The controversy began in 2002, with an allegation that the twins, popular celebrities in France for hosting science-themed TV shows, had obtained PhDs with nonsensical work.
Rumors spread on Usenet newsgroups that their work was a deliberate hoax intended to target weaknesses in the peer review system that physics journals use to select papers for publication.
While the Bogdanov brothers continued to defend the legitimacy of their work, the debate over whether it represented a contribution to physics spread from Usenet to many other internet forums, eventually receiving coverage in the mainstream media.
The incident prompted criticism of the Bogdanovs' approach to science popularization, led to a number of lawsuits, and provoked reflection among physicists as to how and why the peer review system can fail.
According to Sternheimer, the twins viewed themselves as "the Einstein brothers" and had a propensity to voice vague, "impressionistic" statements; he considered guiding their efforts "like teaching My Fair Lady to speak with an Oxford accent.
"[1] As he told The Chronicle of Higher Education, Sternheimer did not consider himself an expert in all the topics Grichka Bogdanov included in his thesis, but judged that those portions within his specialty were PhD-quality work.
[1] Both of the brothers received the lowest passing grade of "honorable", which is seldom given, as Daniel Sternheimer told The New York Times science reporter Dennis Overbye.
[11] Niedermaier suggested that the Bogdanovs' PhD theses and papers were "spoof[s]", created by throwing together instances of theoretical-physics jargon, including terminology from string theory: "The abstracts are delightfully meaningless combinations of buzzwords ... which apparently have been taken seriously.
"[11][6] Copies of the email reached American mathematical physicist John Baez, and on 23 October he created a discussion thread about the Bogdanovs' work on the Usenet newsgroup sci.physics.research, titled "Physics bitten by reverse Alan Sokal hoax?
The New York Times reporter George Johnson described reading through the debate as "like watching someone trying to nail Jell-O to a wall", for the Bogdanovs had "developed their own private language, one that impinges on the vocabulary of science only at the edges.
One of the scientists who approved Igor Bogdanov's thesis, Roman Jackiw of the Massachusetts Institute of Technology, spoke to The New York Times reporter Dennis Overbye.
[8]In May 2001, the journal Classical and Quantum Gravity (CQG) reviewed an article authored by Igor and Grichka Bogdanov, titled "Topological theory of the initial singularity of spacetime".
Eli Hawkins, acting as a referee on behalf of the Journal of Physics A, suggested rejecting one of the Bogdanovs' papers: "It is difficult to describe what is wrong in Section 4, since almost nothing is right.
"[12] Jacques Distler voiced a similar opinion, proclaiming "The [Bogdanovs'] papers consist of buzzwords from various fields of mathematical physics, string theory and quantum gravity, strung together into syntactically correct, but semantically meaningless prose.
[12] The physicists commenting on Usenet found these claims and subsequent attempts at their explanation peculiar,[12][27][28] since the trajectory of a Foucault pendulum—a standard museum piece—is accurately predicted by classical mechanics.
[12][26] Damien Calaque of the Louis Pasteur University, Strasbourg, criticized Grichka Bogdanov's unpublished preprint "Construction of cocycle bicrossproducts by twisting".
In Calaque's estimation, the results presented in the preprint did not have sufficient novelty and interest to merit an independent journal article, and moreover the principal theorem was, in its current formulation, false: Grichka Bogdanov's construction yields a bialgebra which is not necessarily a Hopf algebra,[31] the latter being a type of mathematical object which must satisfy additional conditions.
But if one accepts that the papers about these difficult questions don't have to be just a well-defined science but maybe also a bit of inspiring art, the brothers have done a pretty good job, I think.
[34]Motl's measured support for "Topological field theory of the initial singularity of spacetime", however, stands in stark contrast to Robert Oeckl's official MathSciNet review, which states that the paper is "rife with nonsensical or meaningless statements and suffers from a serious lack of coherence," follows up with several examples to illustrate his point, and concludes that the paper "falls short of scientific standards and appears to have no meaningful content.
Critics cite examples from Avant Le Big Bang including a statement that the "golden number" φ (phi) is transcendental, an assumption that the limit of a decreasing sequence is always zero, and that the expansion of the Universe implies that the planets of the Solar System have grown farther apart.
[15] In October 2004, a journalist from Ciel et Espace interviewed Shahn Majid of Queen Mary, University of London about his report on Grichka Bogdanov's thesis.
[49] In 2006, Baez wrote on his website that for some time the Bogdanovs and "a large crowd of sock puppets" had been attempting to rewrite the English Wikipedia article on the controversy "to make it less embarrassing to them".
[12] In September 2006, the case was dismissed after the Bogdanovs missed court deadlines; they were ordered to pay 2,500 euros to the magazine's publisher to cover its legal costs.
[64][55] During the heyday of this affair, some media coverage cast a negative light on theoretical physics, stating or at least strongly implying that it has become impossible to distinguish a valid paper from a hoax.
[26] On the other hand, George Johnson's report in The New York Times concludes that physicists have generally decided the papers are "probably just the result of fuzzy thinking, bad writing and journal referees more comfortable with correcting typos than challenging thoughts.
Regarding the Bogdanov publications, physicist Steve Carlip remarked: Referees are volunteers, who as a whole put in a great deal of work for no credit, no money, and little or no recognition, for the good of the community.
"[3] As of October 2018[update], the Bogdanovs' most recent paper was "Thermal Equilibrium and KMS Condition at the Planck Scale", which was submitted to the Chinese Annals of Mathematics in 2001 and appeared in 2003.
Worried by what he considered a "more-or-less explicit rejection of the rationalist tradition of the Enlightenment", Sokal decided to perform an experiment which he later cheerfully admitted was both unorthodox and uncontrolled, provoking a maelstrom of reactions which, to his surprise, received coverage in Le Monde and even the front page of The New York Times.
[71] Igor and Grichka Bogdanov have and had vigorously insisted upon the validity of their work, while in contrast, Sokal was an outsider to the field in which he was publishing—a physicist, publishing in a humanities journal—and promptly issued a statement himself that his paper was a deliberate hoax.
Replying on sci.physics.research,[72] Sokal referred readers to his follow-up essay,[73] in which he notes "the mere fact of publication of my parody" only proved that the editors of one particular journal—and a "rather marginal" one at that—had applied a lax intellectual standard.