How to stop a colleague from asking for my help in solving a very difficult problem?

Question

Summary: My colleague is asking for my help in solving fundamental problem. They are having troubles on basic level, and I don't have time to guide them through it. How I can politely avoid wasting their time AND my time?

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I am a computer scientist (research focused on machine learning and statistics) and where I work I have a mathematician colleague. He is a bit obsessed with millennium problems (things like P vs NP, SSP, etc.) and so far he has tried to come up with ways to solve these two problems, but his 'solutions' so far are poor at best mostly due to his ignorance on the subject.

Now, I admire the interest and tenacity he goes about these things. However, he doesn't know much about algorithm complexity, hasn't given me any indication that he has read about what approaches have been tried/used, keeps trying random stuff and asking me to check if I think his ideas are sound or to verify them, which I find annoying since it takes a lot of time to disprove him or to refute each of his attempts (specially because I don't want to be hostile, since I barely know him).

So, I'd like a polite way to either discourage him from working on these problems because I don't want to dedicate time to this (I need to read and study to enter a PhD program and I also believe he's clearly underestimating the problems) or to discourage him from asking me about it without being rude.

Answer 1

You describe pretty well in your question what you want to communicate, so use that:

Hey X, while I admire your interest and tenacity for these problems, these are very hard problems and I do not have the time to help you with this.

Simple, straightforward, you commend him for his motivation and do not comment on their skills, you give the motivation to not do this purely based on your own motives (lack of time).

Answer 2

Like a lot of things, "I-statements" work well, taking any lack upon yourself, which means they aren't out there and perhaps perceived as criticism or arguing points.

You know, I've been thinking about all these problems. These are problems that the best mathematicians on the planet haven't found approaches to solve. They have fiendish subtleties or missing knowledge. They get amateurs regularly convinced they have answers, who have basic knowledge compared to that needed for a serious attempt.

I admire the effort, but I can't actually help. If your papers have rudimentary beginner errors, then they don't work, and if they don't have rudimentary beginner errors, [REMOVED SEE COMMENTS] I don't have anything like the skill or time needed to check for non-rudimentary errors. Which to be honest, they will probably turn out to have.

Half a job is no job at all, and I don't have the skill, and I don't want to make you think I could, even if I had the time.

I have to prioritise my own work, and I know how much work a good honest review takes. And you'd want reviews of approaches to problems that have defied giants. I don't have even close to that kind of time available, to track errors down or form any kind of useful opinion. I'm sorry. It's not possible, even slightly.

Pick what's useful out of that lot, and adapt it as needed, but that sort of approach overall.

If argued, you could read, and perhaps tactfully remind him, what happened with another problem of that level, Fermat's Last Theorem. World class mathematician reckoned he would have to dedicate close to a decade to master all relevant knowledge and techniques, asked other world class specialists in the field to check his work - and even then between them, they missed the errors while working on the problem.

You just don't have that level of skill or time. Be honest, say so, and tell him you won't lie to him, about that, or the time needed to check proofs to get an idea if they may work.

Answer 3

From a comment:

I want to discourage him from trying to solve it while underestimating the problem or that he stops bothering me about it.

Okay, so you have something between conflicting or hazy priorities here. First, I'll recommend that you get your priorities straight, specifically: (1) you stop wasting time on it, and (2) your colleague stops wasting time on it. It would be nice if you could do both. But failing that, your top priority is to yourself; and after all, you can control your actions, but not another person's, so this is the only feasible ordering.

I'll say that I've brushed up against this kind of thing once in a while, so I know the frustration you're talking about. A few years back I had a student indeed fall into the Collatz Conjecture, despite both the textbook and myself warning him that it's been a time-waster for generations of mathematicians. He was sending me pages of gobbldeygook and asking if he was making progress (this being a community-college student who couldn't reliably prove that 2x + 6 was even for an integer x). I gave him one clear warning that he should definitely stop and focus on our classwork. As he didn't follow that advice, I basically had to wash my hands of him and simply hope for the best.

So in that regard, I suggest a like single attempt: advise your colleague that they should probably not pursue this path, because it's an overwhelmingly deep subject. Do that once, period. If you don't do that, that it's entirely possible that you'll be dragged down with your colleague's obsession.

Now, if you really can't find any way to say "I'm not doing this anymore" without sounding rude, you might consider a truthful-but-diplomatic approach, like:

I'm really busy right now, so I'm not sure when I'll have a chance to get to this. I'll put it on my tasklist and see if I can get to it after other priorities.

Then do that. If you do in fact get some free time a week or a month later, maybe look at it if you're curious. If not, so be it. If he continues to send stuff after that, prioritize appropriately. Maybe next time it takes months or a year before you have space for it.

Another thing to consider is to expect to see some single "big idea" that convinces you he's got a never-before-seen strategy that gives him a leg up that no one else has seen to date, before you spend any time on reading the body of a paper. Avoid getting lost in the weeds of details. R.J. Lipton has written on this in the past, in the context of P = NP Proofs; and some of the links there in comments to other sites are interesting, as well.

But frankly just finding some way for you to stop dealing with it should take the topmost priority.

Answer 4

From the comments you say " if I just let him waste years on this without telling him he could be using his time on more fruitful results".

So tell him exactly this. Tell him that he may spend 5 years trying to solve this problem, with possible no outcome, or he can tackle other problem with a time-span of 1-3 years. Remind him that money/grants/bursaries for young researhcer are granted on the basis of what has been done in the previous 1-3 years, so he may very well end up with nothing in his hands in 3 years, and no funding possibilities in 3 years.

Then, it is his call, not yours, to judge how they spend their time.

When you say, "I wouldn't be true to my own researcher principles if I just let him waste years on this without telling him he could be using his time on more fruitful results" I miss your point. Results are not the goal of science. The way to getting the results is science. So he may very well not get any results (and that is perfectly fine, in research in an ideal world), but the issue is that he is not doing good science, not that he will get no results.

If you do not want to cut him off completely, focus on teaching him how to fish (it will not take you much time), not in providing the fish :) .

By the third time you explain him how to find the relevant literature for his problem, he will either give up getting in touch with you or get on the right path.

Answer 5

Here are two useful questions you can ask yourself;

1. "How would I want someone to set boundaries with me if the situation were reversed?", and
2. "How would I approach this same situation if this were my child?"

You can never know how someone else thinks, or how they will react to a situation. But these two questions will help give you the best perspective on this situation.

Why? Because the first question will help you frame your communication compassionately and respectfully, while the second question will remind you that your goal here is not to solve their problems for them.

It's to support them and encourage them into becoming their best, all by themselves.

Answer 6

Adding to @Jeroen's answer, what about something like this?

I admire your tenacity at wanting to make a contribution to these problems. If you want to make a contribution in these areas, you'll need to read up on <INSERT THEORIES HERE> to get the foundation, then I recommend you start reading papers on <INSERT KEYWORDS HERE> to get a sense of what has been tried already and what theoretical results have already been proven. That will also give you a sense of any gaps in your knowledge that you will need to fill with classes or self-study. You may even need to go for a (second?) PhD. It's going to be a long and tedious road involving a ton of learning (I would expect it to take <INSERT TIMEFRAME HERE, E.G. YEARS>), but once you're fully immersed in the background theory of the problem and the work that's been done and being done on it by others, you'll be prepared to begin working to make a contribution on it yourself. That in itself will be a life-long journey, with many false starts and many thousands of hours spent learning, experimenting, and collaborating with others to (hopefully) make tiny gains, but it's worth it to be one of the <INSERT NUMBER HERE> CS researchers working to advance our collective knowledge on these problems if this is a commitment you're willing to make. But obtaining the necessary theoretical knowledge and learning from others is key to doing any kind of research, and this is especially true for a problem of this magnitude (if the colleague is a researcher consider rewording this last part as it might sound rude).

Basically treat them like a graduate student you're advising (though respectful of the fact that they're a colleague). Hopefully they will either decide to take this seriously and become a productive member of the research community working on these problems, or they'll realize how big of a commitment is involved and walk. Either way problem solved.

If the colleague ignores this advice and continues with the "hey check my proof" queries without any attempt at self-study, then I recommend @Jeroen's answer. And this approach won't work if the colleague in question is a true crank (vs. someone who is just naive about what research is).

Answer 7

If your colleague is struggling with fundamental math questions, and he is very enthusiastic in dedicating their time, there is a very good solution.

Explain him once that any serious attempt at these fundamental questions will need a very formal formulation. Then refer him to Metamath, software and community. In the same email, inform him that you are short in time, and so you cannot provide any timely assistance. Be polite, Be concise. No justifications whatsoever.

After that...

So, I'd like a polite way to either discourage him from working on these problems because I don't want to dedicate time to this (I need to read and study to enter a PhD program and I also believe he's clearly underestimating the problems) or to discourage him from asking me about it without being rude.

If he asks again about these problems: "Sorry, I'm short on time to properly reply. How did you progress with Metamath?"

If he says that is having trouble expressing something with Mathmath, reply: "Sorry, I could not help you with that."

Automate these replies, in email and in conversations.

Answer 8

"I respectfully recommend that you not waste too much of your time on this problem at this stage of your career. And I am afraid that my own free time is too precious to waste on this problem. I am sorry I can't be of any help."

If you try to be more polite, you will be misinterpreted.