Very brief of the situations that happened from Jan 2021 : Living in a 3rd world country. I completed my masters in math in Jun 2020. Then I wanted to study some additional topics before applying in Europe. So, took 1 year break and went home. Studied fine till Jan 2021, then constant verbal abuse started by my father and occasionally by my mother (they earlier also used to verbally abuse me but I didn't do my bachelors and masters in my native city, so less impact was on me).
Admitted to mental hospital for 10 days in Feb and misdiagnosed with schizophrenia (I have depression). Verbal and emotional abuse continues and again admitted to different hospital in March for 11 days, diagnosed with depression. Verbal abuse again continues after some days of discharge. So, I move out taking a part time job to sustain myself in different city on 1 July and learning some new math topics alongside. Thinking about suicide since March 2021 but postponed to try 1 more year if I am not able to get a phd position as learning and doing math is the only thing I like.
(Reason of verbal abuse: parents wanted me to do full time job and not math research so that I can settle early and also wanted me to take a career like medical doctor or engineer which is more earning and takes less time to settle time). I could only study 1 month of math in these 6 months.
How much should I mention the situation due to my 6 months of my life are being wasted in my CV when applying to PHD position in Mathematics? Will the admission by me that I have suffered from depression affect my selection for Phd i.e. how it would be taken by selection committee?
I don't think I should lie as I would be really weird to make up what I was not doing as what I was doing. I really need advice.
Also, I think if I don't mention it in CV then certainly I will be asked in interview about the gap in studies (and then I will have to explain in very few lines which will obviously change the course of interview to an entirely different thing if it is not known to the prof. beforehand).
Certainly, I am not mentioning it for any sympathy but I think I should write about it very briefly as I write CV in a bit timeline form; if I just left a gap or don't mention it then certainly it would be thought that I have been less productive because of the lower number of things I studied. (But there is a very valid reason of being less productive).
Edit : I feel that I should at least mention it because it is due to abuse by my parents that I have been so depressed and I wasted precious time and I would have certainly been better if my parents were able to understand what I want to do with my life.