Writing a Math Paper

[Anonymous No.8559540]

Any tips for writing/structuring good proofs/papers?

I've broken it all down into lemmas, but my lemmas are really awkward to prove because of how trivial they are. I feel like I'm just stating facts and it comes off as weird. I guess the main theorems I have are alright. Although, I'm sure there are still tips some of you might know that could help me make them better.

[Anonymous No.8559547]

If the lemmas are that trivial, why bother making them outside the proofs you're using them for?

Lemmas are really only useful for stating technical results so you don't overload your other proofs with cumbersome details, or repeat the same lengthy argument over and over again.

[Anonymous No.8559556]

>>8559547
I dunno. Having some of the lemmas I have do help my main theorems flow better, and I also felt a bit awkward just claiming something to be true without offering explanation why mid-proof.

I might just trying reading some more papers in the same topic as mine and just try to do what they do as far as brevity/detail goes.

[Anonymous No.8559563]

Try to maintain a colloquial voice in your paper. Try to mimic how richard feynman explains concepts.

Of course stay rigorous in the math, but try to make it sound like a person is behind the paper, not a robot.

[Anonymous No.8559834]

>>8559540
Just leave them as an exercise for the reader.

[Anonymous No.8560302]

>>8559556
If the proofs are short, it is easy to provide a proof inside the proof of the theorem.