Equation for the number of unlabeled trees on n vertices

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Discussion Overview

The discussion revolves around the challenge of finding an equation to count the number of unlabeled trees on n vertices. Participants explore the nature of research, the difficulty of the problem, and the value of the learning process involved in tackling such open problems.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants express frustration over the lack of a known equation for counting unlabeled trees on n vertices, suggesting it is a difficult problem.
  • There is a discussion about the definition of a researcher, with some arguing that attempting to solve an unsolved problem qualifies as research.
  • One participant acknowledges their lack of mathematical knowledge but emphasizes the importance of the skills and knowledge gained through the process of attempting to solve the problem.
  • Another participant shares a personal anecdote about attempting to solve the Collatz conjecture, highlighting the unexpected difficulty of seemingly simple problems.

Areas of Agreement / Disagreement

Participants generally agree that the problem is difficult and that attempting to solve it can be a valuable learning experience. However, there is no consensus on the nature of research or the significance of solving the problem itself.

Contextual Notes

Participants express varying levels of confidence in their mathematical abilities and the potential for novel approaches to the problem. The discussion reflects a range of perspectives on the relationship between effort, learning, and the resolution of complex mathematical questions.

TheMathNoob
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Why has no one figured out yet an equation to count the number of unlabeled trees on n vertices?. I also have this dilemma between researchers and non-researchers. A researcher is just someone who is trying to find a solution to a problem for which no solution has been found yet. Right?, so if I try to find this equation, am I already doing research?
 
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TheMathNoob said:
Why has no one figured out yet an equation to count the number of unlabeled trees on n vertices?. I also have this dilemma between researchers and non-researchers. A researcher is just someone who is trying to find a solution to a problem for which no solution has been found yet. Right?, so if I try to find this equation, am I already doing research?
No one has figured it out because it apparently is a difficult problem.
If you solve it, yes, that would qualify as research.

While I don't want to sound patronizing or discourage you to try it, in general a difficult open problem is, well, ..., difficult. Using your studying time efficiently is part of the art of studying.
But who knows? Maybe you have some novel idea to tackle the question that no one else thought of. It is possible, but a rare occurrence in the history of Mathematics.
 
Samy_A said:
No one has figured it out because it apparently is a difficult problem.
If you solve it, yes, that would qualify as research.

While I don't want to sound patronizing or discourage you to try it, in general a difficult open problem is, well, ..., difficult. Using your studying time efficiently is part of the art of studying.
But who knows? Maybe you have some novel idea to tackle the question that no one else thought of. It is possible, but a rare occurrence in the history of Mathematics.
Yes, I understand what you are saying, but maybe it doesn't actually matter if I get to the solution or not. What matters is the knowledge and skills that I will acquire along the way. I also know that I still lack a lot of mathematical knowledge to give it a try, but maybe in the future XD. Why is it too hard?. It's just trees xd.
 
TheMathNoob said:
Yes, I understand what you are saying, but maybe it doesn't actually matter if I get to the solution or not. What matters is the knowledge and skills that I will acquire along the way. Why is it too hard?. It's just trees xd.
Absolutely, try to tackle it for a (short) while if you like the problem, nothing wrong with that. At the very least it will give you some insight into why it is hard.

Many years ago I wasted some time at another "easy" problem: the Collatz conjecture. It is so elementary in its statement that I thought it should be relatively easy to solve. There was a little voice in my head that warned me that brighter minds had tried it for decades, but still, I tried too. :oldsmile:
 

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