Dramatis Personae
Professor Guy E. Gaux Prof. Gaux was an important political person in the world of mathematics. He had a reputation as one of the country’s near-top mathematicians. He had acquired this reputation through his association with some of the world’s best mathematicians, to whom he made himself useful, and through self-promotion. We will call Guy’s university, Good U. At the time, it was quite good in Guy’s field.
Professor Ed Visor Ed only plays a peripheral role. He had a reputation for producing outstanding young mathematicians. He was a well-known mathematician in his own right, but his brilliant students gave him an even greater status. He taught at an unnamed (here) outstanding university.
Doctor Truly* Brilliant Truly was one of Prof. Visor’s best students. The career path of such a student usually follows a standard trajectory at the beginning. The graduate gets a special 3-year position at either Harvard, Yale, Chicago, Princeton or UC Berkeley. They teach (just a little) and do research, usually working with one of the country’s top mathematicians. Then they go on to a permanent position at an outstanding school. That’s the trajectory Truly followed – initially; but other characters in this story, sadly and evilly in my mind, cut his brilliant career off at the pass. We will refer to his school, one of those top six, as Great U.
*(I used the name Truly in the original version of this story in order to make it hard to identify anyone. Now that I have posted a letter – see below – from “Truly”, it will be obvious that Truly is not a woman. But I’m too lazy to change the name, so I only changed the pronouns.)
Doctor Jess O. Kay Jess was also one of Prof. Visor’s students. He wasn’t nearly in the category of Truly, so he took a post-doctoral position at Good U. Dr. Talented (described below) once told me that the only reason Good U. hired Jess was that they wanted to curry favor with Ed Visor.
Dr. H.I. Lee Talented Lee was an outstanding mathematician in his early thirties. He came to Good U. as a visitor, but he hoped to get hired as a tenured professor, and that did happen – after the proof was purloined by him.
Professor I. William “Will” Whotevor Will plays a role in a latter attempt to keep Truly down.
Me I was at Good U. during the year the paper rustling occurred and was a close eyewitness to the events as they happened, though I didn’t know it at the time.
The Proof – Its Importance
The best way to explain the importance of the purloined proof is this excerpt from a document describing Lee’s work and career.
“…One particularly important achievement of Lee’s early work was his collaboration with Jess O. Kay which led to the [P-Method]…a formative contribution to the field…that was later to become wavelets, a powerful technique that…revolutionized digital signal processing and image compression….”
[“P-Method” is my description. They use a different description, but, for me, P stands for “purloined”.]
The Story – A Brief Version
A very senior mathematician asked me (a very junior mathematician) if I would look at a letter (See Mike Wilson Original Proof and fixed reversed page, Mike Wilson Original Proof fixed page. )that he had received from Truly. Here is why he asked, and what he wanted to know.
Many years earlier, my senior colleague had proved a theorem. Now, Truly had just proved the same theorem using a different method. Since Truly was still a junior mathematician, he appropriately sent his proof in a letter to my senior colleague to make sure that he wasn’t using his method, and to let him know that he had proved the theorem. Though Truly didn’t need to do this – since his method truly was different – it was appropriate to ask my colleague before he published it.
Now, rather than look at his proof himself, my colleague gave it to me to look at. As a young mathematician that gave me an opportunity to study Truly’s proof. He was known to be quite talented since he had already achieved a solution to a problem that top mathematicians hadn’t solved. It never hurts to study the work of such a brilliant mathematician. Their methods are usually new, very creative, and very useful. Also, my senior colleague was well known, and his work was certainly worth studying.
I commenced to study Truly’s proof; and I had help.
Lee Talented and I worked in the same field of mathematics. We became friends and spent a lot of time discussing math. Though he was only in his early thirties, he was an outstanding mathematician who received his PhD at a young age. I learned a lot from him.
I showed Truly’s proof to Lee. We studied it carefully together. Lee told me that Truly’s work was brilliant. He even suggested that I change some work that I was doing with the senior mathematician and use Truly’s brilliant method, the P-Method. (Truly, not knowing how useful his method was, didn’t give it this name. Lee did, and only later, when he claimed it for his own.)
So I went to the senior colleague that I was working with and tried to show him Truly’s P-Method. But my senior colleague, a nice but moody and, at times, irascible guy, wouldn’t even look at Truly’s method. He said he just cared if it was like his, which it wasn’t. So I never got to show it to him.
Lee asked me if I showed Truly’s proof to my senior colleague. I told Lee what had happened. Lee said that it was a shame that we weren’t going to use Truly’s P-Method. (Obviously, we would have given Truly credit for his work, which I assumed he would publish.)
At this point I dropped out of the story as a participant. I was an observer; though I didn’t understand what I was observing till much later.
What I Saw Next (From My Perspective at the Time)
Before I tell what I saw – and later learned – I need to digress to explain something about mathematical research – something that Lee, himself, pointed out to me once.
It usually takes about 6 years after attaining a PhD before a researcher knows his field well enough to know the implications of his work. There is just too much to learn. He will be able to prove theorems as well, or better, than excellent experienced mathematicians, but, in many cases, will be unaware of their importance. That is exactly what happened here.
(The lack of total awareness of what is important is the reason why the very best fresh PhD’s will study for three more years at one of the top math departments, answering important mathematical questions that their senior colleagues have.)
As I explained earlier, Truly had proved a theorem, first proved by my senior colleague, but with a very different method – his P-method. This is the idea that went on to be extremely important as is explained in “The Proof – Its Importance”, above. Yet Truly didn’t recognize his method’s importance. In his letter (which I still have a copy of), he notes that the method he used to get his result was very interesting, making it clear that he did not realize how useful that method could be.
Now, I will write what I saw – and didn’t understand – at the time. (It was much later, as described below, in the section The Lecture Where I Began to See the Light that I realized what had happened.)
One day I was talking to Lee. He told me that Truly had essentially plagiarized, on one of his papers, from one of the world’s most famous mathematicians, who was even at the university where he was working!
I, like most busy people, had no time to follow through and see if Truly had really done this; but, years later, when we suspected something, a colleague and I did investigate the claim.
My colleague and I independently concluded that it was a gigantic stretch to say that Truly had done anything wrong. What Truly had done was use a result of the famous mathematician in his own work, giving him full credit for his ideas. This is standard. Maybe, most importantly, Truly had now been accused by Lee, of stealing the same idea that he so brilliantly – on his own – saw how to use in his P-Method.
Lee did not have the reputation to destroy Truly on his own, but he went to Prof. Gaux (Guy). Guy began to pass on Lee’s claim about Truly. I was later told by colleagues that Truly’s career was almost devastated. He certainly did not get a permanent job at a top university.
Lee and Jess Publish Their Big Result
(Again, this is from my perspective at that time.)
Within a few months I heard from Lee that he was working with Jess on a big project. He had come up with a new method, something he called the P-Method. I was told by a leading mathematician that what Lee and Jess had done was very important. They also showed many applications of their work. I was impressed that my colleague Lee was doing so well. He got tenure and soon was promoted to full professor.
A few years later Guy gave a series of invited talks about work based on the P-Method. He and Jess and Lee published a book based on those talks.
(I learned much later (from Truly) that Truly had attended those talks. He recognized his work and talked to the three (Guy, Jess and Lee) about it. He told me that he was told that his work and their work must have been done independently.)
The Lecture Where I Began to See the Light
A few years after this happened, I saw Jess give a talk about the work that Jess and Lee had done. It was delivered by Jess. As I watched the talk unfold, I realized that Jess was doing nothing more than explaining the method that Truly had used in the proof that I showed Lee! Nothing less, nothing more.
I felt strongly that I should let Truly know what had happened. Unfortunately, at this point in my career, there were other things going on that I felt were important enough that their outcome should not be risked by taking such a bold step against Guy and Lee. (I will later write about those “other things” because they involve yet another unsavory view into what higher education has become, and how much it has lost its “soul”.)
Still I felt that I needed to do something. I went to the senior colleague who had originally asked me to look at Truly’s proof. I told him that Jess’ talk looked very “similar” to what he asked me to look at. He didn’t say much at the time, but later he asked me if I still had a copy, that he couldn’t find his. He asked this in a very off-hand way.
I gave a copy to the senior colleague. I noted that he immediately took it to Guy. He never said anymore to me about it.
Will Whotever Accuses Truly
Several years go by and my other matter is not an obstacle anymore. Now, I can contact Truly; but another wrench gets thrown into the works. This time, I am able to overcome it.
Here is what happened.
Will Whotever appeared on the scene in an important political, and powerful, role. I thought I got to know him pretty well. An important mathematician who was familiar with my work had told him to seek me out to do some research together. He did and we became friends and colleagues.
DIGRESSION
As I write this story, I’m getting embarrassed. I can’t believe I was so naïve.
I think I understand, though.
I always wanted to be a professor. I loved reading, not only math, but philosophy, etc… , and I thought professors had high ideals – like the ones I read about in Plato and Aristotle and Camus. I thought a professor would be like them. I did not realize that many professors read these texts, not to think about them in any meaningful way, but only to show that they, the professors, are smart. I had romanticized what a professor was. Bad idea.
END OF DIGRESSON
I had asked a few colleagues whom I trusted (so I thought) to look at Truly’s letter and Jess and Lee’s paper to make sure I wasn’t making a mistake. They all said the proofs were the same. One of those people was Will. (Will had also been a professor at the same school where Jess and Truly studied for their PhD’s. That is an important fact.)
So, now that my important matter was done with, and I was free to contact Truly about what had happened, I dropped by Will’s office to ask him if he knew what Truly was doing now. Boy, did I get a shocking answer.
In his inimitable way, Will bellowed,
“Oh Truly, Truly never had an idea in his life. He takes all of his work from other people, including me.”
He told me that Truly was up for a big promotion at his institution, and that Guy had asked him to write a letter to his school, explaining how he was dishonest and not very good.
I was shocked – and angry. I asked Will if he included in that letter that Lee had stolen his proof. The look on Will’s face changed. It was now clear to him that, now, I knew who he was. I left.
A wrench had been thrown in the works. Will was in a very powerful position when it came to my career. I did not want to directly tell Truly about Will’s letter. I did call him though and told him all but about the letter. He later told me that some of his promotion file and been lost, but that he would be promoted. Thus, I didn’t broach the topic of Will’s letter.
What Happened to the Players?
Will, Guy, Jess and Lee went on to bigger and better things.
Guy has been honored by his institution and has served on important national committees.
Lee went on to a great career.
Jess got a good job at a good school.
Truly has a good job at a midlevel university.
Will has been honored and went on to important and powerful positions and is very well known.
A Warning for Students and Parents
I hope that, after reading this story, everyone sees two things. The system is corrupt; and, no one should trust these people with anything – including being honest educators. They will do whatever.
(For a view of unethical behavior from someone at the highest levels of mathematics, see the bottom quote from Alexandre Grothendieck on the quotes page.)