I've seen situations like the below happen quite a few times.

Alice writes a paper. It's well-received and receives a hundred citations. Bob also works in the area, and he engages a student Charlie to study the paper. Shortly after starting, Charlie tells Bob he couldn't get from equation 10 to equation 11, in fact he thinks the derivation is incorrect. Bob is incredulous (after all the paper is well-received and has a 100 citations) and tells Charlie to check it again. A few weeks later, Charlie tells Bob he still can't get equation 11, and in fact he's increasingly convinced the derivation is wrong because he's tried it in a few different ways and always gets the same result.

Bob starts looking at the paper himself and after another few weeks he also runs out of ideas. Finally they write to Alice asking for details. Alice responds quickly with, "you've made this mistake. After correcting it and making this transformation, equation 11 follows."

The specific details vary, but the core of what happens is the same: Bob and Charlie can't do what Alice has done, but instead of asking Alice for help, they insists on trying it themselves. After weeks of struggling and many tins of coffee, they finally give up and ask Alice, who proceeds to solve the problem very quickly.

The question: why would Bob and Charlie grind away for weeks when help is just an email away? If I managed a team of employees who refused to ask each other for help, especially when someone has already solved the problem, I'd be quite annoyed. After all, time is precious.

I find this especially surprising because virtually every professor I've seen teach encourages their students to ask questions. Instructors tell their students they're welcome to interrupt during class, to approach TAs, or to visit them during office hours. They discourage their students from working without progress for weeks before asking for help, and yet they're reluctant to ask for help themselves. Why?

The only reason I can think of is that Bob and Charlie want to be sure that the results are robust. If Alice made a mistake, then they would not be able to duplicate the results, but if they just ask Alice for help, then they're at risk of making the same mistake. But this doesn't seem like a strong reason: they can ask for help but then critically examine what Alice says.

• I meant Alice, Bob, Charlie, A and B as five different people, although I could edit it if it's confusing. Edit: changed names. – Allure Mar 13 '19 at 22:26
• I think it would make the question more understandable to continue to use Alice, Bob, and Charlie throughout. – mkennedy Mar 13 '19 at 22:29
• You assume people do not ask for help, but in my experience many do. Also, possible problems: 1) colleagues do not have time to answer.2) they are direct competitors in the field, 3) teacher wants students to learn by figuring out themselves trivial details... – Greg Mar 14 '19 at 0:27
• ... also, many of us are in academia in part because we like to figure things out by ourselves, even if it takes a few weeks (or more) :) – MBaz Mar 14 '19 at 0:56
• Two reasons: 1) working things out by ourselves is quite enjoyable and it gives us a sense of accomplishment, especially if it involves working out the thinking of some 'top' researcher(s), and hence, by extension, places us at the same level as the author(s), 2) we do not want others to decipher what we are up to before we get to publish it. – Prof. Santa Claus Mar 14 '19 at 2:24

I have never been fully immune from this kind of behavior, though I've suffered less from it than others, a fact that most likely helped me land two really nice jobs. Let me survey a few reasons why I think it happens.

Note: I'm talking of mathematics, where "robustness" is not a thing, and talking to someone does not "contaminate" your thinking (unless you are really careless).

1. Bob and Charlie are too proud. They don't want to be seen asking possibly stupid questions in writing.

2. Charlie feels that he doesn't know enough to even pose a good question, and Bob doesn't care enough. (Students generally tend to have trouble gauging their level, and I have occasionally blundered into conversations I wasn't prepared for by asking a too-advanced question.)

3. Bob and Charlie have seen their questions ignored too often. (My personal experience is that the usefulness of emailing an author about a paper they wrote declines sharply with the age of the paper. If the paper is 15+ years old, they most likely don't remember anything and have the same perspective as any other reader.)

4. Bob and Charlie don't want anyone to know they are reading the paper, as they are worried of creating expectations. (This sometimes does happen -- in that an author takes a question as a stronger sign of interest than it was intended. Though it does not appear to be a big deal, but more of an awkward moment.)

5. Bob and Charlie are worried Alice will view their question as a personal attack or at least as a threat. (In my career of reporting errors, this has happened 1-2 times out of somewhere near 50. But this sort of risk aversion isn't exactly out of character for much of academia...)

• +1 for "If the paper is 15+ years old, they most likely don't remember anything and have the same perspective as any other reader.)" :-) – user3624251 Mar 14 '19 at 13:27

Bob and Charlie are not only looking to know the result or to verify it; they are also interested in understanding and having insight into the result, possibly with the goal of extending it.

If Charlie understands the result the same way Alice understands it, then Charlie is unlikely to have any insights into extending the result other than the insights that Alice has. Hence, Charlie's goal is to develop independent understanding of the result which is different from Alice's understanding.

If Charlie just asks Alice, then Charlie will now have the same understanding that Alice has (only to an inferior degree), and hence will have difficulty extending the result in directions Alice didn't think about.

• This isn't a bad explanation, but I'm feeling like it's somewhat of a just-so story. I doubt this is the main motivation behind Bob's and Charlie's reluctance to contact Alice. – darij grinberg Mar 14 '19 at 1:40

If everyone did it...

Imagine getting an email every time someone doesn't know how to proceed from A to B in one of your papers. Imagine answering each of those emails, every time.

Imagine learning exactly how to derive B from A every time you're stuck. Now you never actually have to put effort into understanding a paper anymore. Say you start out asking for help every time you don't understand it if you didn't get it in a day. Everyone is always happy to answer you, you ask every time you don't get it. What's very likely going to happen is that you start sending the email earlier and earlier...

Academics are good at what they're doing. They probably got there by being stubborn at trying.

Finally, I remember reading (but I forgot where) that one of the best predictors of mathematical skill is the amount of time you're willing to spend on a problem before you give up. Assuming that the average population of academia ranks decently high on mathematical skill, you'd expect them ot be more stubborn than the average person at solving problems.

• If everyone decided to shower at the same time, problems would arise, but that's not a good argument for not showering yourself. – Tomáš Zato - Reinstate Monica Nov 7 '19 at 16:42
• @TomášZato true, but also irrelevant to the point made here. If anything, ironically, Stackexchange is exactly the kind of place where one can see clearly how badly questions of the "please do my homework for me" variety can be received. – Tasos Papastylianou Nov 7 '19 at 20:21

I'm going to have to assume that this is some field of mathematics that you are discussing. I can't really visualize it in other, unrelated, fields, even Physics, for example, unless it is highly theoretical physics that depends, like math, on deduction.

I think that Bob and Charley are acting completely rationally and normally and congratulate them for not giving up. But to see why depends on a deeper understanding of mathematics and mathematicians that the "non-anointed" don't share.

Bob and Charlie seem to believe that they have found a gap in an argument that Alice has left too wide for understanding or has made an error of deduction. Either could be the case.

If you aren't a mathematician you likely think that mathematics is about the results. About the theorems. The theorems need to be proven. There can be no gaps but trivial ones. But trivial to you and trivial to me can be quite different things, depending on our training and experience.

I'll note that many (many) papers have been published just like Alice's. Alice could be a world renowned mathematician and can make wider jumps of logic than you or I, but Alice can also make mistakes of logic. Some arguments are tremendously complicated and it is easy to get a bit twisted up. Reviewers might not catch what is happening, so papers get published.

But, in fact, and you may need more than a doctorate in mathematics to realize it, mathematics isn't about the results.

Mathematics is about insight. And insight is tremendously difficult to gain if you have studied mathematics in a traditional way. A professor presents a theorem on the board, then proceeds to prove it. You may think that is the essence. But somewhere, perhaps long ago, perhaps last week, someone had to wonder why that statement written on the board might be a theorem at all and not just a random positioning of neat ideas. This takes insight. What problems are worth pursuing? It isn't obvious. There isn't a clear path from A to B if A is known and B is a statement that might or might not follow.

Without insight, "mathematicians" would just be wandering around in the dark, finding the occasional interesting thing, but without any method to follow beyond random guessing. Theorems don't write themselves.

So, back to the story. Lets assume that Bob (the advisor) is a real mathematician, and wants Charlie to become one. He puts Charlie to the task of studying Alice's paper, not primarily to follow the argument there, but to gain insight into the problem(s) posed. Charlie doesn't yet have the insight to see why we can expect Alice's conclusions to be right or wrong, so needs to depend on the proofs/arguments. He can't make it happen. Bob, on the other hand may have enough insight to believe the conclusions, but again, can't follow the argument. But, since insight isn't infallible, they have a problem.

Bob's real problem is that either (a) Alice is wrong or (b) he lacks the proper insight into why she is right. This is galling. So he has an even stronger incentive to gain that insight than Charlie does, so he pounds and pounds, looking for the answer.

If he just asks Alice, Bob will short circuit his search for enlightenment. Having it explained represents failure. He will never be able to gain that insight if told the answer. So he resists. And resists. Only yielding when his own work is impeded by not knowing.

A corollary to this is that when professors in math and related fields are asked for help by students they should give minimal helps, to overcome misconceptions, say. Giving the answer denies for all time the possibility that the student can grow in understanding. It isn't about the facts. It is about the insights.

An anecdote. There is a certain kind of tricky program in CS that I know can be solved, since there are well known solutions. But I've never been able (over about 40 years) to come up with the solution on my own. I don't think of it very often anymore, but I reject any hints about how I might do it, since I want that "a ha" moment for myself.

I'll also note that I already had a doctorate in mathematics before I really knew the centrality of insight. Advisors need quite a lot of it so that they can help doctoral students find reasonable and important problems. Even better if they can impart some of that insight to the students, but it doesn't always happen.

The story you describe has people behaving irrationally. If everyone behaved rationally, this would not happen. Asking why people "tend to" behave irrationally is not well defined.

Alice. It could be that Bob and Charlie are assuming that Alice is irrational, and want to avoid contacting her. This is belied somewhat by Alice's prompt, helpful response (though, one could argue that she should not have had something so difficult in her paper without explanation).

Charlie. It is reasonable that Charlie, as a student, would assume he is missing something obvious and does not want to waste Alice's time. Indeed, having Charlie spend a few days digging into this is probably a helpful exercise for him. But after he spends some days doing his due diligence, it is time for him to contact his advisor, which is exactly what he seems to have done.

Bob. It is reasonable that Bob will spend a few hours with Charlie to gauge his understanding of the problem and related work as a whole. Further, them trying to figure it out together is a useful pedagogical and (potentially) even mathematical discussion for both of them. But after a few hours of this, it is clear that Charlie is up to speed and Bob cannot get the answer after a reasonable amount of time. This is where they should have called Alice -- any time spent beyond this is irrational and difficult to justify (unless Alice is indeed so difficult to work with [irrational] that it's better to avoid her at all cost).