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.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?
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.
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.
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.
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.
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.