The creation of open problems in Mathematics

In summary, finding unsolved problems in mathematics at the research level is not difficult as there is no shortage of them. However, finding problems that are both interesting and within one's abilities to solve can be challenging. The level of education does not necessarily determine one's ability to formulate new problems, but it can aid in knowing where to look for them and understanding their significance. These problems often arise naturally through research and may not always lead to groundbreaking insights, but rather small improvements on existing knowledge. Unless one is working in a specific field, it is unlikely that they will come across major unsolved problems like the Goldbach conjecture.
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flamengo
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I have a question about mathematics at the research level. How difficult is it to formulate new open problems in mathematics? For example, can a master's student create such problems? And a doctoral student? Or are only experienced mathematicians able to do this? Does this depend on the research area? Could someone give me a detailed answer?
 
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Finding new or unsolved problems is easy, and there is no shortage of problems. Finding new problems that you can solve is more difficult. Finding interesting problems that are difficult enough to lead to a publication, but still within your abilities, can be challenging on its own.
 
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flamengo said:
I have a question about mathematics at the research level. How difficult is it to formulate new open problems in mathematics? For example, can a master's student create such problems? And a doctoral student? Or are only experienced mathematicians able to do this? Does this depend on the research area? Could someone give me a detailed answer?
What do you think? That there are periodical meetings where professors sit together and create unsolved problems? These problems arise naturally by doing research as one will always find new unanswered questions. The level of education can only help to know whether they are really unsolved or who is working in the area and most important: where to look for. Research is to a great extend done in libraries. And usually it's not about ground breaking new insights, but often small improvements on known stuff: another boundary for remainder terms, better estimations on complexity, another class of nilpotent groups and things like that. Unless you don't work in the field, you will rarely meet the Goldbach conjecture, and certainly not "invent" one.
 
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1. What is the importance of creating open problems in mathematics?

Creating open problems in mathematics is essential for the advancement of the field. These problems serve as challenges for mathematicians to solve, leading to new discoveries and developments in various branches of mathematics.

2. How do mathematicians come up with open problems?

There are several ways in which mathematicians can generate open problems. Some may come from trying to solve existing problems and encountering obstacles, while others may stem from observations or patterns found within a specific area of mathematics.

3. Are there any guidelines for creating open problems?

There are no strict guidelines for creating open problems, as they can arise from various sources and in different forms. However, it is important for the problem to be well-defined and have clear parameters for solving it.

4. Can anyone create an open problem in mathematics?

Yes, anyone with a strong understanding of mathematics can create an open problem. However, it is recommended that one consult with experts in the field to ensure the problem is well-posed and has not already been solved.

5. What is the impact of solving open problems in mathematics?

Solving open problems has a significant impact on the field of mathematics. It not only leads to new discoveries and advancements, but it also helps to solidify existing theories and can inspire further research and exploration.

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