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”[1]
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.”[2] 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
Set against this is the fact that, although she graduated
from her Swiss high school with excellent grades in mathematics, Marić later fared less well
at this subject. In the mathematics entrance examination for Zurich Polytechnic
she obtained a mediocre average grade 4.25 (on a scale 1-6).[9] Thereafter her yearly grades were moderately good,[10]
but she struggled with the geometry course taught by Wilhelm Fiedler,[11] and
obtained only grade 5 (on a scale 1-12) in the mathematics component (theory of
functions) of her final diploma examination. (None of the other four candidates
obtained less than grade 11.)[12] Almost certainly her poor mathematics grades were the reason for her
failing to be awarded a diploma in 1900 and again in 1901.[13]
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
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”,[15] 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.[16]
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).[17] (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”[18] (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,[19] 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
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.[20]
I leave readers to decide on the reliability of such
reminiscences from a proud fellow-Serb. (With respect to the relatively
elementary mathematics in Einstein’s 1905 relativity paper, as Jürgen Renn has
remarked, “If he had needed help with that kind of mathematics, he would have
ended there.”)
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”[21]:
...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
[1949]) 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.[22]
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
[1983]) 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 Üxküll.[23] (According to the Einstein biographer
Carl Seelig, Einstein told the story to Üxküll some thirty years after the
event,[24] 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 on the instigation of Pernet.[25] 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.[26]
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
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
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.”[29]
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.[30] 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
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.[33] 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.”[34] 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.[35]
Troemel-Ploetz next cites (p. 420) the great mathematician Hermann Minkowsky, 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 Minkowsky’s
words.)[36] Leaving aside the erroneous assertion that Minkowsky 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.[37] 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”.[38])
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.”[39] 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.[40]
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:[41]
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,[42] 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.
November 2006
Addendum
April 2007
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”.[43] 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
Now the
transcript of the
By chance a friend of mine in
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.[45])
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 [
6. Fölsing, A.
(1997), p. 37.
7. Collected Papers Vol. 1 [
8. Collected Papers Vol. 1 [
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 [
13. Stachel, J.
(2002), p. 29.
14. Collected Papers, Vol. 5 [
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.
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
[1954]). “Autobiographische Skizze.” In
C. Seelig (ed.), Helle Zeit – Dunkle
Zeit: In memoriam Albert Einstein,
22. Einstein, A. (1979 [1949]), p. 15.
23.
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. 1 [
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.
39. Trbuhović-Gjurić, D. (1983), p. 79;
(1991), p. 111.
40. Martinez
(2005), pp. 51-52; Stachel, J. (2005), pp. liv-lxxii.
41. Trbuhović-Gjurić, D. (1983), p. 71;
(1991), p. 109.
42. Fölsing, A.
(1990). Keine
‘Mutter der Relativitätstheorie’. Die Zeit, Nr. 47, 16
November 1990.
43. Michelmore, P.
(1963), p. 41.
44. Rynasiewicz, R.
(2000), p. 162.
45. Reiser, A.
(1930), p. 68.
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