Plagiarism is a bit like the weather. Everybody talks about the topic but nobody does anything much about it. Sure students are admonished not to and punished when caught; but that is about it, other than out-sourcing much of the issue to money-making outfits like turnitin.com. There are many reasons for this and I intend to discuss a few of them.

The Oxford dictionary defines plagiarism as a noun for “the practice of taking someone else’s work or ideas and passing them off as one’s own” and gives the example of usage “there were accusations of plagiarism.” This, like all definitions, leaves open many things, like how much work or how big an idea must be involved. There are legal tomes and screeds on just that subject [3].  But even assuming the definition is clear, the question of why is not mentioned let alone answered.

Why do we care?

Here are three brief answers.

1. We may care because it protects the value in the originator’s work, be it financial or reputational. Some of this overlaps with more general issues of intellectual property. Here I think the matter was put wonderfully by Jefferson:
   

   [1] If nature has made any one thing less susceptible than all others of exclusive property, it is the action of the thinking power called an idea, which an individual may exclusively possess as long as he keeps it to himself; but the moment it is divulged, it forces itself into the possession of everyone, and the receiver cannot dispossess himself of it. [2] Its peculiar character, too, is that no one possesses the less, because every other possesses the whole of it. He who receives an idea from me, receives instruction himself without lessening mine; as he who lites his taper at mine, receives light without darkening me. [3] That ideas should freely spread from one to another over the globe, for the moral and mutual instruction of man, and improvement of his condition, seems to have been peculiarly and benevolently designed by nature, when she made them, like fire, expansible over all space, without lessening their density at any point, and like the air in which we breathe, move, and have our physical being, incapable of confinement, or exclusive appropriation. [4] Inventions then cannot, in nature, be a subject of property.

   This is in a letter from Thomas Jefferson to Issac McPherson (August 13, 1813), collected in The Writings of Thomas Jefferson part 6., and I read it first on page 94 of The future of ideas by Lawrence Lessig, Random House, 2001. That is a full citation but it is now easily found on the Internet: try the lustrous phrase in italics.

2. We may care because originality is a requirement for achieving degrees or passing courses. Such requirements have changed over time and what is improper today may be good practice in 2050. It is unlikely that submitting the same essay in two different undergraduate courses in two different years will ever be kosher. But bundling together one’s own published papers for a doctorate now certainly is. It was not always so.
3. We may care because it helps us verify the genesis and correctness of an idea. This might be for scholarly reasons or it might be to ensure the structural integrity of a bridge. This for me is the main rationale, and keeping this in mind help anchor all my further maundering.

A confession

Let me continue with a confession. I have deliberately plagiarized. In the mid-eighties when I was no-less-foolish than now but a lot younger, I signed a contract to coauthor the Collins Dictionary of Mathematics with Ephraim Borowski. This authoring was both a fascinating and searing experience, as I have discussed at some length in [1].

We allowed ourselves one joke per edition. In the first edition we printed a picture of the null graph. In the second we defined plagiarism as a labour-saving but lawyer-enriching form of research. After this we asserted it was relatively rare in mathematics. We then copied, without attribution, some lovely text from the New York Times about plagiarism in which the Times had quoted liberally, with attribution, from Tom Lehrer’s classic song “Plagiarize.” We could not resist the self-referent pleasure of plagiarizing a definition of plagiarism. After all, who could sue us with a straight face?

The contract we signed had inadvertently left us the “musical and electronic rights.” The latter were later very valuable [1], and Collins, treating us a “trade book,” also told us that we were plagiarizing if we copied eight words in sequel. This test works quite well for “I wandered lonely as a cloud that floats,” but it does not work for science, and especially not in mathematics.

That is because accuracy and originality are often at odds with each other. The best ways of defining an Abelian group or Gaussian curvature have long been known; actually these are both now common nouns so the caps are voluntary.. The last thing we typically need is novelty. The Berne Convention for the Protection of Literary and Artistic Works recognizes this tension and exempts mathematical formulas.

Authority versus authorship

Artistic mimesis or scientific theft? We all plagiarize Shakespeare, Emerson, Franklin, Dylan (Thomas or Bob), Bob Marley, and others. Without borrowing there is no cultural inheritance. With too much attribution, there is only stilted name-dropping conversation. There is nothing new under the sun. (Ecclesiastes 1:9
New International Version (NIV)).

BitTorrent, twitter and the blogosphere have merely roiled the waters. None of my postgraduate students see anything wrong with grabbing whatever copies of research monographs are electronically accessible. Copyright issues are not in their forebrains.  It took only  minutes before the tweat of ‘Thatcher is dead.’ was causing much more traffic as ’That cher is dead.’  Take that, accuracy and ownership.

Who cares? Whether to attribute my new idea to Aristotle or to me depends on the time, the place, and the audience. The balance has changed over the ages, as illustrated in Stephen Greenblatt’s description of the rediscovery of Lucretius’ “The nature of things” in his Pulitzer winning The Swerve.

At this point I wish to flag two important observed phenomena. These are the Matthew effect (unto those who have shall be given) and Stigler’s principle of eponymy (a scientific idea is never named after the first to discover it).

In the sociology of science, the “Matthew effect” was a term coined by Robert K. Merton to describe how, among other things, eminent scientists will often get more credit than a comparatively unknown researcher, even if their work is similar; it also means that credit will usually be given to researchers who already are famous. For example, a prize will almost always be awarded to the most senior researcher involved in a project, even if all the work was done by a graduate student. This was later jokingly coined Stigler’s law, with Stigler explicitly naming Merton as the true discover.

The take-away idea here should be that scholarship is hard and secondary sources are unreliable, while primary ones are often unavailable, inaccessible or impenetrable.

Accusations stick. Remember Fared Zakaria, Jane Goodall, Martin Amis and Jakob Epstein, Stephen Ambrose, Doris Kernes Goodwin? I recalled that each of them have been recently tarnished by plagiarism accusations, but in most cases I had to go look up the events to remind myself of who was accused of doing what to whom and by whom.

All but Martin Amis appear to have broken the rules, and non trivially so — even if a significant amount is explained by their copying material too freely from that digital apple of Eden the world wide web. I quote Jon Sutherland on Amis and Epstein:

Raine and Amis are of the same generation (young), and of the same university, and their careers in literary journalism have intertwined. They are held to belong to a coterie which has been termed – embarrassingly for them, doubtless the New Oxford Wits. Given a degree of literary fraternity, there is no reason why Amis should not have experimented in fiction with Raine’s Martian perspective. The law allows no copyright in technique or device, any more than in ideas. (Jacob Epstein’s offence, allegedly, was to use forms of wording from The Rachel Papers.)

How well an individual survives the accusations depends on objective facts (was it a few lines in a great book?) how much credibility does the accuser have?)and subjective ones (was it a slow news week? does the accused act like an egoistic jerk?)

Fabrication, plagiarism and self-plagiarism

A case I remember more clearly is that of Jonah Lehrer. His is definitely a 21st century dossier. The sheer scale of his fabrications (quotes invented from meetings not held, whole scale recycling of his own blogs, and copious plagiarism) puts him in the big leagues. His disgrace has led not only to his being fired by the New York Times but to his best selling books being recalled by his publisher (see Wikipedia’s list of plagiarism incidents.)

Elsewhere David H. Bailey and I have written about error and fraud in the sciences. The Dutch social psychologist Stapel is arguably in a league with Lehrer. Fabrication is generally a much more serious issue than plagiarism in the sciences. Most scientists aim to be fine researchers not true scholars. So while we care just as deeply when our own priority is filched, with the work of others, while not condoning plagiarism, we are likely more concerned with a result’s correctness and replicability rather than its patrimony.

Intentional bullshit. Perhaps the best known example was the 1996 Sokal hoax, where as we wrote

New York University physics professor Alan Sokal succeeded in publishing a paper in Social Text, a prominent journal in the postmodern science studies field. As Sokal revealed after its publication, he deliberately salted his paper with numerous instances of utter scientific nonsense and politically-charged rhetoric, as well as approving (and equally nonsensical) quotes by leading figures in the field. He noted that these items could easily have been detected and should have raised red flags if any attempt had been made to subject the paper to a rigorous technical review.

More recently computer generated nonsense papers have been accepted by nominally referred conferences. But I digress.

How to plagiarize successfully in mathematics

Here is my recipe. It will not produce breakthrough results. It will produce papers that do what the vast majority of papers do in any field. It places correct results in the literature, adds to a curriculum vitals, and may help secure a job, promotion or tenure. The method is, I fear, largely inapplicable in the experimental sciences, but I suspect it adapts well in the humanities and social sciences.

1. Find an old fairly technical, longish but not too long paper (how old and how long will depend on the field) with no citations. Praise it with language like “In a sadly neglected work Magnus Kopfrechnener produced some lovely results. Our gal is to extend these results and to bring them to the attention of current researchers.”
2. The results must be old enough that notation in the field has changed. In topology, classical algebra, or descriptive set theory this is especially easy. Reproduce the main results verbatim in modern notation, using a nice version of LaTex. If you can, add some neat specializations.
3. Make sure to add some recent references by individuals who are active but not-too active-in the field. Praise them also but modestly.
4. Add some computations in Maple or Mathematica and perhaps even a figure or two.
5. Proofread carefully, and submit to a legitimate if unimpressive journal in a slightly tangential field.

The chances of acceptance are high, and the chances of being accused of misconduct near zero. Moreover, if it is published, you can with a straight face assert that, unlike most recently published papers, it is not only correct but interesting. As Brown, discussing constructivism and intuitionism [2], has written:

Philosophical theses may still be churned out about it, … but the question of nonconstructive existence proofs or the heinous sins committed with the axiom of choice arouses little interest in the average mathematician. Like Ol’ Man River, mathematics just keeps rolling along and produces at an accelerating rate “200,000 mathematical theorems of the traditional handcrafted variety … annually.” Although sometimes proofs can be mistaken—sometimes spectacularly—and it is a matter of contention as to what exactly a “proof” is—there is absolutely no doubt that the bulk of this output is correct (though probably uninteresting) mathematics.” (Richard C. Brown)

All of these five steps are hugely assisted by a level of skill in the use of Mathematical Reviews and a fair ability with LaTex. This recipe is not recommended for other than fluent English speakers. Indeed much of the plagiarism I have uncovered as an editor arises with speakers of “globish,” who copy large swathes of good mathematical English, marred only by the errors in their interpolations.

We catch only unsuccessful plagiarists.

How we handle it in the Academy? Some personal experiences

Just as with computer viruses, there is an unending battle being waged between plagiarizers and gatekeepers. It has never been easier to plagiarize, as my suggested recipe intimates, and there have never been so many tools to check for and apprehend plagiarism. Those tools are usually costly and often intrusive Neither eduction nor the research enterprise has been designed to catch crooks.

As with airline travel, too much vigilance aimed at catching a few makes life unpleasant for the many. Arguably it merely trains the determined and catches the inept. Even when caught, legal niceties lead to a lot of, perhaps unavoidable, pussyfooting. An article everyone can see is wholly plagiarized, will have the attention of the reader’s attention drawn to its similarity to the original article. Sometimes everyone is in on the joke. A legendary plagiarizehas a series of plagiarisms and auto-plagiarisms noted in Mathematical Reviews noted by back referencing to the earlier reviews.

I turn to several personal anecdotes relating to treating the symptom, plagiarism, rather than the disease, lack of nous. Plagiarism interruptus. More than twenty-five years ago I sat on the academic appeals committee of a Gof13 Canadian university. Cases that got to us had failed to be resolved despite many hundreds of hours of work by academics, lawyers and others. The cases we saw involved impersonation at an examination, sordid things done to a cat, and much else. Only a few involved plagiarism. One that did was a doozie.

A final year jock, called Jock, had already failed a required sociology course and had to pass it to complete a degree. On the day the final course project was due, his coach begged on his behalf for a two week extension. The day before the deadline, the instructor saw what appeared to be Jock’s essay neatly typed in the departmental secretary’s outbox. The secretary confirmed this to be the case. As this grade was all that stood between the instructor and Christmas, she took it to her office. To her amazement, other than the title page the essay was an exact copy of s paper one of her colleagues had published the previous year. A failing grade was entered and the plagiarism was reported.

Cutting to the chase, Jock gave a simply incredible story as to how his name appeared on someone else’s paper. Nonetheless, we determined that Jock had not committed plagiarism as he had never submitted the paper. He was allowed to submit another essay and ultimately got a pass. Such is the nature of academic decision making when everything is subject to external legal challenge. The effect of cases like this is depressing. Some instructors bail on reporting plagiarism as the anticipated consequences are too daunting. Others become hyper-officious and never allow students any variation from the regulations. In both cases everyone suffers

King Lear, in Africa, twenty years later. I ended up back at the same university and for a year on its reformed disciplinary committee. This time every case we saw involved web plagiarism. Some were simple, even touching. A young man when asked why he plagiarized the 5th assignment in a course replied, “What else could I do?, I got an ‘F’ for my own work on the first four.” Few denied the charges, some did not bother to appear.

This later group included a fourth year Honours English student whose teacher had accused her of plagiarizing an essay on King Lear. As is usual in this case we were presented with a copy of the offending material side-by-side with the original. In this case it came along with a very carefully written, overly detailed description of all related events.

The offending essay started: “King Lear, one of Shakespeare’s great tragedies,” so far so good, it continued with something like “is set in early twentieth-century North Africa just as Turkish power is ebbing away.” In an attempt to finish the essay on time, the student had plagiarized large swathes of the description of a travesty production worthy of Peter Brook on LSD. It had Lear as a Ghadafi character and so on.

All of this was dutifully noted in the plagiarized essay. The student was quickly found guilty of plagiarism. but none of the documentation mentioned the much larger crime of criminal and what Johnson would have called unnatural stupidity:

Why, Sir, Sherry is dull, naturally dull; but it must have taken him a great deal of pains to become what we now see him. Such an excess of stupidity, Sir, is not in Nature. [Samuel Johnson, of Sheridan, from James Boswell, Life of Samuel Johnson (1763)]

How was it possible that an honours student at a good institution knew so little about her subject that the plagiarized text seemed persuasive? And until I brought the matter up, the student’s ignorance played no role in the hearing.

Gratuitous plagiarism. A decade ago I was a thesis committee member for a thesis in chemistry for which I was supposed to vet the mathematics. The mathematics was not great but the chemists seemed satisfied with the chemistry, as did the external reader. He pointed out that the long appendix on the life of Gauss was entirely plagiarized. He explained that he had become suspicious because the English of the appendix was so much better than what came before.

Then the discovery was only a google away. The committee in its wisdom decided that since the plagiarism was not relayed to the meat of the thesis, no action other than a request to remove the offending appendix would occur. So not all plagiarisms are equal.

Accuracy versus originality. In the 2002 second edition of our dictionary we wished to add the Clay institute’s seven Millennium problems (each with a million dollar prize, six are still open) to our list of Hilbert’s 23 problems (which had had a profound influence on twentieth century mathematics). For reasons I can not now explain, rather than asking the institute for permission to quote from their nice descriptions, we wrote our own. Since only two of seven were within our domain of true expertise, it was luck rather than skill if nothing was mangled or at best less clear.

Teaching judgment, not training seals

Despite the frivolous tone of the previous section these are serious matters. Which does less damage: to fail to cite a quote such as “never ascribe to malevolence what is well explained by incompetence” or to attribute it to a current personality after a thoughtless web search? (Napoleon and Goethe both said something like the quote.)

Mathematics has an unusually robust and reliable literature. The sheer scale of academic literature and the speed at which things happen makes it imperative that we teach our students, especially our replacements, how to judge the likely validity of an argument or when to trust a source. That is, teaching good sense is much more important than teaching adherence to the Chicago style manual. This is not meant to condone plagiarism but it is an appeal to dal with the agree issues.

I finish by referring to the following blogs that address many of these points: sloppy science and fraud, sloppy press reporting, reproducibility in scientific research, and the need for stable, non-politically-directed scientific funding to reduce the pressure for hasty press coverage. In these four articles, we have analyzed the reasons such events seem to be occurring with increasing frequency, and have made some suggestions on how to reduce their future occurrence.

References [1] Jonathan M. Borwein, “The Oxford Users’ Guide to Mathematics,” Featured SIAM REVIEW, 48:3 (2006), 585-594. [2] Richard C.. Brown, Are Science and Mathematics Socially Constructed? World Scientific, 2009, [3] Copyright and Piracy: An Interdisciplinary Critique (Cambridge Intellectual Property and Information Law) , Lionel Bently (Editor), Jennifer Davis (Editor), Jane C. Ginsburg (Editor), Cambridge Univ. Press, 2010.

Problems about prime numbers are fundamental and often intractible. In his article “The first 50 million prime numbers” in the Mathematical Intelligencer (1977), Don  Zagier wrote

…there is no apparent reason why one number is prime and another not. To the contrary, upon looking at these numbers one has the feeling of being in the presence of one of the inexplicable secrets of creation.

So real progress on the understanding of prime numbers  is something to celebrate.

Twin prime conjecture

The first of the two latest results concerns what is known as the twin prime conjecture, namely that primes just two apart, such as 3 and 5, 11 and 13, 17 and 19, 41 and 43, etc., continue to appear indefinitely. Numerical searches appear to confirm the conjecture and mathematicians generally believe that it is true. But rigorously establishing it has proven to be enormously difficult.

There is no record of who first proposed the twin prime conjecture — it has been in the mathematical literature for centuries. Several generalizations have been proposed. The Hardy-Littlewood conjecture, for instance, says that the number of primes p for which p+2 is also prime is not only infinite, but indeed the fraction of such primes in the first n integers tends to C₂ n / (log n)², where C₂ is approximately 0.6601618… See the Wikipedia article on the twin prime conjecture and an article by Sadegh Nazardonyavi for additional background.

Technical details are presented in G.H. Hardy and J.E. Littlewood, “Some Problems of ‘Partitio Numerorum.’ III. On the Expression of a Number as a Sum of Primes,” Acta Math. 44 (1923), 1-70, and E. Bombieri, J.B. Friedlander, and H. Iwaniec, “Primes in Arithmetic Progression to Large Moduli,” Acta Math. 156 (1986), 203-251.

On 13 May 2013, Yitang (Tom) Zhang of the University of New Hampshire, Durham, announced a proof that there are infinitely many prime numbers separated by less than 70,000,000. Now 70,000,000 is not two, but this is the first result that has established any finite bound at all. Zhang’s work builds on results of numerous earlier researchers, including Bombieri, Vinogradov, Elliot, Halberstam, Goldston, Pintz, Yildirim and others. Zhang constructed a “sieve,” not unlike a gold-panning system that processes lots of of liquid-suspended ore, leaving a few nuggets, which he then analyzed using  various advanced techniques.

Other leading mathematicians have praised Zhang’s work. Daniel Goldston of San Jose State University, who himself has worked on this problem, said that the result is “astounding.” Andrew Granville of the University of Montreal in Canada, one of the leading living analytic number theorists, declared that

This is one of the great results in the history of analytic number theory. … It’s just extraordinary. I would never have expected it in my lifetime.

He notes that it is “virtually unheard of” for such a significant result to come from a mid-career mathematician who had not previously been noted for research in this highly technical area. Many observers feel that the bound of 70,000,000 will quickly be reduced, once researchers in the field fully understand and further refine Zhang’s techniques. But while it is unlikely to lead to a resolution of the full conjecture, Granville notes

This work is a game changer, and sometimes after a new proof, what had previously appeared to be much harder turns out to be just a tiny extension. … For now, we need to study the paper and see what’s what.

Some additional details on Zhang’s work can be found in a detailed  Simons Foundation news article by Erica Klarreich, which has already been reprinted in Wired, and in a Science article by Dana Mackenzie.

Goldbach conjecture

The second result concerns the Goldbach conjecture, which in its strong form is that every even number greater than two is the sum of two primes, and in its weak form that that every odd number greater than five is the sum of three primes. Note, for instance that 13=3+5+5 and 36=17+19. Again, these conjectures have been studied in great detail, both mathematically and numerically, and are generally thought to be true, but there has been no proof of either. Christian Goldbach (1690-1764) was a German mathematician and lawyer known for his work in number theory and analysis. He stated the conjecture known by his name in a now-famous 1742 letter to Euler.

Various noteworthy mathematicians have worked on this problem. Most progress relies on the so-called Hardy-Littlewood-Vinogradov circle method, which in turn involves Fourier analysis, the familiar tool used by physicists and electrical engineers to decompose a periodic signal into its spectrum  (the frequencies of its harmonic components).

In the 1930s, Dhudakov, van der Corput and Estermann employed an approach of exponential sums due to Vinogradov to show that almost all even numbers can be written as the sum of two primes (in particular, that the fraction of even numbers which can be written in this way approaches unity). In 1975, Montgomery and Vaughan showed that the set of even integers which are not the sum of two primes has limiting density zero. See the Wikipedia article on Goldbach’s conjecture and the above-mentioned article by Sadegh Nazardonyavi for additional background.

On the same day as the twin prime announcement, Harald Helfgott, a 35-year-old mathematician at the Ecole Normale Superieure in Paris, announced a proof of the weak Goldbach conjecture.

In 1923, Hardy and Littlewood showed that by constructing a function whose spectrum consists of prime numbers, and then cubing it, one could establish the second Goldbach conjecture by showing that no odd-numbered frequencies are missing. Previous mathematicians had established that all frequencies above 10¹³⁰⁰ were present. Inspired by the so-called GPY paper, Helfgott was able to reduce this bound to “only” 10³⁰.

Such a large number was once considered too big to be of any practical use, but, given modern computer technology, that is no longer the case. Indeed, Helgoft’s colleague David Platt numerically verified the required condition for every number below this limit, a computational tour-de-force that required 40,000 CPU-hours of computer run time (about 4.5 CPU-years). To put this in context, the present bloggers recently expended nearly 2000 CPU-years of BlueGene computation time on an interesting but much less worthy cause, namely computing inaccessible bits of certain constants.

Fields medalist Terence Tao of the University of California, Los Angeles, who last year proved that any odd integer is the sum of at most five primes, cautiously endorses the result, although, as with the twin prime result mentioned above, it must survive the scrutiny of careful review by several leading mathematicians.

Some additional details on Helfgott’s work can be found in the above-mentioned Science article, and also in a blog post by Artem Kaznatcheev and Kate Zen. Helfgott’s latest manuscripts are available here and here.

Some concluding observations

Analytic number theory has seen much productive usage of high-powered computation. In the case of the Green-Tao Theorem on the existence of arbitrarily long arithmetic sequences of primes, it was the computation of a sequence of length 24 that convinced the authors the result was true.

Additionally, it was computation regarding the twin prime distribution that in 1994 unveiled the Pentium bug. That said, any number-theoretic conjecture that relies on very slowly growing functions and even vast ammounts of seemingly good evidence can be misleading or unconvincing. Such is the case for much of the computational work on the Riemann hypothesis.

It is also worth noting the analogy of the Goldbach proof to that of the Four Color Theorem, namely the assertion that, under certain reasonable conditions, only four colors suffice to color any planar map so that no two adjacent regions have the same color. The only proofs of this result to date have required computer-assisted analysis of many individual cases. Will Helfgott’s result or the Four Color Theorem eventually be proven without the aid of computation? Perhaps. But, as we argued in the first chapter of Mathematics by Experiment, there is no guarantee that such a proof exists.

What is also interesting about both of these landmark results is that neither involves a big new idea. Rather, they rely on painstaking, careful and incremental application of previous work (the shoulders of giants).  As was noted in the Science article, a Prime Week for Number Theory,

[a]fter generations of glacial progress on both problems, however, number theorists like Roger Heath-Brown of the University of Oxford in the United Kingdom were delighted to see signs of a spring thaw. “Despite hundreds of years of history, number theory is still moving on,” Heath-Brown says. “That’s what I find most exciting about these two theorems.”

As such they are more representative of how most mathematical progress takes place; not, as is commonly believed, from earthshaking, paradigm shifting ideas by very young, primarily male researchers.

[Added 4 Jun 2013: In the weeks following the announcement of the twin primes result, other mathematicians have reduced the limit from 70,000,000 to just a few million. As of this date, the current record is 4,802,222, held by Scott Morrison of the Australian National University in Canberra, Australia. Other details are given in a Online article.]

The world of economics was shaken two weeks ago with the report that a key paper and accompanying book in the field of macroeconomics (which have been cited by Paul Ryan and by other politicians internationally in their calls for austerity and debt reduction) is in error, the result of a faulty Excel spreadsheet and other mistakes, all of which could have been found had the authors simply been more open with their data.

Yet, experimental error and lack of reproducibility have dogged scientific research for decades. Recall the case of N-rays (supposedly a new form of radiation) in 1903, clever Hans, the horse who seemingly could perform arithmetic until exposed in 1907, and the claims of cold fusion in 1989.

Medicine and the social sciences are particularly prone to bias, because the observer (presumably a white-coated scientist) cannot so easily be completely removed from his or her subject. Double-blind tests (where neither the tester and the subject know for sure whether the test is real or just a control) are now required for many experiments and trials in both fields.

Deliberate fraud

Of even greater concern are proliferating cases of outright fraud. The “discovery” of the  Piltdown man in 1912, celebrated as the most important early human remain ever found in England, was only exposed as a deliberate fraud in 1953.

An equally famous though more ambiguous case is that of psychologist and statistician Sir Cyril Burt (1883-1971).  His highly influential early work on heritability of IQ was called into question after his death. After it was discovered that all his records had been burnt, inspection of his later papers left little doubt that much of his data was fraudulent—even though the results may well not have been.

Perhaps the most egregious case in the past few years is the fraud perpetrated by Diederik Stapel. He is/was a prominent social psychologist in the Netherlands who, as a November 2012 report has confirmed, committed fraud in at least 55 of his papers, as well as in 10 Ph.D. dissertations written primarily by his students (who have largely been exonerated; though it is odd they did not find it curious that they were not allowed to handle their own data).

An analysis by a committee at Tilburg University found that the problem goes far beyond a single “bad apple” in the field. Instead the committee found a “a general culture of careless, selective and uncritical handling of research and data” in the field of social psychology. “[F]rom the bottom to the top there was a general neglect of fundamental scientific standards and methodological requirements.” The committee faulted not only Stapel’s peers, but also “editors and reviewers of international journals.”

In a private letter now making the rounds, Daniel Kahneman (a 2002 Nobel behavioural economist) has implored social psychologists to clean up their act to avoid a potential “train wreck.” He specifically discusses the importance of replication of experiments and studies on priming effects, wherein earlier exposure to the “right” answer, even in an incidental or subliminal context, affects the outcome of the experiment.

There are certainly precedents for such a “train wreck”.

Perhaps the best example was the 1996 Sokal hoax, where New York University physics professor Alan Sokal succeeded in publishing a paper in Social Text, a prominent journal in the postmodern science studies field. As Sokal revealed after its publication, he deliberately salted his paper with numerous instances of utter scientific nonsense and politically-charged rhetoric, as well as approving (and equally nonsensical) quotes by leading figures in the field. He noted that these items could easily have been detected and should have raised red flags if any attempt had been made to subject the paper to a rigorous technical review.

Needless to say, the postmodern science studies field sustained a major blow to its credibility in the wake of the Sokal episode.

Regrettably if unsurprisingly, the Stapel affair is not an isolated instance in the present-day scientific world. As we described earlier in the Conversation, on 12 October 2012, the English edition of the Japanese newspaper Yomiuri Shimbun reported that “induced pluripotent” stem cells (often abbreviated iPS stem cells) had been used to successfully treat a person with terminal heart failure. Eight months after being treated by Japanese researcher Hisashi Moriguchi at Harvard University, the front-page article emphasized, the patient was healthy.

The newspaper declared that this was the “first clinical application of iPS cells,” and mentioned that the results were being presented at a conference at Rockefeller University in New York City. However, a Harvard Medical School spokesman denied that any such procedure had taken place.

As it turned out, Moriguchi’s results were completely bogus, as was his claimed affiliation with Harvard. There were certainly reasons to be suspicious of this report. Moriguchi claimed to reprogram stem cells using just two specific chemicals, but prominent stem cell researcher Hiromitsu Nakauchi responded that he has “never heard of success with that method,” and, what’s more, that he had never heard of Moriguchi in his field before this week. Within seven days Moriguchi had been fired by the University of Tokyo.

Another instance closer to home is the case of Australian medical researcher William McBride, who was one of the first to blow the whistle on the dangers of thalidomide in the 1960s, but in 1993 was found guilty of scientific fraud “over his experiments with another anti-morning sickness drug, Debendox.” Ironically, Frances Kelsey, who was credited with stopping Thalidomide being used in the USA, had a reputation for never approving new drugs at the FDA where she worked for 45 years.

Clearly the scientific press completely failed in exercising due diligence in such cases. How many other such cases have eluded public attention because of similar systemic failures? Indeed, given the maxim “Where there is smoke, there is fire,” it appears that scientific fraud may be on the increase.

Why do scientists and other academics  cheat?

All of this raises the question, “Why do scientists cheat?,” and, for that matter, “Why are scientists sloppy?” Possible answers, other than “scientists are people, fame is fame and money is money”, include:

1. Deliberate or unintended bias in experimental design and cherry-picking of data. Such effects run rife in large studies funded by biotech and pharmaceutical firms.
2. Academic promotion pressure. Sadly, “publish or perish” has led many scientists to prematurely rush results into print, without careful analysis and double-checking. This same pressure leads some to publish papers with relatively little new material, resulting in plagiarism and self-plagiarism.
3. Overcommitment. Busy senior scientists can end up as coauthors of flawed papers that they had little to do with details of. A famous case is that of 1975 Nobel Prize winner David Baltimore, regarding a fraudulent 1986 paper in Cell.
4. Ignorance. Despite E.O. Wilson’s recent protestations, many scientists and most clinical medical researchers and social scientists know too little mathematics and statistics to challenge or even notice inappropriate use of numerical data: such as whether it is too precise, or whether digit distrbution should be uniform or follow Benford’s law.
5. Self-delusion. Clearly many scientists want to believe that they have uncovered new truths, or at least notable results on a long-standing problem. One example here is the recent claimed proof of the famed “P vs NP” conjecture in complexity theory by Vinay Deolalikar of HP Labs in Palo Alto, California, which then quickly fell apart. There appears to be a mathematical version of the Jerusalem syndrome, which can afflict amateurs, cranks and the most serious researchers when they feel they have nearly solved a great open problem.
6. Confirmation bias. It sometimes happens that a result turns out to be true, but the data originally presented to support the result were enhanced by confirmation bias. This is thought to be true in Mendel‘s seminal mid-nineteenth century work on the genetics of inheritance; and it may have been true in early experimental confirmation of general relativity by Eddington and others.
7. Deadline pressure. One likely factor is the pressure to submit a paper before the deadline for an important conference. It is all too easy to rationalize the insertion or manipulation of results, under the guise that “we will fix it later.”
8. Pressure for dramatic outcomes, and the difficulty of publishing negative results. Every scientist dreams of striking it rich—publishing some new result that upends conventional wisdom and establishes him/herself in the field. When added to the difficulty in publishing a “negative” result, it is not too surprising that few scientists feel motivated to take a highly critical look at their own results. Leading journals such as Nature and Science are not without sin. Nature‘s great editor John Maddox managed to publish a totally implausible paper on homeopathic memory in water. Science played games with its own embargo policy to get maximum publicity for an arsenic-based life article by a telegenic NASA-based scientist that fell apart pretty quickly.
9. Quest for research funding. Scientists worldwide complain of the huge amounts of time and effort necessary to secure continuing research funding, both for their student assistants and to cover their own salaries. Is it surprising that this pressure sometimes results in dishonest or “stretched” results? Granting agencies and their political masters  are also culpable. All funded research must be rated hyperbolically as “world-class,” “leading-edge,” “a break through,” and so on. Merely “significant,” “careful” and “useful” are not enough.
10. Thrill? Some scientists are apparently driven by the pure thrill of getting away with cheating. At the least, it is clear that some, including Stapel, take some pride in outwitting their peers. Like any addiction, what may start out as marginal misbehaviour can grow explosively over time.

In most cases it is clear that those perpetrating scientific fraud, like those of compromised integrity in various other fields, did not wake up and say “I’m bored. I think I’ll write a fraudulent scientific paper today.” Instead, just like Ebenezer Scrooge’s deceased partner Jacob Marley, they forged their chains “one link at a time.”

Indeed, this appears to be the case with Stapel: a detailed recent article about Stapel in the New York Times indicates a slow progression from scrupulous to bizarrely unscrupulous. Indeed Stapel, in his own words, grew to prefer clean if imaginary data to real messy data.

One of the saddest and oddest cases is the honey-trap set by Russian/Canadian mathematician Valery Fabrikant. Fabrikant translated papers he had solely authored in Russian years earlier. He then added the names of senior academics in Engineering at Concordia University in Montreal—who did not demur. When they did not buckle to his threats of blackmail, and he was refused tenure, Fabricant went on a rampage. He is currently in jail for the 1992 murder of four “innocent” faculty members at Concordia.

What can be done?

Clearly academic fraud — while still the exception not the rule —  is a complicated problem, and many systemic difficulties need to be addressed.

But one major change that is needed is to move more vigorously to “open science,” wherein researchers are required (by funding agencies, journals, conferences and peers within the community) to release all details of approach, data, computation and analysis, perhaps on a permanent website, so that others can reproduce the claimed results, if and as necessary.

Another form of fraud occurs after publication. All metrics regarding citations are subject to massage. A stunning example of manipulation of the impact factor by editors is to be found in the 2011 article Nefarious numbers.

In Australia, it seems clear that bibliometrically-driven assessment exercises such as Excellence in Research for Australia are likely to exacerbate the pressures on academic (and other institutions) to “bulk-up” their dossiers.

Additionally, as the Australian has recently pointed out, it is potentially dangerous, especially for junior staff, to be whistle blowers. Moreover, current law in many countries impedes full investigation of academic misconduct and leaves accusers open to legal suit.

A recent conference held at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University in Rhode Island addressed the reproducibility them in detail, focusing mostly on the fields of scientific computation and mathematics, but with conclusions that have much broader reach. The Simons Foundation has published a detailed report on the conference. We have also written about it in the Huffington Post, while the conference report itself is available here.  

[Added 9 May 2013: One additional interesting instance of fraud is that of the Schon scandal, wherein German physicist Jan Hendrik Schön published some remarkable results about semiconductors that were later found to be fraudulent.]