From Notices of the American Mathematical Society, August 2005:

Letter to the Editor

By Seth Braver

History of Mathematics from a
Mathematician’s Vantage Point

The AMS, one of the most important mathematical organizations in the
world, has recently put its imprimatur on a shoddily written and ineptly
plagiarized version of Morris Kline’s Mathematical Thought from Ancient
to Modern Times. This ostensibly new book is entitled History of Mathematics
from a Mathematician’s Vantage Point. Nicholaos K. Artemiadis claims to be the author.
I will provide one specific example of plagiarism for the sake of those
fortunate enough not to have wasted fifty dollars on this book. Consider the
striking thesis that Artemiadis propounds at the conclusion of his chapter
on the history of abstract algebra (pages 377–8):

“We can say that abstract algebra in a sense ‘undermined’ its own role
in mathematics. The various notions and principles were introduced in it,
in order to unify the apparently different situations. This was achieved
by group theory. But after the formulation of the abstract theories,
mathematicians gradually distanced themselves from the concrete structures
and concentrated their research on these abstract structures. Hence,
with the introduction of hundreds of particular notions, the object of study
was divided into other more specific activities, which were more or less independent
from one another and were not related to the concrete areas that
were considered initially. In other words, the unification mentioned
above was followed by diversification and specialization. Hence we have
reached the point where many who work in the area of abstract algebra
ignore the tools of the abstract structures that they study and furthermore
they are not interested whether the results have any applications in
concrete areas.”

Indeed, the thesis is a bit too striking; rather like a playwright whose
character muses, “Shall I live, or shall I not live? That is the problem.” The
original passage occurs on page 1157 of Kline:

“However, abstract algebra has subverted its own role in mathematics. Its
concepts were formulated to unify various seemingly diverse and dissimilar
mathematical domains as, for example, group theory did. Having
formulated the abstract theories, mathematicians turned away from the
original concrete fields and concentrated on the abstract structures.
Through the introduction of hundreds of subordinate concepts, the subject
has mushroomed into a welter of smaller developments that have little
relation to each other or to the original concrete fields. The unification
has been succeeded by diversification and specialization. Indeed, most workers
in the domain of abstract algebra are no longer aware of the origins of
the abstract structures, nor are they concerned with the application of
their results to the concrete fields.”

These two paragraphs are isomorphic.

Artemiadis has not merely summarized Kline’s thought without
citation, he has copied it line by line. Differences in word choice are merely
the inevitable product of translating Kline into Greek and then translating
the translation back into English. In a single hour I located a dozen
or so such “borrowings” before putting Artemiadis’s book away in
disgust. Sentences, paragraphs, even whole pages of “his” text are stolen
from Kline. Readers with access to both works who are skeptical of my
claims may wish to compare, for example, Artemiadis’s chapter on
topology (pp. 345–56) with Kline’s chapter entitled “The Beginnings of
Topology” (beginning on page 1158). Such a comparison reveals that
Artemiadis stole almost every sentence in his chapter. Or compare
Artemiadis’s take on Omar Khayyam and Arabic mathematics (page 163,
beginning with the second paragraph, “Even though the solutions…”) to
Kline’s treatment of the same topics (page 193, beginning with the third
paragraph, “Though the Arabs gave algebraic solutions…”). The next page
or so of the two texts will be found to be nearly identical, right down to the
diagrams and the labels thereupon. On page 143 of Artemiadis’s book he
writes, “We present some of the problems considered by Diophantus.” As
one might expect, that plural pronoun “we” is not mere scholarly convention.
Rather, the Diophantine problems selected by Artemiadis are
exactly the same as those selected by Kline for page 142 of his book.
One can also find bits of Carl Boyer’s history in Artemiadis’s text as well,
the most obvious example being the idiosyncratic chronological table
which appears in an appendix. I could cite further examples, but
in classic mathematical tradition, I will leave this as an easy exercise for
the interested reader.

Since the AMS is one of the largest and most visible organizations of
mathematicians in the United States, the books it publishes ought to be
distinguished by high standards of writing and editing. It is hard for me
to believe that Artemiadis’s book was edited for style or content at all.
Understandably, an editor may not have time to scrutinize each and every page
of a manuscript that ends up on his desk, but surely it isn’t too much to
ask that he will at least examine the first page of chapter one. This page,
in Artemiadis’s book, contains the following paragraph:

“‘Moscow’s Papyrus’ dates back to 1850 B.C. The most interesting result
included in this papyrus is the calculation of the volume V of a truncated
square pyramid. If b = 0, then this formula gives the volume of the
square pyramid.”

In this passage, a completely superfluous
symbol (V), never subsequently referred to, is introduced,
while a mysterious quantity (b), never previously defined, plays a vital but
necessarily incomprehensible role. Did the editors decide that these
compensating errors somehow nullified one another and could therefore
remain in the book? Had the editors paid enough attention to notice such
shoddy writing, they might have noticed the rampant plagiarism as well.
Artemiadis should bear the heaviest share of the guilt in this case, but the
editors have a lot to answer for as well.

—Seth Braver
University of Montana
(Received March 22, 2005)

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From Amazon.com:

Plagiarism, March 24, 2005
Reviewer: "Reb Hastrev"

Consider a brief and somewhat controversial passage from Morris Kline's "Mathematical Thought from Ancient to Modern Times" (occuring on pg. 23):

"[T]he Egyptians and Babylonians were crude carpenters, whereas the Greeks were magnificent architects. One does find more favorable, even laudatory, descriptions of the Babylonian and Egyptian achievements. But these are made by specialists who become, perhaps unconsciously, overimpressed by their own field of interest."

Compare this with a passage appearing on page 149 of the new AMS publication, "History of Mathematics from a Mathematician's Vantage Point", written (according to the book's cover) by Nicolaos Artemiadis.

"[T]he Egyptians and the Babylonians were "clumsy carpenters" while the Greeks were "magnificent architects". Of course, there exist historians who gave a more favorable judgment regarding the achievements of the Babylonians and the Egyptians. But these judgments were made by specialists who were perhaps unconsciously impressed more than necessary by the object of their interest."

The title page of Artemiadis' book explains that it is an English translation of a book originally published in Greek in the year 2000. The title page neglects, however, to mention that the ostensibly original Greek text is largely a translation of an English history - Morris Kline's "Mathematical Thought from Ancient to Modern Times". Morris Kline is given no credit whatsoever in the body of Artemiadis' text (apart from being listed in the bibliography), despite the fact that he wrote much of it. Although the translation and retranslation process has altered many of Kline's individual words, even a superficial inspection reveals that sentences, paragraphs, and even whole pages of Artemiadis' writings are clearly isomorphic to passages in Kline's classic history. To put matters bluntly, "History of Mathematics from a Mathematician's Vantage Point" is a work of blatant plagiarism.

I have occasionally joked with students that "if you must cheat, at least have the good sense to cheat well." Apparently, Artemiadis never heard this advice. Rather than playing it safe and stealing from an obscure source, he chose to pilfer prose from a standard history of mathematics familiar to most mathematicians. Still worse, he made the mistake of plagiarizing the writings of a highly literate iconoclast whose ideas are easily identifiable both by their novelty and by their very phrasing.

Morris Kline, incidentally, is not the only victim, though he is the most conspicuous. If nothing else, many readers will recognize the chronological table which appears in the back of "History of Mathematics from a Mathematician's Vantage Point" as a slightly abbreviated version of the table appearing in Carl Boyer's, "A History of Mathematics".

This is an appalling book - the sort of thing one hears about, but rarely actually holds in one's hands (in an AMS publication no less! How did this get by the editors?) The idea that this inept thievery is supposed to represent the "mathematician's viewpoint" only adds insult to injury.