Who did Einstein’s Mathematics?: A Response to Troemel-Ploetz
By Allen Esterson
In an article in Time magazine in July 2006 Walter Isaacson, president of the Aspen Institute and former chairman of CNN, stated that Einstein’s first wife Mileva Marić was a “Serbian physicist who had helped him with the math of his 1905 [special relativity] paper”
From the unequivocal way that this information was presented by Isaacson, readers would be forgiven for assuming that this is a straightforward factual statement. Yet this is far from the case. For a start, the mathematics in the 1905 relativity paper is quite elementary: as Jürgen Renn, an editor of the Albert Einstein Collected Papers, observes, “If he had needed help with that kind of mathematics, he would have ended there.” Then there is the fact the, contrary to myth, Einstein was highly proficient at mathematics.
Einstein’s precocious talent in mathematics has been recorded by Max Talmey, a medical student who knew the Einstein family when Albert was in his early teens. After Einstein had worked through Euclid by himself around the age of eleven, he tackled books on analytical geometry, algebra and calculus, and Talmey reports that soon “the flight of his mathematical genius was so high that I could no longer follow.” When he left the Luitpold Gymnasium in Munich at the age of fiifteen to join his parents who had emigrated to Italy, his mathematics teacher provided him with a letter stating that his mathematical knowledge was already at matriculation level. This letter was instrumental in his being given special dispensation to take the entrance examination for the prestigious Zurich Polytechnic the following year (1895) when he was still only sixteen, some two years below the normal age. Having spent a year without formal education, he failed this exam, but his grades in physics and mathematics were exceptional. Although he was a year younger than his classmates, at the end of a year spent at the high school in Aarau in Switzerland he came second in the school leaving examinations, obtaining maximum grades in algebra and descriptive geometry, and in his Matura (university entrance level) examinations he obtained the best grade of the nine candidates. Despite neglecting mathematics to follow his extra-curricular interests in physics, in the mathematical component of the final examination for the physics and mathematics teaching Diploma at the Zurich Polytechnic he achieved grade 5½ (on a scale 1-6).
Set against this is the fact that, although she obtained an excellent grade in mathematics at the Royal Classical High School in Zagreb in 1894 (her grades at the Swiss girls' high school from which she graduated in 1896 are unavailable), Marić later fared less well at this subject. In the mathematics entrance examination for Zurich Polytechnic she obtained an undistinguished average grade 4.25 (scale 1-6). Thereafter her yearly grades were moderately good (mostly physics topics), but she struggled with the geometry course taught by Wilhelm Fiedler, and obtained only grade 2½ (scale 1-6) in the mathematics component (theory of functions) of her final diploma examination. (None of the other four candidates obtained less than grade 5½) Her poor mathematics grades were the reason for her failing to be awarded a teaching diploma in 1900 and again in 1901.
The above information alone suffices to dispose of the notion that Einstein would have needed help with the rather elementary algebra and calculus he used in his 1905 special relativity paper, and further confirmation comes in the glowing report on his mathematical abilities in the “Expert Opinion” on his Ph.D. thesis submitted to Zurich University in 1905. The Professor of Physics Alfred Kleiner wrote: “The arguments and calculations to be carried out are among the most difficult ones in hydrodynamics, and only a person possessing perspicacity and training in the handling of mathematical and physical problems could dare to tackle them.” The mathematical difficulties were such that the opinion of Professor of Mathematics Heinrich Burkardt was sought, and he reported that he found Einstein’s calculations “correct without exception, and the manner of treatment demonstrates a thorough command of the mathematical methods involved” (emphasis in original).
So how did the notion that Mileva Marić assisted Einstein with the mathematics of the 1905 special relativity paper (and much more) become widely circulated? The most likely direct source of the claim is a paper published in 1990 by the linguist Senta Troemel-Ploetz with the title “Mileva Einstein-Marić: The Woman Who Did Einstein’s Mathematics”, and it seems that in our era of mass communications it is only necessary to make such claims in the public domain for them to become widely accepted regardless of the paucity of the evidence. And the evidence provided by Troemel-Ploetz is very feeble indeed, and, as we shall see, is almost entirely dependent on the highly unreliable claims of Marić’s Serbian biographer Desanka Trbuhović-Gjurić.
In the course of her article Troemel-Ploetz falsely describes Marić as “a mathematician”, and even inflates Marić’s abilities to that of a “mathematical genius”, (pp. 420, 421) while correspondingly depreciating Einstein’s. Nowhere does she cite the fact that Marić badly failed the mathematics component of the Zurich Polytechnic teaching diploma, though at the time her article was published this information was available in the first volume of the Einstein Collected Papers (which she actually cites elsewhere in her article in a different context [p. 417]). Nor is she able to cite a single documented example of Marić’s achievements in mathematics other than in the course of her education – her evidence lies elsewhere. But first let’s look at the evidence she provides for Einstein’s supposed relatively poor mathematical ability.
First part of the case made by Troemel-Ploetz
One part of the case made by Troemel-Ploetz consists of a purported demonstration that Einstein was a poor mathematician. For instance, she states (p. 420) that Einstein “needed at various points someone ‘to solve his mathematical problems’.” She continues, starting with a quote attributed to Einstein:
“I encountered mathematical difficulties which I cannot conquer. I beg for your help, as I am apparently going crazy” (Trbuhović-Gjurić, 1983, p. 96) he wrote to a friend Marcel Grossman, who then helped him.
Now Trbuhović-Gjurić was in error when she stated that this quotation comes from a letter Einstein wrote to Grossman (an old friend of Einstein’s from his student days who had become professor of mathematics at Zurich Polytechnic) – it comes from a report by Louis Kollros, another of Einstein’s old student friends, of something Einstein said to Grossman after they had met up again when Einstein returned to Zurich in late 1912 to take up a post at Zurich Polytechnic (now ETH). (I leave aside that the quotation is an embellished version. In common with many of the quotations in Trbuhović-Gjurić’s book, it is not specifically referenced, so it is impossible to know where she got it from, or how accurately she has reproduced it from that source.) More important, the claims of Troemel-Ploetz (following Trbuhović-Gjurić) that Einstein’s reported words reveal his general dependency on other people for solving mathematical problems only serves to illustrate her ignorance of Einstein’s actual achievements, and the reason he requested help from Grossman.
In 1912 Einstein had reached a stage in his attempts to develop a theory which incorporates accelerated systems into a general theory of relativity for which he required an esoteric branch of mathematics involving tensor calculus. His old friend Grossman was able to seek out for him what he needed, and to provide assistance in applying it to the work Einstein was doing. That this help was needed illustrates the difficult level of mathematics necessary for the purpose, not that Einstein was weak in mathematics. In fact in a letter supporting Einstein’s candidacy for a chair of mathematical physics at ETH (previously Zurich Polytechnic) the year before, Marie Curie had written that she believed that “mathematical physicists are at one in considering his work as being in the first rank” (Curie had met Einstein at the 1911 Solvay Conference, to which he had been invited most of the leading European physicists, including Nernst, Planck, Lorentz, Poincaré, Rutherford and de Broglie.)
Troemel-Ploetz opens her article with a reference to Trbuhović-Gjurić’s biography of Mileva Marić, and much of what follows is based on claims made in that volume. However, as I have noted elsewhere, most of Trbuhović-Gjurić’s contentions are based on third or fourth-hand reminiscences of friends and acquaintances of the Marić family and remaining family members, reported more than 50 years after the events in question, with all the unreliability and inaccuracies inherent to such recollections.
Having introduced Trbuhović-Gjurić’s book, Troemel-Ploetz immediately reports (p. 415) that “Einstein’s admission, ‘My wife does my mathematics,’ is general knowledge at the ETH in Zurich…”. The “admission” alluded to is a paraphrased version of words that Trbuhović-Gjurić claims were uttered by Einstein (of which more below), but what is interesting is that Troemel-Ploetz clearly implies that the “general knowledge” is recognized as a joke – “…although it serves only as a starter for jokes along the same lines”– and one can imagine Einstein self-deprecatingly making such a quip.
Later in the article (p. 418) Troemel-Ploetz gives what is presumably the original source of her paraphrased quotation: “He [Einstein] told a group of Serbian intellectuals in 1905: ‘I need my wife. She solves all the mathematical problems for me’ (Trbuhović-Gjurić, 1983, p. 106).” This is stated as if it were a documentable fact. Examining the source one finds that the words reported by Trbuhović-Gjurić supposedly were said by Einstein at a reunion of young intellectual friends of Miloš Marić, brother of Mileva, at some unspecified occasion on which Einstein was supposedly present. The report apparently comes from one Dr Ljubomir-Bata Dumić (of whom no information is supplied by Trbuhović-Gjurić), who is also quoted as having written:
We raised our eyes towards Mileva as to a divinity, such was her knowledge of mathematics and her genius… Straightforward mathematical problems she solved in her head, and those which would have taken specialists several weeks of work she completed in two days… We knew that she had made [Albert], that she was the creator of his glory. She solved for him all his mathematical problems, particularly those concerning the theory of relativity. Her brilliance as a mathematician amazed us.
I leave readers to decide on the reliability of such reminiscences from a proud fellow-Serb.
As supposed evidence for Einstein’s serious mathematical limitations, Troemel-Ploetz writes (p. 421) that “it is interesting to look at some self-evaluations of Albert Einstein before he had to play the role [sic] of genius of the century”, and she provides an extract from a passage that Trbuhović-Gjurić quotes from Einstein’s late “Autobiographical Sketch”:
...higher mathematics didn’t interest me in my years of studying. I wrongly assumed that this was such a wide area that one could easily waste one’s energy in a far-off province. Also, I thought in my innocence that it was sufficient for the physicist to have clearly understood the elementary mathematical concepts and to have them ready for application while the rest consisted of unfruitful subtleties for the physicist, an error which I noticed only later. My mathematical ability was apparently not sufficient to enable me to differentiate the central and fundamental concepts from those that were peripheral and unimportant. (Trbuhović-Gjurić, 1983, p. 47)
In her ignorance of the subject matter, Troemel-Ploetz fails to understand that by the standards necessary for most of physics at that time, Einstein’s knowledge of, and ability at, mathematics was extremely good. What he is doing here is explaining why, when he was a student at Zurich Polytechnic, he neglected to investigate more advanced pure mathematics. He expresses this perhaps more clearly in the “Autobiographical Notes” (1979 ) that he contributed to the volume Albert Einstein: Philosopher-Scientist (1949). After reporting that “At the age of twelve through sixteen I familiarized myself with the elements of mathematics together with the principles of differential and integral calculus”, he said of his time at Zurich Polytechnic:
There I had excellent teachers (for example, Hurwitz, Minkowski), so that I should have been able to obtain a mathematical training in depth…The fact that I neglected mathematics to a certain extent had its cause not merely in my stronger interest in the natural sciences than in mathematics but also in the following peculiar experience. I saw that mathematics was split up into numerous specialties, each of which could easily absorb the short lifetime granted to us. Consequently, I saw myself in the position of Buridan's ass, which was unable to decide upon any particular bundle of hay. Presumably this was because my intuition was not strong enough in the field of mathematics to differentiate clearly the fundamentally important, that which is really basic, from the rest of the more or less dispensable erudition. Also, my interest in the study of nature was no doubt stronger; and it was not clear to me as a young student that access to a more profound knowledge of the basic principles of physics depends on the most intricate mathematical methods. This dawned upon me only gradually after years of independent scientific work.
To put this more specifically, in the decade after graduating from the Polytechnic the mathematical knowledge he had acquired sufficed for his purposes. It was only then that he found he had need of more specialist fields of mathematics if he were to make progress with developing his general theory of relativity.
Misinterpreting the words of Einstein’s she has quoted as indicating that he regarded himself as weak in mathematical ability, Troemel-Ploetz goes on to assert that “others agreed with his evaluation”. She then quotes (translating from Trbuhović-Gjurić ) a Zurich Polytechnic professor, Jean Pernet, saying to Einstein: “Studying physics is very difficult. You don’t lack diligence and good will but simply knowledge. Why don’t you study medicine, law, or literature?” As is frequently the case, Trbuhović-Gjurić provides no reference for this quotation, and its source has to be hunted down to examine the context (and the accuracy) of the report. Evidently it comes originally from a commemorative article written by a former student at Zurich Polytechnic at the time Einstein studied there, Margarete von Uexküll. (According to the Einstein biographer Carl Seelig, Einstein told the story to Uexküll some thirty years after the event, and it was recalled some years later, so the accuracy of the quotation cannot be regarded as reliable.)
Missing from Trbuhović-Gjurić’s reporting of Pernet’s words is the fact that Einstein was out of sympathy with the teaching methods of the professor in question; he frequently skipped Pernet’s classes (among others) to follow up his own extra-curricular interests in physics, and received an official reprimand at the instigation of Pernet. Evidently Einstein’s independent attitude provoked Pernet into making the disparaging comments to him, so obviously at variance with Einstein’s later achievements.
Troemel-Ploetz (p. 421) now recounts that a former student of Einstein’s recalled an occasion when he “got stuck in the middle of a lecture missing a ‘silly mathematical transformation’ which he couldn’t figure out.” He told the class to leave a space and just gave them the final result. “Ten minutes later he discovered a small piece of paper and put the transformation on the blackboard, remarking, ‘The main thing is the result not the mathematics, for with mathematics you can prove anything’. (Trbuhović-Gjurić, 1983, p. 88).”
Though Trbuhović-Gjurić provided no reference for this report to enable its accuracy to be checked, she cites Dr Hans Tanner as the source. Fortunately a lengthy quotation from Tanner’s recollections of Einstein is provided by Seelig in his biography of Einstein.
The first thing to note is that there is no mention of Einstein’s discovering “a small piece of paper” in Tanner’s account of the incident in question (the only one of its kind he could recall). On the contrary, he says: “Some ten minutes later Einstein interrupted himself in the middle of an elucidation. ‘I’ve got it.’…During the complicated development of his theme he had still found time to reflect upon the nature of that particular mathematical transformation. That was typical of Einstein.” So whence comes the piece of paper? A couple of paragraphs earlier Tanner had reported that in the lectures given by the newly appointed Einstein as professor of theoretical physics at Zurich University in 1909, “The only script he carried was a strip of paper the size of a visiting card on which he had scribbled what he wanted to tell us. Thus he had to develop everything himself and we obtained some insight into his working technique.” It is evident that Trbuhović-Gjurić garbled the account, so that she erroneously has the piece of paper playing a role in the classroom incident she recounts.
The next thing of note is that the words “The main thing is the result… with mathematics you can prove anything” was not reported by Tanner in the context of the incident Trbuhović-Gjurić recounts, but in a completely different social setting, when Einstein had invited some of his students to return with him to his apartment to examine some work he had received from Planck in which he had perceived there had to be a mistake. Tanner was one of two students who accepted the invitation, and who told Einstein that they could find no error and that he must be mistaken. Einstein responded by pointing out why, on the grounds of “a simple dimensional datum”, there must be an error somewhere. When Tanner suggested writing to Planck to inform him of the mistake, Einstein reportedly said: “…we won’t write and tell him that he’s made a mistake. The result is correct, but the proof is faulty. We’ll simply write and tell him how the real proof should run.” It is at this point he is reported as having said: “The main thing is the content, not the mathematics. With mathematics one can prove anything.”
This puts a very different complexion on Einstein’s latter remark than that which Troemel-Ploetz presents. Equally important, here we have an instance where we are able to check Trbuhović-Gjurić’s report, uncritically recycled by Troemel-Ploetz, and find that it misrepresents the context of Einstein’s remark about mathematics. (This leaves aside that we cannot be sure of the accuracy of the reported words, recalled many years after the event.) Troemel-Ploetz, however, having misinterpreted the quotation in question as a further indication of Einstein’s supposed deficiencies in mathematics, follows it with the evidence-free assertion that he “did not have to worry about the [mathematical] proofs because Mileva Einstein-Marić was doing them.”
Summing up this passage in Troemel-Ploetz’s article, she is recycling an unreferenced report by Trbuhović-Gjurić which is both inaccurate and also misrepresents the context of the quoted remark attributed to Einstein. As a result she completely fails to understand the rationale of the remark from a scientific point of view. This is a further illustration of how unreliable are the numerous unverifiable quotations Trbuhović-Gjurić sprinkles throughout her book – she cannot even be relied upon to recount accurately the reports she is reproducing for her readers (frequently themselves from an unreliable third-hand source). Yet Troemel-Ploetz relies heavily on Trbuhović-Gjurić for the great bulk of the evidence that she provides to support her central thesis.
More direct evidence (allegedly)
Continuing our examination of Troemel-Ploetz’s case, she writes (pp. 419-420) that a biographer of Einstein, Peter Michelmore, who “had much information from Albert Einstein”, said: “Mileva helped him solve certain mathematical problems. She was with him in Bern and helped him when he was having such a hard time with the theory of relativity.”
Consulting the citation Troemel-Ploetz provides (in Trbuhović-Gjurić’s book), one finds that only the first sentence of the words attributed to Michelmore are given: the rest is added by Troemel-Ploetz herself. The first quoted sentence certainly can be found in Michelmore’s book (though, characteristically, no page reference is given by Trbuhović-Gjurić). It occurs in the middle of a somewhat imaginative account of the period encompassing Einstein’s production of the celebrated papers of 1905. According to Michelmore, after the publication of the paper on the photoelectric effect Einstein wrestled with the problem of relativity: “Frustration drove him to wander the farm lands around Berne. He took time off from the office. Mileva helped him solve certain mathematical problems, but nobody could assist with the creative work, the flow of fresh ideas.”
Michelmore provides no evidence for his claim that Marić helped Einstein solve mathematical problems, nor does he give the least indication what these might be. (Recall that nothing in the mathematics that he required for his work at that time would have taxed Einstein’s knowledge and abilities.) Earlier Michelmore had made assertions relevant to this issue that are manifestly false. He writes, referring to Marcel Grossman, who was in Einstein’s group at Zurich Polytechnic, but majored in mathematics: “Generously, Grossman took detailed notes on all lectures and drummed them into Einstein at the week-ends… His [Einstein’s] other close friend was Mileva Maric… She was as good at mathematics as Marcel and she, too, helped in the week-end coaching sessions.”
Most of this is imaginative fiction. The only time Einstein made use of Grossman in this way was immediately prior to his diploma examinations, when he borrowed his meticulous notes for self-study. This puts the notion that Marić assisted in these supposedly regular weekend sessions well into the realms of fiction. (If anything, the indications are that it was Einstein who assisted Marić in her studies: In a letter in December 1901 Einstein wrote to her: “Soon you’ll be my ‘student’ again, like in Zurich.”) Even more fantastical is the assertion that Marić was as good at mathematics as Grossman. This is negated by a comparison of their respective grades at both intermediate and final diploma examinations: Marić received lower grades than Grossman in every single mathematics topic that they both took for these exams. Moreover, whereas Marić failed her diploma exam, almost certainly because of her poor mathematics grade, Grossman went on to become a professor of mathematics at Zurich Polytechnic at the early age of 29. He also, of course, assisted Einstein in the application of highly abstruse mathematics to general relativity theory.
Clearly Michelmore’s book, with its numerous imaginative scenarios, is not a reliable source of information about any supposed contribution Marić made to Einstein’s mathematical work. Note also that the assertion by Troemel-Ploetz that he “had much information from Albert Einstein” is erroneous. The book was published some seven years after Einstein’s death, and in his “Author’s Note” Michelmore makes no mention of ever having met Einstein. He did spend two days interviewing Einstein’s elder son, but acknowledges that neither his notes, nor the book manuscript, were checked for accuracy by Hans Albert Einstein. In any case, Hans Albert was an infant at the time Einstein wrote his 1905 papers, and could not have passed on any first-hand knowledge of relevant events.
As we have seen from the above material, Michelmore’s account is too unreliable to take from it any definitive statement about alleged contributions by Marić to Einstein’s mathematical work. One may add that Michelmore’s propensity to invent scenes and dialogue disqualifies his book (which lacks references and a bibliography) as a serious work of biography. For instance, he has Einstein saying, at the end of the evening when Einstein had a crucial discussion with his friend Michele Besso prior to his breakthrough to the special theory of relativity: “I’ve decided to give it up – the whole theory.” This is at totally at variance with Einstein’s own account, in which he reports how Besso’s perspicacious contributions led, that evening, to his coming to understand where the key to the problem lay.
Troemel-Ploetz next cites (p. 420) the great mathematician Hermann Minkowski, one of Einstein’s professors at Zurich Polytechnic, who, she writes, “knew him well and was his friend”, and who is reported as having remarked to Max Born in relation Einstein’s producing the theory of [special] relativity: “This was a big surprise to me because Einstein was quite a lazybones and wasn’t at all interested in mathematics” (Trbuhović-Gjurić, 1983, p. 47 [1991, p. 104]).
In her book Trbuhović-Gjurić cites Carl Seelig for this quotation, and in fact it can be found in Seelig’s biography. (The English language edition has a slightly different translation of Minkowski’s words.) Leaving aside the erroneous assertion that Minkowski knew Einstein well as a friend (he was at Göttingen University in Germany from 1902 until his death in 1909, and they scarcely met or corresponded), his reportedly saying of Einstein that “he never bothered about mathematics at all” is consistent with what we know – that Einstein neglected mathematical studies at Zurich Polytechnic, preferring to spend his time on his own extracurricular interests in physics. It bears not at all on the issue of Einstein’s ability to make use of mathematics when he needed it.
This is followed by a statement (p. 420) that “Bodanović, a mathematician in the Ministry of Education in Belgrade who was well acquainted with Mileva Einstein-Marić, is reported to have said that she had always known that Mileva Einstein-Marić had helped her husband a great deal, especially with the mathematical foundation of his theory, but Mileva Einstein-Marić had always avoided talking about it (Trbuhović-Gjurić, 1983, p. 164).”
One wonders what value one should put on something that someone is reported to have said by another party about information she was not privy to, and which the person concerned had not spoken about! Consulting Trbuhović-Gjurić’s book we find that she actually claims that Milica Bodanović recalled that it was Malvina Gogić, a mathematics inspector at the Ministry of Education at Belgrade, who was the one who reportedly had said that Marić helped with the mathematical foundation of “his theory” [what theory? Trbuhović-Gjurić’s report is without scientific context], but that Marić refused to talk about it. But much more important than this minor error is the fact that Troemel-Ploetz should deem it worth recycling a report of such vagueness and doubtful reliability as if it were of genuine evidential value. (Alberto Martinez places such reports at the very bottom of a twenty point scale of historical reliability in his article on “Handling evidence in history”.)
Troemel-Ploetz now reports (p. 419), referencing Trbuhović-Gjurić: “Abram F. Joffe, the famous Russian physicist who was then an assistant to Röntgen (a member of the editorial team that examined the articles sent to Annalen der Physik for publication) wrote in his Erinnerungen an Albert Einstein (Joffe, 1960) that the original manuscripts [of Einstein’s three celebrated 1905 papers] were signed Einstein-Marić.” However, an examination of what Joffe actually wrote shows that he did not say that the original manuscripts were signed Einstein-Marić. In this passage Troemel-Ploetz is (characteristically) recycling Trbuhović-Gjurić’s assertions as if they were indubitable historical facts, without caveat. In her customary unscholarly fashion, in the paragraph in question Trbuhović-Gjurić fails to quote Joffe’s actual words, but provides a much truncated (and inaccurate) paraphrase in such a way that readers would have no way of knowing that Joffe identified the single author of the papers as “a bureaucrat at the Patent Office in Bern”, in other words, Albert Einstein. Furthermore, the reader would not be able to discern from Trbuhović-Gjurić’s presentation that the information about Röntgen’s supposedly having seen the original manuscripts does not come from Joffe, but is nothing but an evidence-free surmise on the part of the author that receives no support from relevant writings by Joffe.
Note: In his book “Meetings with Scientists” Joffe writes that when he was assistant to Röntgen the latter advised him, in preparation for defending his Ph.D. thesis in 1905 (prior to the publication of Einstein’s relativity paper), to study what we would now call the prehistory of Special Relativity theory. Had Röntgen refereed Einstein’s original manuscript a short time later, as Trbuhović-Gjurić asserts, Joffe could hardly have failed to have stated so. But he makes no mention of any such occurrence, and we may conclude that the whole basis of Trbuhović-Gjurić’s claims about Joffe is without foundation. (A. F. Joffe, Begegnungen Mit Physikern, 1967, pp. 23-24).
A little earlier (p. 418), on the unwarranted presumption that Marić had co-authored the 1905 papers, Troemel-Ploetz posed the question: “Why did [Einstein] not immediately insist on a correction when Mileva Einstein-Marić’s name was dropped as an author of the articles that appeared in the Leipzig Annalen der Physik?” In addition to the points made above, Stachel notes that the three papers in question contain many authorial comments in the first person singular. This means, were one to accept Troemel-Ploetz’s underlying assumption here, that the editor of Annalen der Physik Paul Drude, and his advisor on theoretical physics Max Planck, would have not merely duplicitously omitted a co-author’s name, they would have had to have effected appropriate changes of first person plural pronouns to first person singular throughout the articles. It is also worth observing that physics papers co-authored by spouses would not have set a precedent; Marie and Pierre Curie had published such papers, and together had been awarded a share in the 1903 Nobel Prize for physics.
For a comprehensive refutation of all the claims made by Trbuhović-Gjurić and others in relation to Joffe, readers should consult Stachel’s editorial Introduction to the 2005 edition of Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics, pp. liv-lxxii. See: http://www.esterson.org/Stachel_Joffe.htm
A full critique of the whole of Troemel-Ploetz’s article would take many more words, and be on much the same lines as the above. (Some additional items have been examined in my article “Mileva Marić: Einstein’s Wife”: http://www.esterson.org/milevamaric.htm.) But it is worth looking at just one more passage (p. 420), in which Troemel-Ploetz translates the words of Trbuhović-Gjurić (1983) commenting on the 1905 special relativity paper:
It’s so pure, so unbelievably simple and elegant in its mathematical formulation – of all the revolutionary progress physics has made in this century, this work is the greatest achievement.
Even today when reading these yellowing pages printed almost 80 years ago, one feels respect and cannot but be proud that our great Serbian Mileva Einstein-Marić participated in the discovery and edited them. Her intellect lives in those lines. In their simplicity, the equations show almost beyond a doubt the personal style she always demonstrated in mathematics and in life in general. Her manner was always devoid of unnecessary complications and pathos.
As Fölsing points out, there is not a single known document containing any mathematical work by Marić for us to compare with the paper in question, so Trbuhović-Gjurić’s statement that the equations show almost beyond a doubt Marić’s personal style inhabits the realms of fantasy. That Troemel-Ploetz recycles it uncritically is one more illustration of the unscholarly nature of her article. Most egregiously, she repeatedly reproduces Trbuhović-Gjurić’s reports without any attempt to check sources to judge their accuracy or reliability, and fails to raise even the faintest question mark about the reliability of Trbuhović-Gjurić’s numerous unverifiable third-hand reports obtained many decades after the events in question and provided by far from disinterested sources. One can only arrive at the conclusion that her deeply flawed article does not remotely bear out her claims about Marić’s alleged contribution to Einstein’s mathematical work.
For further discussion of the issues raised in Troemel-Ploetz’s article, including a few not touched upon above, readers should consult the comprehensive articles in John Stachel’s book Einstein from ‘B’ to ‘Z’ , pp. 26-38, 39-55.
There is a passage above that needs qualifying in the light of further information that I have come across in Walter Isaacson’s book Einstein: His Life and Universe. In that passage I cast doubt on Michelmore’s statement that at the end of the exchanges Einstein was having with Besso, on the evening before his breakthrough leading to the special theory of relativity, he stated, “I’ve decided to give it up – the whole theory”. Now Isaacson also reports (p. 122) that Einstein said to Besso, “I’m going to give it up.” However, he has Einstein saying this in the middle of a discussion while the two friends were walking to work at the patent office. Furthermore, according to Isaacson’s version, it was while they were still discussing it that Einstein said, “I suddenly understood the key to the problem.” Then the next day Einstein told Besso in a state of great excitement: “Thank you. I've completely solved the problem.”
For this report Isaacson references Albert Einstein: A Biographical Portrait, written by Einstein’s son-in-law (under the pseudonym Anton Reiser), and a talk given by Einstein in Kyoto in 1922 on the creation of special relativity.
Now the transcript of the Kyoto lecture actually consists of notes of Einstein’s unscripted talk made by a theoretical physicist, Jun Ishiwara, later translated into Japanese. The notes were translated into English and published in Physics Today in 1982. The relevant passage reads:
By chance a friend of mine in Bern helped me out. It was a beautiful day when I visited him with this problem. I started the conversation with him in the following way: “Recently I have been working on a difficult problem. Today I come here to battle against that problem with you.” We discussed every aspect of this problem. Then suddenly I understood where the key to this problem lay. Next day I came back to him again and said to him, without even saying hello, “Thank you. I've completely solved the problem.” An analysis of the concept of time was my solution. Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity. With this new concept, I could resolve all the difficulties completely for the first time.
It is evident that, at least according to Ishiwara’s notes, Einstein did not in his Kyoto talk quote himself saying “I’m going to give it up” in relation to his struggle to arrive at a satisfactory theory of relativity in 1905. Presumably the citing of the talk by Isaacson relates only to the discussion with Besso and Einstein’s saying the next day that he had solved the problem. So we are left with Reiser’s account, which, in addition to the “give it up” quotation, differs in regard to the circumstances in which the conversation with Besso occurred. (Einstein’s reported account has him visiting Besso, and understanding where the key to the problem lay, in the course of the discussion, whereas Reiser’s has him saying he is going to give up on the problem as he leaves Besso at his [Einstein’s] apartment house door.)
Now Reiser published his Biographical Portrait in 1930 with the approval of Einstein. However it is far from a closely documented biography, and seems to be the only source of the quotation “I’m going to give it up”. (Michelmore’s account so closely follows Reiser’s that it is evident that that was his source.) My own view, for what it’s worth, is that in the light of the seven years (on and off) that Einstein had spent struggling with the problem of relative motion, and his recognition of the fundamental importance of arriving at a solution, it is unlikely in the extreme that he would have seriously contemplated giving up on it in 1905. It seems most likely that in his rather sketchy biography Reiser over-dramatized Einstein’s account of the episode and provided his own imaginative version of what happened.
Allen Esterson’s homepage: http://www.esterson.org/
NOTES (Citations refer to books and articles listed in the Bibliography.)
2. Quoted in Highfield, R. and Carter, P. (1993), pp. 114-115.
3. Talmey, M. (1932), pp. 162-164.
4. Reiser, A. (1930), pp. 42-43; Frank (1948), p. 27.
5. Collected Papers, Vol.1, doc. 7.
6. Fölsing, A. (1997), p. 37.
7. Collected Papers, Vol.1, doc.19; Fölsing (1997), p. 45; Isaacson (2007), pp. 30-31.
8. Collected Papers, Vol.1, doc. 67.
9. Trbuhović-Gjurić, D. (1988), p. 60.
10. Trbuhović-Gjurić, D. (1983), p. 43; Trbuhović-Gjurić, D. (1991), pp. 49-50.
11. Renn, J. & Schulmann, R. (1992), p. 12.
12. Collected Papers, Vol.1, doc. 67.
13. Stachel, J. (2002), p. 29.
14. Collected Papers, Vol. 5, doc. 31.
15. Troemel-Ploetz, S. (1990). Women’s Studies Int. Forum, 13(5), pp. 415-432.
16. Trbuhović-Gjurić, D. (1983). Im Schatten Albert Einsteins: Das tragische Leben der Mileva Einstein-Marić. Bern: Paul Haupt [German translation of the original book by D. Trbuhović-Gjurić, published in Yugoslavia in 1969]; Trbuhović-Gjurić, D. (1991). Mileva Einstein: Une Vie (trans. from the German). Paris: Antoinette Fouque.
17. Pais, A. (1983), pp. 212, 226n; Fölsing, A. (1997), pp. 314; 778, n.45.
18. Clark, R. W. (1971), p.191.
19. Esterson, A. (2006). Mileva Marić: Einstein’s Wife
20. Trbuhović-Gjurić, D. (1983), p. 93; (1991), p. 106 [my translation – A. E.].
21. Einstein, A. (1956 ). “Autobiographische Skizze.” In C. Seelig (ed.), Helle Zeit – Dunkle Zeit: In memoriam Albert Einstein, Zurich, 1956.
22. Einstein, A. (1979 ), p. 15.
23. Clark, R. 1971, pp. 61, 788n.
24. Seelig, C. (1956), pp. 40-41.
25. Fölsing, 1997, p. 57.
26. Seelig, C. (1956), pp. 100-106.
27. Trbuhović-Gjurić, 1983, p. 72 [1991, p. 103].
28. Michelmore, P. (1963), p. 41.
29. Michelmore, P. (1963), p. 31
30. Fölsing, A. (1997), pp. 53, 748 n.22; Einstein, A. (1979), p. 17.
31. Renn, J. & Schulmann, R. (1992), p. 71.
32. Collected Papers, Vol. 5, docs. 42, 67; Trbuhović-Gjurić, D. (1991), p. 70.
33. Michelmore, P. (1963), p. ix.
34. Michelmore, P. (1963), p. 41.
35. Fölsing, A. (1997), pp. 155, 176, 177.
36. Seeling, C. (1956), p. 28.
37. Trbuhović-Gjurić, D. (1983), p. 164; (1991), p. 215.
38. Martínez (2005) , p. 54.
39. Trbuhović-Gjurić, D. (1983), p. 79; (1991), p. 111.
41. Trbuhović-Gjurić, D. (1983), p. 71; (1991), p. 109.
42. Fölsing, A. (1990).
43. Michelmore, P. (1963), p. 41.
44. Rynasiewicz, R. (2000), p. 162.
45. Reiser, A. (1930), p. 68.
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Einstein, A. (1956 ). “Autobiographische Skizze.” In C. Seelig (ed.), Helle Zeit – Dunkle Zeit: In memoriam Albert Einstein, Zurich: Europa Verlag, 1956.
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Esterson, A. (2006). Critique of Evan Harris Walker’s Letter in Physics Today, February 1991.
Frank, P. (1948). Einstein: His Life and Times. London: Jonathan Cape.
Fölsing, A. (1990). Keine 'Mutter der Relativitätstheorie', Die Zeit, Nr. 47, 16 November 1990. (English translation here.)
Fölsing, A. (1997). Albert Einstein. (Trans. by E. Osers.) New York: Penguin Books.
Highfield, R. and Carter, P. (1993). The Private Lives of Albert Einstein. London: Faber and Faber.
Isaacson, W. (2007). Einstein: His Life and Universe. New York: Simon & Schuster.
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& Albert Einstein: Their Love and Scientific Collaboration. Kranjska, Slovenia: Didakta.
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Michelmore, P. (1963). Einstein: Profile of the Man. London: Frederick Muller.
Pais, A. (1994). Einstein Lived Here. Oxford University Press.
Renn, J. and Schulmann, R. (eds.) (1992). Albert Einstein and Mileva Maric: The Love Letters. Trans. by S. Smith. Princeton University Press.
Reiser, A. (1930). Albert Einstein: A Bibliographical Portrait. New York: Boni.
Rynasiewicz, R. (2000). "The Construction of Special Relativity." In D. Howard & J. Stachel (eds.), Einstein: The Formative Years 1879-1909. Boston/Basel/Berlin: Birkhäuser, pp. 159-201.
Seelig, C. (1956). Albert Einstein: A Documentary Biography. London: Staples Press.
Stachel, J. (1996). Albert Einstein and Mileva Marić: A Collaboration that Failed to Develop. In H. M. Pycior, N. G. Slack, and P. G. Abir-Am (eds.), Creative Couples in the Sciences, Rutgers University Press. Reprinted in Stachel, J. (2002). Einstein from ‘B’ to ‘Z’, Boston/Basel/Berlin: Birkhauser, pp. 39–55.
Stachel, J. (2002). Einstein from ‘B’ to ‘Z’. Boston/Basel/ Berlin: Birkhäuser.
Stachel, J. (ed.) (2005). Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics. Princeton University Press.
Talmey, M. (1932). “The
Relativity Theory Simplified And the Formative Period of its Inventor.” New York: Falcon Press.
Trbuhović-Gjurić, D. (1983) . Im Schatten Albert Einsteins: Das tragische Leben der Mileva Einstein-Marić. Bern: Paul Haupt. (The German language edition is an edited version of the book by Trbuhović-Gjurić originally published in Serbo-Croat in Yugoslavia in 1969.)
Trbuhović-Gjurić, D. (1991), Mileva Einstein: Une Vie (French translation of Im Schatten Albert Einsteins: Das tragische Leben der Mileva Einstein-Marić). Paris: Antoinette Fouque.
Troemel-Ploetz, S. (1990). Mileva Einstein-Marić: The Woman Who Did Einstein’s Mathematics. Women’s Studies International Forum, Vol. 13, No. 5, pp. 415-432.