to unlikely parts of the world, and I went to eastern Siberia with a small group of fellow nature lovers. Second, on my return, I received the news that I would receive the national Literary Market Place (LMP) Award for Individual Editorial Achievement in Scholarly Publishing, to be presented at the New York Public Library the following year. Third, Trevor Lipscombe, PUP’s acquisitions editor in physics at the time, discussed with me the prospect of publishing a book of quotations by Einstein. Like all those familiar with Einstein’s life, Trevor was aware that the physicist was multidimensional and fearless in expressing opinions on a variety of topics of interest to many: there was much more to him than relativity theory. Unbeknownst to Trevor, I had already collected many quotations while working on the indexes and copyediting the first few volumes of the Collected Papers—simply because they had struck a chord with me. When I showed him my blue box of index cards containing the quotations, he suggested I write the book myself rather than find someone else to do so. I was excited at the prospect of being on the other side of the author/editor relationship.

The Quotable Einstein is born

Soon after I returned from another adventure trip about a year later, this time into the Amazon Basin in northeastern Peru, the first edition of The Quotable Einstein was published. It contained four hundred quotations and their sources, arranged by topic, such as Einstein on religion, on his family, on Jews, on politics, on science and scientists, and so forth. The initial print run was modest, as there were doubts that the book would have wide appeal. The volume quickly sold out, however, and was reprinted six times. For a long time, it was at the top of PUP’s sales list, which I admired in disbelief and awe whenever one was posted on the bulletin board. Three more enlarged editions followed at approximately five-year intervals, and more than twenty-five foreign-language translations have been contracted, some in obscure languages I had never heard of. I believe these books were successful because they showed Einstein in all his guises, in his own uncensored words—a human being beyond the prevailing hagiographic and absent-minded-professor myths and falsely attributed quotations. The Ultimate Quotable Einstein, containing about 1,600 documented quotations and published in 2008, was my fourth and final contribution to this series of quotation books.

Because of the success of these volumes, I was now, to my surprise, perceived as an authority. I was asked to give talks for nonacademic audiences and participate in television shows and documentaries. I was invited to the German embassy to celebrate the special relativity centennial in 2005, and sat next to the German ambassador for lunch. I had book signings. I appeared on Ira Flatow’s “Science Friday” at the NPR studio in New York, along with Dennis Overbye of the New York Times. I have to confess that I found these new challenges difficult. I felt more comfortable doing research and writing, so I agreed to write three more books for other publishers who approached me.

Now, well into retirement in California, I am back with PUP for my swan song in the Einstein genre. Having often felt the need for a concise Einstein reference guide while doing research, I had submitted to the publisher an informal proposal to write An Einstein Encyclopedia. My expertise on specialized topics relating to Einstein is limited, so two Einstein scholars with broad experience on the Einstein Papers Project, historian Robert Schulmann and physicist Dan Kennefick, fortunately agreed to join me in this project as co-authors. Our final proposal was accepted, the three of us had a productive long-distance collaboration, and, best of all, we managed to stay friends throughout the process. As our reward, we are now the proud authors of a reference book that we expect will be of use and interest to an eclectic readership.

Alice Calaprice is a renowned authority on Albert Einstein and the author of several popular books on Einstein, including The Ultimate Quotable Einstein (Princeton).

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

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.

This 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 Princeton 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.

Working 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.

J. P. Ostriker

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

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

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

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

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

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

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

Train tracks image from Shutterstock, copyright: phildaint