Should one mention outside influences that negatively impacted grades on their PhD applications? I'm applying for PhD programs at the moment in pure mathematics and was wondering if there was any sort of general wisdom regarding mentioning bad things that happened to you that have negatively impacted your grades. In the winter and spring quarters of my junior year my father was in and out of life threatening surgeries and it generated a lot of anxiety in my life that made it difficult to keep up with school the way I had in the past. He is thankfully doing alright now and is only getting better, but it was really touch and go for a while.

Before those terms I had taken a lot of graduate level courses in mathematics and consistently got As, but there was a dip during that period to B+s and Bs. The difficult thing for me is that, now that I'm not dealing with those things anymore, I don't really have time to show on my applications that it was a temporary issue for me. Is this sort of thing worth mentioning on my applications?

Personally I'm a very private person and the thought of mentioning it makes me a little nervous, but my application before this happened was quite unambiguously strong and I don't really know if it's appropriate to mention or if people would take it into consideration when looking at my transcripts.
In the graduate school I manage (UK Russell Group), you will need to meet specific requirements to even be considered for a place in the PhD programme. If your grades (or English proficiency or industry experience or any other prerequisite you choose to identify) do not meet this threshold, no amount of explanation in your personal statement will be satisfactory. This is the first hurdle. 

If you are able to surmount this first hurdle, then no specific explanation is necessary to include in your personal statement about the reason you feel your grades were negatively impacted. You are only required to state that there were personal circumstances of a limited nature that were the cause of the dip in your performance. There are three reasons for this:


Your grades have already been determined. An explanation will not change them. We will use your grades plus other evidence to rank you against all other applicants. Your reason will not be relevant in this ranking process. You will fall into one of three categories. If you are in the "clear accept" category or in the "clear reject" category, then your explanation is irrelevant to us. If you are in the "more information" category, when we will seek further information from you in the form of an interview, for example.
We have no way of confirming that the explanation you provided in your personal statement is accurate.
Your reasons may be highly private. If so, they will be difficult for you to write and difficult for us to read.


Please be clear about what I am saying. I am not saying that the reason is immaterial. Quite the contrary, in fact. What I am saying is that the reasons you declare will be considered in due course and we will invite you to respond and provide evidence if and when we require it. We will also specify the nature that evidence is to take.

Thus, in response to your question, I would advise the following:


DO mention that your performance over a specific number of semesters was atypical and impacted your overall GPA negatively.
DO mention that the reason for this atypical performance was of a significant personal nature.
DO mention that this issue has since resolved.
DO mention that you will be able to provide evidence should we require it.
DO NOT provide us specific details.


An example of such a statement is


  During two trimesters in academic year 2016/17, my academic performance was affected by a serious personal issue that has since resolved. This has negatively affected my overall GPA. The academic performance improved in the next academic year. I will be able to provide relevant evidence for your review upon request.


Finally, it is quite common for us to issue offers conditional on the receipt of further evidence. Not knowing your specific circumstances beyond the information you've already provided, it is likely that this will be the result that you will receive.

I wish you the best of luck.