Reflecting on my math journey

Some days ago, a math professor asked us how we should define a differential operator -- are closed under addition and scalar multiplication together with product rule enough? To be honest, I still don't know the answer to this question. It dawned on me that 'How do we define integration? How do we define differentiation? What are the tools? What are the motivations for this?' are questions that I seldom ask. I realised I was not studying properly all these years. I was just being spoonfed everything. I accepted everything without a moment of thought. I memorised the definitions without thinking about why they are defined that way. I'm literally 'learning' everything but not studying any. On a positive note, it is not too late now for me to realise this! From now on, I will re-learn every single concept and really try to THINK! I hope I can develop more intuition about math.