I uploaded my work to the Arxiv on the 29th of April, 2021.
Thom's Gradient Conjecture Paper
So I was astonished recently to come across a paper by Beomjun Choi and Pei-Ken Hung, uploaded on 27th May 2024, with almost exactly the same title and abstract as my own paper. Like my paper, they use the Lyapunov–Schmidt reduction approach to reduce the problem to the finite dimensional case. Beomjun Choi is from the department of mathematics at Pohang University of Science and Technology in Korea, and Pei-Ken Hung is from the department of mathematics at the University of Illinois Urbana-Champaign in the United States.
Someone Steals my Thom's Gradient Conjecture Paper
Even more astonishing was that, despite it's profound similarity to my own paper, it made absolutely no mention of my paper at all. My paper is not mentioned in the abstract, it's not mentioned in the introduction, and it's not mentioned in the extensive references.
I then noticed that the same two authors also uploaded another paper, 14 months earlier, on Thom's gradient conjecture in infinite dimensions called "Asymptotics for slowly converging evolution equations". Again totally without attribution despite the fact that some of the ideas were taken from my own preprint.
Earlier paper also borrowing from my ideas without attribution
On Beomjun Choi's personal page, he notes his preprint as follows:
Thom's gradient conjecture for nonlinear evolution equations, with P.-K. Hung. (2024). This is major improvement over the previous preprint 'Asymptotics for slowly converging evolution equations' with P.-K. Hung.
In other words, he mentions how his latest preprint draws upon his own previous preprint, improving and completing the attempted results in that paper. Yet he makes no mention of how both preprints heavily draw on ideas from my own preprint.
This is quite simply disgraceful.
Before beginning to write a paper, the first thing a scientist or mathematician must do is a literature review to make sure no one has already published the result. Otherwise, you'll spend months or years doing again something that has already been done. Work that copies or duplicates other people's work can't be published, and academics need publications to get jobs. But even besides that, one begins with a literature review simply to find all the relevant papers which might be useful in their work.
Beomjun Choi and Pei-Ken Hung decided to write a paper on the topic of Thom's gradient conjecture in infinite dimensions. A search on the Arxiv for "Thom's Gradient Conjecture" at that time would have shown my paper in the number one position. How could they remain totally unaware that this was my idea, and I had already written a paper on it?
I decided to contact the authors.
"We have indeed read your preprint when we wrote our paper," they said.
Indeed, they didn't stumble upon exactly the same idea as me by coincidence. Rather, they lifted the idea from my own work, benefiting from my own mind, time and labour.
But they didn't just "read my paper", as they put it. They got the whole idea to generalise Thom's gradient conjecture to infinite dimensional parabolic evolution equations, and to do so using Lyapunov-Schmidt reduction, from my paper. They stole enormously from my work by taking my idea, and chose not to even mention that they had taken this idea from me. Among an extensive list of 58 references, the paper they got the whole idea from is not even mentioned. It takes a considerable investment of time to prepare a paper like the one they have. Why did they devote so much time to my idea, rather than one of the many great ideas of their own? Clearly, they believed my idea was much better than any of their own ideas. So much so that they were prepared to risk any reputational damage that might result from appropriating someone else's preprint. Yet I wasn't deserving of any acknowledgement or credit in their paper? Not even a footnote in small font?
Beomjun and Pei-Kin both work full time as pure mathematics researchers, and there's two of them. It's likely that the pair of them worked full time on their paper for somewhere between 1 and 3 years. It's pretty embarrassing that they need to steal ideas from an individual who can only do research with a small amount of spare time outside of work.
The authors also told me that they believed there was an error in my paper. They apparently believed that, if there is a mistake in a mathematician's preprint, another mathematician may swoop in, write their own very similar paper, and get 100% of the credit for the result on account of being technically the first over the finish time with a totally correct paper. This is not a point of view I subscribe to. If I hadn't written and uploaded this preprint, their paper simply would not exist today. Period. So my contribution to their paper is substantial. In fact, when a professor provides an idea for a paper to his PhD student of postdoc, he or she is often not only an author but first author, even if the student did almost all of the work and ironed out all the details.
Mathematicians and other researchers regularly use preprints to share early and unfinished work with other researchers. It's simply taken as a matter of integrity that other researchers will not attempt to finish the work first and steal credit from the person who had the good idea for the paper in the first place.
Now, there are a few different kinds of errors in mathematics. When you write 20 or 30 pages of symbolic calculations, it's likely there are some small mistakes and typographical errors. But these mistakes are not considered to invalidate the work, as they are easily fixed. Next, there are things that are indeed substantially wrong, but also do not really invalidate the paper as the author can usually fix the argument or find an alternative, "plugging the gap". Sometimes, it is obvious that the overall thrust of the proof is correct, even if some of the details need fixing. Finally, there are errors that are absolutely critical, where the whole methodology of the paper simply will not work, and the authors need to put the entire paper in the bin and go back to the drawing board.
So where on the spectrum did the error they had identified in my paper lie? It appears that the error is simply in some of the details, and the overall approach of using Lyapunov–Schmidt reduction to reduce the problem to the finite dimensional case is sound. Indeed, they used it themselves after getting the idea from my paper.
Now, I knew when I uploaded the paper that there might be an oversight. I lacked the time to proofread it extensively, and not working as an academic anymore, I didn't have coauthors to check it, nor a pair of peer reviewers to do further checking. (I decided not to submit it to a journal, as the editorial process and reformatting requirements are quite time consuming, and I don't have a lot to gain). But, I didn't think it mattered. By uploading a draft, I was still sharing my idea with the mathematical community, and if anyone took an interest in the paper and communicated to me any issues, I could fix those issues at that time. Isn't the purpose of the Arxiv partly to allow people to upload draft papers, which might not be in their final state yet? Indeed, the behaviour of these authors totally undermines the ability of researchers to discuss their work with the community until it is totally complete and published, for fear of having their idea stolen. I believe the academic community refers to this activity as "scooping" someone else's paper. If I continue to upload preprints that might not be perfected yet, perhaps Beomjun and Pei-Ken or others like them will continue to swoop in, publish their own versions of my papers and congratulate themselves on getting all the credit. Contrary to what these two authors believe, a paper that is unfinished or not as yet correct is not worthless. On the contrary, the final version of any paper will draw heavily on earlier incorrect iterations it passed through. By uploading draft papers, an author is valuably participating in the academic process.
There are two courtesies that are common in research. The first is that, if the idea for the paper came from someone else, the authors will usually thank such and such for suggesting the topic of the paper. The second is that, if you find an error in someone's paper, you notify them so they can address it. The author will then add a note in their paper thanking such and such for pointing out that there was an error in a previous version. In general, people will often have an acknowledgement section where they will say things like, "I'd like to thank such and such for interesting conversations..." It is a long standing and important academic tradition to acknowledge other contributing persons.
Had they contacted me to point out any error, I would have set about rectifying it and thanked them in my paper for pointing it out. Yet they never contacted me, either about an error, or to express interest in the work I had done. Nor to suggest working together on this or a related paper. Had I been unable to correct the paper by myself in the limited amount of time I could commit to it, perhaps they could have become coauthors and shared credit. Since I was the one who had the idea for the paper, and had already put a lot of time into it, it seems eminently reasonable that I should be one of the authors on any subsequent publication.
I can guess why they never contacted me to point out the error or discuss collaboration. They didn't want to tip me off to the fact that they were attempting to scoop my work, until they had already completed theirs.
Instead, they began quietly preparing their own paper on the exact same topic. Their mentality is that, if they can get the first completely "correct" proof published, all the credit goes to them, rather than me. I do not agree with this petty and destructive view of the world, where one may steal an idea from someone else, complete it first, and become the winner. Eventually, they uploaded a paper that made absolutely no mention of the debt they owed me from having lifted the entire idea for this project out of my own work. Instead, they're going to head off to a journal with a paper on exactly the same topic, which they weren't the ones to think of, and making no mention of my considerable efforts on this project, as if the whole idea ought to belong to them.
There are similarities to the incident with the Chinese mathematicians who claimed that there were "gaps" in Perelman's proof of the Poincare conjecture, and rushed off to publication with the gaps filled, hoping to claim the lion's share of credit on account of being first to totally complete the proof, as if Perelman had little to do with it. Now it could be that Perelman's work didn't really have a flaw, whereas my paper has a flaw which ought to be fixed. Nonetheless, I do not agree that people may conduct themselves in a manner to maximise their own reputations, with no regard for their fellow scientists. That they may, upon seeing someone else's allegedly unfinished work, swoop in and finish it and obtain all the credit on account of being technically the first to have a correct and finished paper. Perelman was quoted as saying, "I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest".
The idea to generalise Thom's conjecture to parabolic evolution equations in infinite dimensions was mine alone. It's clear that they got the idea for the paper by lifting it straight out of my own. Having no respect for me or my work, these two "scholars" have intended to take all credit for my idea, not even acknowledging my work.
They simply pretend my paper doesn't exist.
Other mathematicians will have whatever opinions they might have. But to me, this behaviour is not acceptable.
And it doesn't make me regret leaving academia one bit.
Actually, they remind me of the penguins from an Attenborough documentary, who construct their own nests by stealing stones from the nests of other penguins when they're not looking.
Pebble stealing penguins
The sole goal of these researchers (and more like them), is to increase the length of their own publication list. Not respecting colleagues. Not working together towards a common goal. Just focusing on increasing their own status at the expense of everyone else's. If this is how the academic mathematics community intends to treat my contribution, which I make with my very limited spare time, I'll likely stop writing papers and do something else with that time. This is bad news for Beomjun Choi and Pei-Ken Hung, as they're apparently reliant on me for ideas.
A maths academic conducting research:
Gradient flow of the norm squared of a moment map
Searching this paper for the word "Thom", there is only one match, in the references. Finding the place in the text where this reference is cited, we find a discussion with no relationship whatsoever to Thom's conjecture for parabolic equations.
The Ricci flow for simply connected nilmanifolds
This paper mentions Thoms' conjecture (the finite dimensional one) in only one place, in a discussion with no relationship whatsoever to Thom's conjecture for parabolic equations on infinite dimensional spaces.
The Ricci flow in a class of solv manifolds
Searching this paper for the word "Thom", there is only one match, in the references. Finding the place in the text where this reference is cited, we find a discussion with no relationship whatsoever to Thom's conjecture for parabolic equations on infinite dimensional spaces.
There are two courtesies that are common in research. The first is that, if the idea for the paper came from someone else, the authors will usually thank such and such for suggesting the topic of the paper. The second is that, if you find an error in someone's paper, you notify them so they can address it. The author will then add a note in their paper thanking such and such for pointing out that there was an error in a previous version. In general, people will often have an acknowledgement section where they will say things like, "I'd like to thank such and such for interesting conversations..." It is a long standing and important academic tradition to acknowledge other contributing persons.
Had they contacted me to point out any error, I would have set about rectifying it and thanked them in my paper for pointing it out. Yet they never contacted me, either about an error, or to express interest in the work I had done. Nor to suggest working together on this or a related paper. Had I been unable to correct the paper by myself in the limited amount of time I could commit to it, perhaps they could have become coauthors and shared credit. Since I was the one who had the idea for the paper, and had already put a lot of time into it, it seems eminently reasonable that I should be one of the authors on any subsequent publication.
I can guess why they never contacted me to point out the error or discuss collaboration. They didn't want to tip me off to the fact that they were attempting to scoop my work, until they had already completed theirs.
Instead, they began quietly preparing their own paper on the exact same topic. Their mentality is that, if they can get the first completely "correct" proof published, all the credit goes to them, rather than me. I do not agree with this petty and destructive view of the world, where one may steal an idea from someone else, complete it first, and become the winner. Eventually, they uploaded a paper that made absolutely no mention of the debt they owed me from having lifted the entire idea for this project out of my own work. Instead, they're going to head off to a journal with a paper on exactly the same topic, which they weren't the ones to think of, and making no mention of my considerable efforts on this project, as if the whole idea ought to belong to them.
There are similarities to the incident with the Chinese mathematicians who claimed that there were "gaps" in Perelman's proof of the Poincare conjecture, and rushed off to publication with the gaps filled, hoping to claim the lion's share of credit on account of being first to totally complete the proof, as if Perelman had little to do with it. Now it could be that Perelman's work didn't really have a flaw, whereas my paper has a flaw which ought to be fixed. Nonetheless, I do not agree that people may conduct themselves in a manner to maximise their own reputations, with no regard for their fellow scientists. That they may, upon seeing someone else's allegedly unfinished work, swoop in and finish it and obtain all the credit on account of being technically the first to have a correct and finished paper. Perelman was quoted as saying, "I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest".
The idea to generalise Thom's conjecture to parabolic evolution equations in infinite dimensions was mine alone. It's clear that they got the idea for the paper by lifting it straight out of my own. Having no respect for me or my work, these two "scholars" have intended to take all credit for my idea, not even acknowledging my work.
They simply pretend my paper doesn't exist.
Other mathematicians will have whatever opinions they might have. But to me, this behaviour is not acceptable.
And it doesn't make me regret leaving academia one bit.
Actually, they remind me of the penguins from an Attenborough documentary, who construct their own nests by stealing stones from the nests of other penguins when they're not looking.
Pebble stealing penguins
The sole goal of these researchers (and more like them), is to increase the length of their own publication list. Not respecting colleagues. Not working together towards a common goal. Just focusing on increasing their own status at the expense of everyone else's. If this is how the academic mathematics community intends to treat my contribution, which I make with my very limited spare time, I'll likely stop writing papers and do something else with that time. This is bad news for Beomjun Choi and Pei-Ken Hung, as they're apparently reliant on me for ideas.
A maths academic conducting research:
UPDATE:
The two authors have replied to me to make the following claim: "The infinite dimensional Thom’s conjecture is an open problem and well-known in the community. It was not your idea to consider it."
That's surprising, because when I decided to work on this topic I found no existing research, or I would have cited it. They have provided four references to prove that the topic is well-known. Below, I show that not one of these references mentions Thom's conjecture for parabolic evolution equations. Not one of them mentions Thom's conjecture in an infinite dimensional context. All four papers simply site the original finite dimensional version of Thom's conjecture to prove results that are entirely unrelated to the topic of the paper they plagiarized from me.
Arnold Thom Gradient Conjecture for the arrival time
This is the only one of the four papers that has the remotest similarity to the topic of their own (and my) paper. And the similarity is remote. They are studying the solution of a particular elliptic equation. Not a parabolic equation, not the class of all parabolic equations - a single elliptic equation. They're not even studying the elliptic equation itself, but the function that solves it. They show that, if one were to for some reason consider the gradient flow of this finite-dimensional solution function, it would satisfy the original finite dimensional Thom conjecture. At no point do they consider Thom's conjecture for any parabolic evolution equation or any infinite dimensional context. Nowhere do they suggest Thom's conjecture for all parabolic evolution equations in infinite dimensions, much less study it. Interestingly, this paper is not cited by Choi and Hung in their own paper. If they consider this to be their primary source for this "well-known" idea, why have they not cited it? The remaining three papers aren't cited either. Probably because they have no relevance whatsoever to Thom's conjecture in infinite dimensions.
The two authors have replied to me to make the following claim: "The infinite dimensional Thom’s conjecture is an open problem and well-known in the community. It was not your idea to consider it."
That's surprising, because when I decided to work on this topic I found no existing research, or I would have cited it. They have provided four references to prove that the topic is well-known. Below, I show that not one of these references mentions Thom's conjecture for parabolic evolution equations. Not one of them mentions Thom's conjecture in an infinite dimensional context. All four papers simply site the original finite dimensional version of Thom's conjecture to prove results that are entirely unrelated to the topic of the paper they plagiarized from me.
Arnold Thom Gradient Conjecture for the arrival time
This is the only one of the four papers that has the remotest similarity to the topic of their own (and my) paper. And the similarity is remote. They are studying the solution of a particular elliptic equation. Not a parabolic equation, not the class of all parabolic equations - a single elliptic equation. They're not even studying the elliptic equation itself, but the function that solves it. They show that, if one were to for some reason consider the gradient flow of this finite-dimensional solution function, it would satisfy the original finite dimensional Thom conjecture. At no point do they consider Thom's conjecture for any parabolic evolution equation or any infinite dimensional context. Nowhere do they suggest Thom's conjecture for all parabolic evolution equations in infinite dimensions, much less study it. Interestingly, this paper is not cited by Choi and Hung in their own paper. If they consider this to be their primary source for this "well-known" idea, why have they not cited it? The remaining three papers aren't cited either. Probably because they have no relevance whatsoever to Thom's conjecture in infinite dimensions.
Gradient flow of the norm squared of a moment map
Searching this paper for the word "Thom", there is only one match, in the references. Finding the place in the text where this reference is cited, we find a discussion with no relationship whatsoever to Thom's conjecture for parabolic equations.
The Ricci flow for simply connected nilmanifolds
This paper mentions Thoms' conjecture (the finite dimensional one) in only one place, in a discussion with no relationship whatsoever to Thom's conjecture for parabolic equations on infinite dimensional spaces.
The Ricci flow in a class of solv manifolds
Searching this paper for the word "Thom", there is only one match, in the references. Finding the place in the text where this reference is cited, we find a discussion with no relationship whatsoever to Thom's conjecture for parabolic equations on infinite dimensional spaces.
