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I have attended quite a few large conferences in mathematics where experts from different fields participate. Naturally I talked to some people and asked them a very basic question: what they are working on. In some cases the answers were not very precise and even rather misleading. I had the feeling that these people tried to make an impression that they work in one field while they work in another one.

One of the worst examples of such discussions was as follows. The person said that he works in interplay of random series and quantum fields. I never heard that there is a connection between the two subjects and asked to elaborate. His explanations were chaotic: he started to explain on random series without any mention of quantum fields. I asked again how it is related to the latter. He said something about quantum field without mention of random series. After a couple more questions he continued to jump between the two subjects without explaining the relation. The funny thing is that after this discussion I found his list of publications and realized that all his publications belong to a third area which has apparently nothing to do with the two above topics. To my greater surprise, this person is actually a respected mathematician from a good math department.

My impression is that the situations as above are not exceptional. Am I wrong? How typical they are? Is there any rational explanation of such a behavior?

My question might be non-appropriate for this site, sorry about that. Personally I find the situations I have been in quite strange, and I would like to have any comment if it is something typical in academia (at least in mathematics) or not.

  • Could it be a case of working in a third area on problems motivated/inspired by questions from the other two? – Anyon Aug 5 at 11:08
  • My impression it was not the case. But even if it was the case, it is misleading to say that he he works on random series/quantum fields: he still works in the third area! – user111559 Aug 5 at 11:12
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    In my experience, this is also really common in applications for grants. Number theory students from my university for example are advised to write about what great applications Number Theory has (in cryptography and physics), even if they do nothing appliciable at all. – user111388 Aug 5 at 13:44
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    This is more rant than question. – Anonymous Physicist Aug 6 at 2:45
  • Not all connections are easily seen or explained, and sometimes it's just a hunch. See for instance Langland's programme. Assuming that your conversation partner who was not able to explain what he was thinking about is actively trying to mislead is a very unfriendly interpretation. – Captain Emacs Aug 6 at 21:36
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There is nothing strange about this. Not everyone is good at translating the very technical problems they are working on, without advance preparation, on demand and at a moment’s notice, into a polished speech that a random person they encounter (mathematician or not) will find understandable. I think the correlation between what you observed and the quality of this person’s work is essentially zero.

As for the fact that you found his description “misleading” because his papers suggest he usually works on other topics: well, he may be trying to do new work in an area he hasn’t worked on before. This is often my situation, and my own answer when people ask me what I’m working on (especially if the question is posed in the present tense as in your description) will occasionally have little or nothing to do with anything I’ve published.

  • This might be possible, but I think I observed not the situations when a person was not ready to give a technical explanation. My question was about his general fields of interests and not on which concrete problem he is trying to solve right now. If he answered that he is working on interactions between field A with a very different field B, I expect he should be able to explain at least some concrete connection between them. And I repeat, I think there is a pattern in such behavior, not just one example I described. – user111559 Aug 6 at 7:02
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    @user111559 well, all I can say is that I don’t see the strangeness in your description of what you experienced. In particular I don’t see any reason why the professor would intentionally mislead you about such an innocuous question and in the way you feel you were misled. People are sometimes self-aggrandizing in contexts where they think it might benefit them, but this doesn’t sound like a situation where that would make sense as an explanation. Only you were there though, so my feedback probably has limited value anyway. – Dan Romik Aug 6 at 16:29
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What you get in such situations is the "elevator talk". Some basic suggestion of what the person is "thinking about" that can be "explained" in the time length of an elevator ride. It isn't very well formed. If it were well formed then it would probably be already a publication or one in process and you would get conclusions, not speculations. They are ill-formed thoughts that come prior to the insight necessary to put it together.

Doctoral students are advised to have an elevator talk prepared in advance about their research so that they don't sound so disjointed as the example you give. This is because the people you meet might have some small suggestions to help with those insights. But mostly just so that you don't stutter when asked, casually, what you are working on.

It may also be that in the case you describe the person was talking about his/her long term goals, not something considered to be imminent. That would explain why the published work seems quite different. You are being told "I think there is some relationship here, but don't really see it yet. Looking hard, though." Chaos may be entirely normal at the early stage of a new exploration. If it weren't, math and science wouldn't be as hard as it is.

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Part of it is the imperfection of human nature amplified by the imperfections of society. In an ideal world, the answer to the casual question "What are you currently working on?" would be "I'm currently stuck on this particular lemma" followed by the formulation a decent graduate student working in the field would easily understand. Then it would be your turn to channel the conversation into various ways from "What do you want to use it for?" to "What partial cases can you solve?" to "What techniques have you tried and where is the difficulty" to... depending on how good/bad your erudition, understanding of the subject, technical skills, and the ability to think on the fly of a new topic are.

The imperfection of the human nature is that one often wants to make a good impression more than to convey the information, so one starts with some "big" picture he believes his work fits in and tries to justify the importance of his project and, in the worst case scenarrio, of himself too. It takes some courage to openly declare that no human being and/or project have any particular importance or value in the grand design of this Universe, so we'd better drop all pretense and just try to cooperate in the most efficient ways to achieve something before our time as individuals or species runs up. One often perceives the question "What are you doing?" as "How can you justify your existence?" and tries to answer that instead as if the asking person were a prosecutor on the Last Judgement.

The society imperfections amplify this in several ways. First, there is an objective problem of allocating limited resources to competing individuals. This leads to direct comparisons of really incomparable things and, since no really meaningful comparison can be made (or, rather, too many justifiable comparisons exist with contradicting results), the pseudo-measures like "importance", "general interest", and many others abound. The worst case scenario is that they are measured on scale from 0 to 10 and the points are then added up with some fancy weights. There is nothing one can do about it until the supply exceeds the demand (which is not going to happen soon), so one is constantly kept on guard in academia and elsewhere as to how he is going to present his work, where to submit his papers, what to do to get good student evaluations, etc. This insecure feeling may easily extend to the cases where there is absolutely nothing to fear of, hide, or fight over, like casual conversations about science. However, this is only half-evil because this insecurity can also serve as a drive to do something instead of lying on the sofa and spitting at the ceiling.

The real "root of all evil" is the oxymoronic expression "intellectual property" and the whole convoluted culture around it. Some people will never openly tell you what they are really working on just because they are afraid that you may "steal their ideas" (as if an idea, by its very nature, were not a subject for sharing to the extent that sharing it is the only way to support its very existence), or may "want some share of credit", or for other equally non-sensical reasons (IMHO). This is how many people perceive it even if their scientific reputation is beyond any need to defend at each corner. It also gets reflected even in popular publications about science. I recall the passage about Andrew Wiles somewhere, the sense of which was "Now he had a difficult task to find a person who would be able to help to fix the gap but not take the whole credit for the proof" (Richard Taylor). The NY Times article puts it less bluntly but you'll easily see that the underlying meaning is there. This creates extremely distorted attitudes towards the meaning of the whole endeavor (again, IMHO), which are rather widespread.

At last, there are fashions. You have as many people who want to boast about working in fashionable fields as those who want to wear fashionable dresses and haircuts. That usually is responsible for various "buzzwords" in introductions to mathematical articles or on hiring committee discussions (currently it is "big data", before that we had "mathematical biology" and "nano-science", I'm not trying to predict what comes next) and can spill even into casual conversations when two people are sniffing each other for the first time. As any fashions, the mathematical ones may make sense or make no sense, but they are all destined to come and go. Unfortunately, we'll see the distilled product our generation of mathematicians produced only 50-100 years later, which is beyond the lifespan for most of us.

So, I would say, make nothing of that conversation except the usual conclusion that when you are asked the same question, try not to behave in the way you disliked. I'm not saying "Try to be always straight and honest": if you ever write a grant proposal, prepare a file for promotion, or try to convince other members of the hiring committee that your candidate is "the best", you'll find that this is plainly impossible in this world if you want to get something more than to preserve your "integrity" (the latter is possible in principle but the price is the one Grisha Perelman paid and there was a lot of misunderstanding there on both sides as far as I can tell). Just try to impose some limits on stretching your conscience and look at the mirror now and then before judging others too hard (I certainly will plead guilty myself to whatever "crime" I described in this long rant if somebody wants to bring the charges).

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