I have gotten many different opinions on this and thought I would ask here. I am an international student about to start grade 11, I took the new SAT with essay in June and got 1580 (Math 800, R+W 780) but I got a pretty bad essay score, 6/3/6 (reading, analysis, writing). I want to know if it’s worth retaking it, I don’t want to retake it unless absolutely necessary, since it’s very expensive outside the US (also I hate SATs) and I still have to worry about subject tests. English is not my first language, but I took Cambridge Advanced English last year and got a nearly perfect score in writing (207/210) and I will probably take Proficiency in a few months, expecting a similar result, so I think I’m good at writing essays.
My top schools are Stanford and MIT, for a math major. I don’t yet have a full list of colleges I’ll apply to, but some don’t require the essay. Do you know if there’s a way to not include essay scores for colleges that don’t require them? If a school doesn’t require them, will a 3 raise a red flag?
I think I have a strong application otherwise, my current GPA is 9.7/10, top of my class, national math medals with hopes of international before I apply, I’ve been to a selective math camp and will probably return next summer, I’ll start IB this year and aside from math olympiads, my hobbies are reading, art (I might include an arts supplement) and I recently started playing the violin. I don’t know if this is a stupid question but I am a little scared about it. Thoughts?
A lot of STEM focused schools don’t care about the essay (and the ones that do don’t look at it much) . You’re fine.
The universities are not placing a lot of weight on the essays because they really don’t have a enough data to determine how consistent the scoring will be. You are at a greater risk to lower your grade by retaking it. I would use that score and write an explanation about why you feel that score is low on the “additional information” section of the applications. Congratulations on the excellent score.
Many STEM schools don’t put emphasis on writing section. MIT specified that they don’t look at writing section much
The writing section no longer matters. You’re fine - more than fine in fact, congratulations on your achievements. 
Just to be completely clear, while it is completely true that schools like MIT, who crunch data, have found that the SAT with writing correlates a lot less with success at MIT than any other SAT, and so they do not value it much, that does not mean that the ability to write is unimportant for these schools. Its just that they choose to evaluate it through the essays that they set as part of the application rather than through the SAT with writing.
There is a big difference between the schools you list. Stanford requires the SAT with essay or ACT with essay, and while they recommend the TOEFL for students for whom English is not their first language, they note that "The TOEFL cannot replace the SAT with Essay or ACT with Writing. " (http://admission.stanford.edu/application/freshman/testing.html). Whereas MIT does not require the SAT with writing for non-native speakers and for them, they will allow the TOEFL to replace the SAT with writing. (http://mitadmissions.org/apply/freshman/tests). If you are focused on MIT, I would recommend the TOEFL.