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gmvh
gmvh
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I'm pretty sure almost all mathematicians have been in a situation where they found an interesting problem; they thought of many different ideas to tackle the problem, but in all of these ideas, there was something missing- either the "middle" part of the argument or the "end" part of the argument. They were stuck and couldn't figure out what to do.

  1. In such a situation what do you do?
  2. Is the reason for the "missing part" the incompleteness in the theory of the topic that the problem is related to? What can be done to find the "missing part"?

For tenure-track/tenure professorprofessors, maybe this is not a big deal because they have "enough" time and can let the problem "stew" in the "back-burner" of their mind, but forwhat about limited time-time positions, for e.g.- PhD students, postdocpostdocs, etc., where the student/employee has to prove their capability to do "independent" research so that they can be hired for their next position,? I think for these people it is quite a bit of a problem because they can't really afford to spend a "lot" of time thinking about the same problem.

I'm pretty sure almost all mathematicians have been in a situation where they found an interesting problem; they thought of many different ideas to tackle the problem, but in all of these ideas, there was something missing- either the "middle" part of the argument or the "end" part of the argument. They were stuck and couldn't figure out what to do.

  1. In such a situation what do you do?
  2. Is the reason for the "missing part" the incompleteness in the theory of the topic that the problem is related to? What can be done to find the "missing part"?

For tenure-track/tenure professor, maybe this is not a big deal because they have "enough" time and can let the problem "stew" in the "back-burner" of their mind, but for limited time positions, for e.g.- PhD, postdoc, etc., where student/employee has to prove their capability to do "independent" research so that they can be hired for their next position, I think for these people it is quite a bit of a problem because they can't really afford to spend "lot" of time thinking about the same problem.

I'm pretty sure almost all mathematicians have been in a situation where they found an interesting problem; they thought of many different ideas to tackle the problem, but in all of these ideas, there was something missing- either the "middle" part of the argument or the "end" part of the argument. They were stuck and couldn't figure out what to do.

  1. In such a situation what do you do?
  2. Is the reason for the "missing part" the incompleteness in the theory of the topic that the problem is related to? What can be done to find the "missing part"?

For tenure-track/tenure professors, maybe this is not a big deal because they have "enough" time and can let the problem "stew" in the "back-burner" of their mind, but what about limited-time positions, e.g. PhD students, postdocs, etc., where the student/employee has to prove their capability to do "independent" research so that they can be hired for their next position? I think for these people it is quite a bit of a problem because they can't really afford to spend a "lot" of time thinking about the same problem.

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It'sMe
It'sMe
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What do you do when you're stuck?

I'm pretty sure almost all mathematicians have been in a situation where they found an interesting problem; they thought of many different ideas to tackle the problem, but in all of these ideas, there was something missing- either the "middle" part of the argument or the "end" part of the argument. They were stuck and couldn't figure out what to do.

  1. In such a situation what do you do?
  2. Is the reason for the "missing part" the incompleteness in the theory of the topic that the problem is related to? What can be done to find the "missing part"?

For tenure-track/tenure professor, maybe this is not a big deal because they have "enough" time and can let the problem "stew" in the "back-burner" of their mind, but for limited time positions, for e.g.- PhD, postdoc, etc., where student/employee has to prove their capability to do "independent" research so that they can be hired for their next position, I think for these people it is quite a bit of a problem because they can't really afford to spend "lot" of time thinking about the same problem.