The following questions and answers are based on an informal conversation with a highly reputated Professor in Mathematics (not sharing the name for now, will take permission then, I will share the name)-
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Question 1: What is important research? How can one decide whether a work or a research direction is important?
Question 1: What is important research? How can one decide whether a work or a research direction is important?
Answer:
Who are you to decide what is important—and who am I to decide it for you?
Work on whatever genuinely comes to your mind, whatever question arises from your own insight, curiosity, and inner conviction. Do not begin by worrying too much about whether a particular task is fashionable, prestigious, or immediately useful. It is good to have a broad direction, but you do not always need a rigid plan.
The most important thing is to follow the questions that you truly feel compelled to understand.
When you pursue such a question seriously, you naturally develop a deep understanding of the subject. You begin to see structures, difficulties, and connections that are invisible from the outside. From that depth, new and useful mathematics can emerge.
Therefore, do not choose a problem only because others call it important. Choose a direction in which you feel that you have something to understand, discover, or say. If the question comes from genuine mathematical insight and you investigate it deeply and honestly, the work will have value. Its importance may not be immediately visible, but deep understanding is never wasted: it will contribute to your own mathematics and may eventually become useful to others as well.
Question 2: COMING SOON-- will write slowly slowly... --
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