Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes.
How important is neatness in math?
Does having messy writing put you at a disadvantage?
What is the tradeoff of speed vs. neatness?
Should I look to increase the neatness of my writing?
What are some simple tips to prevent mistakes that can be solved by simple organization / tidyness/structure?
In timed settings (exams), neat vs. speed?
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It may just be my fanatical opinion, but I think that clarity is one of the most important attributes of performing mathematics, regardless of level.
For your purposes, let me present an example: Regardless of what course I am teaching, whether it be first year calculus or fourth year topology, I always have students who submit messy, poorly structured, incomprehensible nonsense on their assignments. They typically receive a very poor mark as a result, even if their answer/solution is entirely correct. They of course come and complain that because their answer is correct, they should receive full marks. This is my response:
"A mathematical solution is not just a correct number at the end of a computation: it is a logical sequence of events which is clearly motivated, explained, and justified at every step. If you present non-sense that happens to give you the right number, then while your answer may be correct, your solution is wrong."
Of course, this idea should transcend undergraduate mathematics and manifest in research mathematics as well. A proof is not a proof unless the community can verify your result.
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I find this interesting myself as I also have messy writing.
For me I always try to keep equal signs aligned and leave equal spacing. I also prefer using paper landscape as opposed to portrait but this is all just personal preference.
As for speed vs. neatness, I think it really is just about finding a fine line between them, neatness is important but you don't want to jeopardize leaving things incomplete.
My handwriting is pretty bad, I love $\LaTeX$, I've lectured on chalkboards/blackboards a couple of times, and given computerized presentations.
My general feeling is that you should make the general direction of everything you write in exams crystal clear, and keep letters/symbols distinct, but otherwise don't waste too much time on lovely handwriting. Structure and layout is far more important. Brief, simple sentences saying what you're about to do, bullet points, headings are all sensible measures.
Lecturing and teaching, however, are different. People should never even think about your handwriting. It should be completely out of their minds - completely normal, legible, consistent, boring.
The magic is always in the maths, and its flow through structured discussion, nowhere else.