How often do you put your research into trash? A  soft question.
I am a PhD student, at early stages of my academic career; and have personally experienced the following many times. Sometimes you come up with a result, that you are not quite happy with (for whatever reason, maybe you think is not novel, or is simple, or has no applications, etc.)? How often do you put your research into trash? 
Yet another question, I have seen people publishing sometimes papers that they don't feel quite happy about publishing, but every now and then, these papers start getting lots of citations, and being recognized. What do you think about this? Do you think unless the quality is really low you'd go ahead an post, at the very least on arXiv; or do you stick to perfectionism? To some degree, I feel like perfect is the enemy of the good!
 A: I have some strong opinions about this:

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*Math is hard and interesting. Don't be snobbish about anyone's math, not least yourself. I have found fruitful research ideas from obscure papers that no-one read, from naive questions by undergraduate students or even my children. Some vague thoughts I had years ago when revisited now become full papers in decent journals since I have more tools and insight to develop them.


*Anything can be turned into a useful experience. That's what I told my kids before any tennis session. If they have to hit with someone weaker, focus on placing the ball perfectly for that person so they can hit it back. That helps them improve their skills and the other kids too. Same for your "weak" results. Try to extend them. Put them in bigger contexts. Write a good introduction. Don't be shy to speculate and ask open questions (but make sure you put some efforts in thinking about them first). These are crucial skills for "bigger" papers too. In this day and age you can always find a non-predatory journal whose quality your note can improve, for instance those published by math societies from countries with little history of math research. Send your note there. And you have done a good thing.


*You can always put them in a file called "Answers to future MO questions"! (-:
