Open research problems still open?

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In summary, the conversation discusses the best way to determine which open research problems in the book "Topics in Geometric Group Theory" have been solved or are still open. This can be achieved by talking to someone knowledgeable in the field or by searching for papers that cite the problem. However, it can be difficult to determine if a solution is recent or if it has been published. The speaker also plans to discuss their progress with their professor and use this initial period to gain insight and improve their skills. They also want to avoid spending time on a problem that has already been solved.
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Newtime
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I'm getting through a book called "Topics in Geometric Group Theory" and there are quite a few open research problems throughout the book - they are denoted as such. The book was published in 2000, so aside from googling and searching for papers published on these topics, how can I know which have been solved/discussed in great detail and which are still relatively or completely open?
 
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By talking to someone knowledgeable in the field? That's your best bet.
 
  • #3
owlpride said:
By talking to someone knowledgeable in the field? That's your best bet.

the most practical solution for sure. I'm reading this book under the direction of a professor who does research in this area and i will hopefully be collaborating with him on a problem or at least working on one under his guidance in the spring but over this winter break (5 + weeks long) i would like to know which problems are worth my thought and which ones are not.
 
  • #4
If a solution has been published yet, you might be able to find it via Google. Solutions are hard to locate though if the problem has been solved as a special case of a bigger problem, or only in a special case. It is also possible that someone has already solved it but not published it yet (since publishing might take over a year), or that someone is working on the problem right now. The only way to find out is to ask someone who is on top of things.
 
  • #5
i would like to know which problems are worth my thought and which ones are not.
They probably all are. If the solution is very recent, then you may have an alternative proof, an interesting lemma, or you may gain a lot of insight. I would recommend you to use this initial period prior to actually working with your prof to get as good as possible. If you just pick out your favorite problem and work on it you will learn a lot and even if it turns out to be solved, your insights will probably help you greatly on lots of related problems.

Anyway for some more direct advice: as owlpride said it can be hard to determine if the solution is very recent, but if you know one of the most prominent papers that discusses the problem, then simply search for papers citing that. If someone publishes a solution it's very likely they start their article with "In this paper we prove a conjecture set forth in [a] and further explored in , [c] and [d] using techniques from [e] and [f]".
 
  • #6
owlpride said:
If a solution has been published yet, you might be able to find it via Google. Solutions are hard to locate though if the problem has been solved as a special case of a bigger problem, or only in a special case. It is also possible that someone has already solved it but not published it yet (since publishing might take over a year), or that someone is working on the problem right now. The only way to find out is to ask someone who is on top of things.

true, and about what i expected. I've scheduled to go back to school 2 or 3 times during the break to discuss my progress with him and I'm sure this will be among the topics we will discuss.

rasmhop said:
They probably all are. If the solution is very recent, then you may have an alternative proof, an interesting lemma, or you may gain a lot of insight. I would recommend you to use this initial period prior to actually working with your prof to get as good as possible. If you just pick out your favorite problem and work on it you will learn a lot and even if it turns out to be solved, your insights will probably help you greatly on lots of related problems.

Anyway for some more direct advice: as owlpride said it can be hard to determine if the solution is very recent, but if you know one of the most prominent papers that discusses the problem, then simply search for papers citing that. If someone publishes a solution it's very likely they start their article with "In this paper we prove a conjecture set forth in [a] and further explored in , [c] and [d] using techniques from [e] and [f]".


also very true, and i hope it didn't sound elitist or something when i said "worth my thought" i simply meant that i don't want to spend a lot of time on a problem only to discover it has been thoroughly solved. however, you make a good point and one that i didn't (but should have) consider.

thanks for the replies.
 

Related to Open research problems still open?

1. What are open research problems?

Open research problems are questions or issues within a particular field of study that have not yet been fully answered or resolved. These problems are typically complex and require further investigation and research to find a solution.

2. Why are open research problems important?

Open research problems are important because they drive scientific progress and innovation. By identifying and studying these problems, scientists are able to expand their knowledge and understanding of a particular subject and potentially make groundbreaking discoveries.

3. How are open research problems identified?

Open research problems are identified through a variety of methods, such as literature reviews, discussions with experts in the field, and analyzing current data and findings. These problems often arise from gaps in existing research or contradictions in current theories.

4. How are open research problems addressed?

Open research problems are addressed through systematic and rigorous scientific research. This can involve conducting experiments, collecting and analyzing data, and collaborating with other scientists. It may also involve proposing new theories or hypotheses to explain the problem.

5. What impact can solving open research problems have?

Solving open research problems can have a significant impact on the scientific community and society as a whole. It can lead to advancements in technology, improvements in healthcare and medicine, and a better understanding of the world around us. Additionally, solving open research problems can inspire further research and open up new avenues of exploration.

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