In 2011, I started my PhD and also started recording every minute I spent working line-by-line through graduate texts and research papers in mathematics. At that time, the majority of my work was spent understanding various branches of mathematics necessary to do research.
I recorded this data in a spreadsheet. It’s important to realize what kind of time I recorded. I recorded only time spent going through books and papers line-by-line. I did not record any time searching the literature, skimming through papers I needed to read, or going to class. In other words, I only recorded highly focused time where I was actively engaging with the material.
I wanted to understand the limits of my mind in terms of how quickly I can absorb new mathematics. Other work is important too, but in my experience tasks like searching the literature or typesetting my thesis require very little effort compared to reading new mathematics line-by-line.
In my measurement, I tried to be precise. During the time intervals I measured, I worked constantly. I did not take any breaks to check email or do anything else. In fact, I did not even have the internet at home during my entire PhD. I always worked at home with no distractions. If any break was required, I stopped the timer, but usually I worked in short intervals of 45-90 minutes where no breaks were required.
Here is what I learned in this exercise of fairly precise measurement:
- Periods of high mental productivity come in cycles. There would always come a period of 2-3 weeks where I just wasn’t very productive. I tried to recognize when that happened and just do other things instead of being upset that I could not work.
- There is a hard limit to how much work your mind can do. In the long run (that is averaged over a period of years including days where I did nothing), I averaged one hour a day.
- On any given day I could do a very hard maximum of 3 hours of intense reading, usually less.
The bottom line is that work comes in phases, and the mind has an upper limit to what it can do. It is like lifting weights. After a certain number of reps at the bench press, you just won’t able to do any more. And moreover, after doing an intense weight workout, you need to take a break to let your muscles recover. It does not make sense to have it uniformly done day after day. When your mind is at its peak power, it will do a lot more than the average per day. Intense mental work like understanding math is much more like anaerobic exercise, rather than aerobic exercise like running.
Everyone has a different level of intensity they can handle. For me, it seemed to come out to a long-term average of an hour a day but other people are different and could average two hours a day. (Remember, this average is over all days of the year.) Also, one hour for some person might mean getting farther in the book with even more understanding than another person can do in two hours.
The mind is a complex machine and if you are going to use it for very intense intellectual work, you need to understand the subtlety of its power, and how to use it well. It needs a combination of a strong effort together without any harshness and it can do amazing things.