What should one do in the case when I'm a worker who has studied mathematics and physics and boss has not studied those things. Then the boss asks to try to solve one problem by given methods and you know and can prove that the given method won't solve the problem or even that the problem can't be solved at all. The boss won't accept my reasoning why the problem is unsolvable and he is not willing to read an proof or the theory where the situation has been proved to be impossible.

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    @Kilisi xkcd.com/1425
    – Walfrat
    Oct 21, 2016 at 12:37
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    Just... DO IT!
    – ANeves
    Oct 21, 2016 at 15:38
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    – AnoE
    Oct 21, 2016 at 15:56
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    Many "impossible" problems can be solved in the specific case but not the general case or closely estimated even if an exact answer is impossible to determine. Does this problem fall into either of those two categories? The rigor of the required in solutions between industry and academia can be very different.
    – Myles
    Oct 21, 2016 at 18:37
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    Antiviruses can be proven impossible, but people make them anyway, and they kinda sometimes work. Are you sure your boss is asking something unreasonable?
    – user541686
    Oct 21, 2016 at 19:03

6 Answers 6


You do the same thing you would do if you thought it might be solvable: you ask for help. Seniors, the internet community, maybe a paid consultant. After a while, if all of those just deliver reports about how it cannot be done, even your boss will be tired of paying yet another consultant to tell him things you told him half a year ago.

However, this is not delivering any value. While your boss is slowly waking up to the fact that what he wants cannot be done, prepare and regularly show him alternatives to his business problem. Chances are, he's not in the business of formulating mathematical proofs. He is in the business of making money. If the problem cannot be solved soundly in mathematical terms, maybe it can be solved in a way that still earns him money? Sometimes "good enough" is all that's needed, although it makes us theoreticians shiver.

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    +1 for promoting pragmatism over perfectionism. Sometimes "good enough" is the right business decision over the perfect answer.
    – toadflakz
    Oct 21, 2016 at 9:26
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    This. In specific technical fields, management doesn't always know what works and what doesn't and often has to rely on buzzwords. I sometimes have to tell my boss, "It will take 19 years to do this the way you asked, but if I do it this other way, it will take 2 weeks." They normally are looking at the end game, not the way to get there. Even if they tell you how they want you to get there, they often are saying it because that's the only way they know. They pay you to know the alternative ways around. And if the endstate is impossible to reach, provide an alternative that is almost the same. Oct 21, 2016 at 17:55
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    Google is a really good example of this. In theory, a lot of the things Google do is "impossible". Search the entire web in less than a second - impossible due to the size of the web, some parts of the web being isolated etc. But Google does a good enough job that it "feels" like you're searching the entire web when you use it. Identify intellectual property in video content - impossible due to distortions from compression, editing etc. But Google managed to do a good enough job. In theory nothing Google does actually works. In practice nothing they do works "perfectly" but is still usable
    – slebetman
    Oct 22, 2016 at 6:18
  • Make sure you have an email or other written record of his request and your explanation that it couldn't be done and why it couldn't be done. And him telling you to do it anyway.
    – Ne Mo
    Oct 22, 2016 at 10:11
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    While the answer is good, the problem is that some consultants are not inclined to say it cannot be done. They are inclined to say that the problem is solvable, then they continue to do busy work and finally claim they have solved the problem. If you point out that they did not solve the problem, they claim "misunderstandings" and oh, here is the bill :(. Oct 24, 2016 at 22:38

Instead of trying to prove that it cannot be done, try to find out what can be done and how you can do it. For example, if your boss asks for an optimal solution to a problem, and you know it cannot be found in any reasonable time, find a way to find a good solution in a reasonable time and present that. (Your boss will likely not be able to prove that it isn't optimal anyway).


Your boss doesn't want you to solve the given problem by a specific method.

In fact, he doesn't necessarily want the problem that he has posed solving at all.

What he does want is to change an unsatisfactory situation that is affecting the business into something more satisfactory. Give him a way to doing that, and he'll forget the specifics of what he actually asked for.

The scenario you described seems like a typical example of an XY problem.

Often, the hardest part of solving an XY problem is discovering what the real problem actually is!


I hope that I am not coming across as glib, considering that none of us has seen either the text of the problem and are not privy to the reasoning why the problem is unsolvable. Here it is:

  1. redefine the problem so that it is solvable while keeping compatibility with the original definition of the problem, thus keeping the needs of the boss met.

  2. solve the problem and refine the solution to optimize the fit to the situation at hand.

When in an argument with the boss, back your argument with documentation. People will have difficulty with accepting your reasoning if your reasoning is not intuitive.


Find another job. While looking, do what others advise and try to find the problem the boss actually wants to solve, and offer a solution. If you succeed and earn the boss's trust and gratitude, you can always cancel your job search.


This question already has several good answers so I'm not sure that this will help.

Try approximating a solution with iterative methods. This is what my experience from when I was studying ME in college suggests to do if possible.

If not it would help if you could boil the proofs down to a graph or simply summarize why there is no solution.

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