I've been studying uses of quaternions to study various types of orbifolds. The important thing here though is that I came across an absolutely incredible result due to Vahlen in 1901, that apparently received no attention until Ahlfors revamped the idea in 1985 using more contemporary methods. The result is central to my current research. In case you're familiar with the concept, it is the construction now called Vahlen matrices.
The problem with Vahlen, as you may have guessed by the title, is that he was about as much of a Nazi as a person could be. He was in the SA, the SS, accused brilliant Jews of plagiarizing Aryans, helped the Third Reich expunge Jews from the scientific community, etc. He even supported the Nazi party before its infamous rise to popularity.
My questions are:
- What is the likelihood that Vahlen's results were neglected due to this political misfortune?
- What are some similar instances, particularly in mathematics?
- What is the etiquette of discussing a great result by a person who lead a morally reprehensible life?
Regarding the third question, Ahlfors simply writes about his math, which I think is the right way to go for a journal article. But what about a lecture or more general discourse among the community? I would feel weird if I were to give a lecture where I'm praising a guy who may have contributed to the extermination of an audience member's family. I have kind of a dark sense of humor, so I'm likely to mention the Naziism and poke fun at it ... maybe use it as an example for why you have to check everyone's results regardless of their other results. Personally I would find it funny to denote the Vahlen matrices by a swastika, but obviously this would be extremely inappropriate in a public setting where the intention (of making fun of Nazis) might be misunderstood.
A more specific issue I'm having is that there is a lot of conflict about the notation for Vahlen's discovery, as other notation was developed for 84 years without it. It is an obstacle because we literally have different definitions for identical symbols all over the place. My feeling as that the clearest notation would be to use a $\mathcal{V}$ for the Vahlen matrices (which I have not seen in any papers thus far) and move on, but I wonder if there is a tendency in the academic community to avoid even that. I don't want even an iota of a suspicion of being sympathetic to this man's priorities.
An important note here is that Vahlen's matrices are in the domain of pure math. That means their development had nothing to do with any sort of experimentation, and are quite disjoint from these other aspects of Vahlen's life.
Follow-up, Feb. 10, 2017: This question has been edited to make it more clear what is being asked and to better align it with the chosen answer, after facing some controversy about its appropriateness for this site. Some things that have since been altered are quoted in the chosen answer (and referred to extensively in comments and other answers) because they were evoking debates and conversations on the site rather than just answers to a question.
Follow-up, Sept. 24, 2017: Without naming any names, I wanted to add that some very established mathematicians I've been discussing my work with have unequivocally recommended omitting Vahlen's name from any constructions I use in my paper, specifically because of the political history. As in, don't call them "Vahlen matrices," call them "Ahlfors matrices," and things like that. Regardless of whether or not one agrees with that sentiment, to me it is concrete evidence of Vahlen's Naziism's effect on what credit he might receive for his mathematical work.
Answer
I think there is no academic issue here.
The problem with Vahlen, as you may have guessed by the title, is that he was about as much of a Nazi as a person could be. He was in the SA, the SS, accused brilliant Jews of plagiarizing Aryans, helped the Third Reich expunge Jews from the scientific community, etc. He even supported the Nazi party before its infamous rise to popularity.
I looked into Theodor Vahlen, and I agree that he was a morally reprehensible individual. But this is irrelevant to a discussion of his work: he proved the theorems that he proved whether he was good, bad, or whatever. As is well known, the Unabomber is a published mathematician. His six papers have eight citations on MathSciNet, three of which came long after his capture, e.g. see here. (Though I do not know for sure that the author of this paper was aware that the T.J. Kaczynski whose work is cited is the Unabomber, it seems likely: the author is an American, and among Americans this name is well known to say the least.)
I was wondering what the likelihood is that his results were neglected due to this political misfortune. I was also wondering if people know of similar instances, particularly in mathematics. It seems like whenever I look up the politics of a respectable mathematician, they are either nonexistent, or equally respectable. I don't know if we tend to discredit people like this, or if people like this tend to not produce good results, or what.
In my opinion this is unlikely. There are very famous mathematicians who were, to lesser or greater extents, participaters in the Nazi movement. Perhaps Ludwig Bieberbach and Oswald Teichmuller are the two leading examples: these are household names in mathematics, and that they were intimately (and reprehensibly) involved in the Nazi movement is also very well known. (For that matter, I am not convinced that Vahlen's work is so little known. It is described in the wikipedia article linked to above, for instance.)
In my personal opinion, it is worth knowing when a mathematician (or other academic) has done reprehensible things in their personal life. Some years ago I compiled a list of "greatest mathematicians" on MathOverflow: I limited myself to choosing at most one mathematician born in a given year, but in some cases I included "honorable mentions." When I got to Teichmuller, I did not want to use the word "honorable" to describe him, so I wrote "dis/honorable mention." That was a personal decision (and by the way, I am partially of Jewish descent, so it is really not for me to forgive or forget such things). But I included him on the list anyway: that he was a terrible person does not influence his mathematics one way or another.
I'd like to just use a big-ol' script V for the Vahlen matrices (which I have not seen in any papers thus far) and move on,
There is no problem with this.
but I don't want even an iota of a suspicion of being sympathetic to this man's priorities.
We don't endorse the life of Teichmuller when we talk about Teichmuller space or Bieberbach when we talk about Bieberbach's Conjecture. We credit them with their work, as we must.
It would also be hilarious to just use a swastika, but that joke might not be funny to some people (understandably).
I am not laughing at all. Please do not do this.
Finally, you can read much more about mathematics in Nazi Germany from this book. Again, I think it is good to know these things.
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