I currently feel like I am not doing maths the best way I could; that is, I'm not making the most out of my time when I'm working on maths problems.
The main thing I feel is that I'm not organizing my mind and my derivations as clear as I could, because I don't have the best "math habits". I feel like if I could develop better math habits, I could significantly improve both my time efficiency and the quality of my thinking.
To show what I mean, I'll compare it with the skill of writing: I used to write in a very unstructured way: I simply started writing with some vague idea of what I wanted to write. Then after having written a paragraph, I would generally be somewhat confused. After 2 paragraphs I'd be more confused. Eventually I didn't have a clear idea of what to write because my mind was so cluttered, as if all my neural pathways were firing un-synchronously, creating a senseless mess. I have now solved this by developing better habits: I started making bullet point lists of my papers that contained the central argument, before I wrote the actual paragraphs. I then wrote one paragraph at a time, focusing only on what that particular one had to convey. Also, I developed a more structured way of structuring paragraphs: rather than just "writing it", I thought about the first sentence separately, and then its relation to the second, and so on... After developing these better habits, I felt like my brain had a much more "lean" and "uncluttered" process it was following, as if my neural pathways fired synchronously, in harmony.
I feel like right now with maths, I am in a similar stage that I used to be with writing. I understand math concepts, and I know how to do many of the methods, and I'm progressing. But whenever I'm working on a math problem, I feel like I'm getting confused, not just because the problem is new and difficult, but because my mind is cluttering and confusing itself, as if I don't have a "process" that is optimized for figuring out new math.
One way this shows, though I don't know if its a cause or a symptom, is that my derivations look like a plate of spaghetti. Yet if I try to write things more structuredly, I'm held back even more, because it puts me into a very "fearful" and paralyzed state of mind (fearful to write something wrong).
So I'm looking for habits that I can develop that will, just like I did with my writing process, turn my "cluttered" mind, into a "harmonic" one. That doesn't mean math will suddenly be easy, but at least the difficulty will be due to the complexity of the math, rather than due to me working against myself.
So I'm interested if any of you have experienced this same thing, and whether there have been specific habits or other things that have helped you overcome this.
To give an example of something that recently has actually helped me somewhat: Whenever I now derive an intermediate result, I write big boxes around it, with a big dense filled circle in the corner, in order to signify that it is an important result. This somewhat declutters my mind, because I no longer have to wade through all the intermediate steps, looking for the important stuff.
ps. I hope this question is not too general or subjective. I know that subjective questions are not the purpose of math.stackexchange, but I thought: there certainly are some objective principles behind what kind of habits work and don't work. And I wouldn't be surprised if I'm not the only one who could benefit.
Thank you for all the great answers! Many of these are actually things I will immediately apply.
Here is a suggestion: There is a certain topic that the answers haven't addressed, so maybe someone can address this with another answer:
How, in a very practical sense, do you write down your derivations, and how do they help make you more effective?
For example, do you have two separate pieces of paper for intermediate results and for details?
Are there any specific ways of organizing your derivations on paper, or in notebooks, that help clear your mind?
Do you write everything linearly, from top to bottom of your notebook, or do you go back and forth on your scrap paper, only writing it linearly when you've found the result?
Do you scratch formulae completely if you've made a mistake, and start over, or do you just correct the formulae?
Do you write derivations quickly on a scratchbook, until you've found the final answer, or do you write them neatly from start to finish?