Explaining undergrad transfer on application to grad school I'm applying to PhD programs in math.  The thing is: I went to a great school coming out of high school, but it didn't work out.  (No GPA problems thankfully; just personal stuff.)  I ended up going to an engineering program, where I eventually understood math was my calling, and everything has been going swimmingly since then.

The question is: do I need to explain myself?  Every program I apply to will be getting the transcript from my first institution.  It seems to me I should explain why I left and how I've gotten to where I am.  That said, only one school I'm applying to actually requires a statement about this kind of circumstance, which has left me a bit confused.  Presumably my having transferred will raise questions that I should strive to address in my application, rather than letting the admissions committees' imaginations fill in the gaps.  That said, I feel as though anything I can say to explain the situation will detract from the positive developments that transpired after I transferred, particularly given the prestige I chose to give up.
If there were no GPA problems at the first school, then there's nothing in that first transcript to look askance at; hence, no explanation needed.

However, the specific change you made, from engineering to pure math, might help your application.  Perhaps a small anecdote will help me explain why.

When I took my Calculus III (multivariate), it happened that my fellow students had no patience for proofs.  They were overwhelmingly engineering students. One of them became a self-appointed spokesman for the impatient majority, and would interrupt the instructor in the middle of a proof of a major theorem: "Excuse me, Ma'am, could you skip the proof, please, and go straight to the applications?"

Not all engineering students are like that; and to be fair, the large number of credit hours they are frequently expected to take per semester isn't conducive to stopping to smell the roses.

Conclusion: a brief mention in the essay or cover letter of your change of major from engineering to math might help your application.