How to get through the rigorous phase of PhD? I am currently a PhD student working out research and also doing mathematics for my PhD research. Most of the time these days I spend on studying -- maybe 15 to 16 hours per day. I believe that I joined the PhD as an active student, but now I am not as active as I used to be in the initial years. My productivity is less these days as I try to avoid mistakes in my research. I have started feeling nervous in front of my colleague as I don't have any publications until now. 

I always try to prepare my best but these days fail quite frequently and make silly mistakes which are annoying. Sometimes I even forget the basic definitions. Looking at myself during my initial two years I find myself a fool these days. I think this is called the rigorous phase of PhD where your ideas have to pass rigorous mathematical proofs and I am quite independent these days. 

Question: How to get through the rigorous phase of PhD?
Take a (short) vacation immediately. 

By working 15-16 hours a day you are making yourself too exhausted and tired to be effective. That is also probably why you make mistakes. You should take a break that is long enough to reset, and when you come back aim at reasonable working hours (depends on a person and circumstances but for most people this is 40-60hrs/week).