Donald Knuth on work habits-problem solving-and happiness
https://shuvomoy.github.io/blogs/posts/Knuth-on-work-habits-and-problem-solving-and-happiness/
Seeing both the forest and the trees in research. "I've seen many graduate students working on their theses, over the years, and their research often follows a pattern that supports what I'm trying to explain. Suppose you want to solve a complicated problem whose solution is unknown; in essence you're an explorer entering into a new world. At first your brain is learning the territory, and you're making tiny steps, baby steps in the world of the problem. But after you've immersed yourself in that problem for awhile then you can start to make giant steps, bigger steps, and you can see many things at once, so your brain is getting ready for a new kind of work. You begin to see both the forest and the trees."
How Knuth works on a project. "When I start to investigate some topic, during the first days I fill up scratch paper like mad. I mean, I have a huge pile of paper at home, paper that's half-used, used on only one side; I've kept a lot of partially printed sheets instead of throwing them away, so that I can write on the back sides. And I'll use up 20 sheets or more per hour when I'm exploring a problem, especially at the beginning. For the first hour I'm trying all kinds of stuff and looking for patterns. Later, after internalizing those calculations or drawings or whatever they are, I don't have to write quite so much down, and I'm getting closer to a solution. The best test of when I'm about ready to solve a problem is whether or not I can think about it sensibly while swimming, without any paper or notes to help out. Because my mind is getting accustomed to the territory, and finally I can see what might possibly lead to the end. That's oversimplifying the truth a little bit, but the main idea is that, with all my students, I've noticed that they get into a mental state where they've become more familiar with a certain problem area than anybody else in the world."
Visualizers vs Symbolizers. Well, you know, I’m visualizing the symbols. To me, the symbols are reality, in a way. I take a mathematical problem, I translate it into formulas, and then the formulas are the reality. I know how to transform one formula into another. That should be the subtitle of my book Concrete Mathematics: How to Manipulate Formulas. I’d like to talk about that a little.
I have a feeling that a lot of the brightest students don’t go into mathematics because–-curious thing–-they don’t need algebra at the level I did. I don’t think I was smarter than the other people in my class, but I learned algebra first. A lot of very bright students today don’t see any need for algebra. They see a problem, say, the sum of two numbers is 100 and the difference is 20, they just sort of say, “Oh, 60 and 40.” They’re so smart they don’t need algebra. They go on seeing lots of problems and they can just do them, without knowing how they do it, particularly. Then finally they get to a harder problem, where the only way to solve it is with algebra. But by that time, they haven’t learned the fundamental ideas of algebra. The fact that they were so smart prevented them from learning this important crutch that I think turned out to be important for the way I approach a problem. Then they say, “Oh, I can’t do math.” They do very well as biologists, doctors and lawyers.
The philosophy behind seeking solutions. "The process of seeking solutions is certainly a big part of a researcher's life, but really it's in everybody's life. I don't want to get deep into philosophy, but the book of Ecclesiastes in the Bible says essentially this:
Life is hard and then you die. You can, however, enjoy the process of living; don't worry about the fact that you're going to die. Some bad people have a good life, and some good people have a bad life, and that doesn't seem fair; but don't worry about that either. Just think about ways of enjoying the journey.
Again I'm oversimplifying, but that's the message I find in many parts of the Bible. For example, it turns up in Philippians 3:16, where the writer says that:
You don't race to get to the goal; the process of racing itself, of keeping the pace, is the real goal.
High minimum more important than high maximum. "I try to do a good job at whatever I'm doing, because it's more fun to do a good job than not. And when there's a choice between different things to spend time on, I try to look for things that will maximize the benefit without making me burn out.
For example, when I was working on the TeX project during the early 80s, hardly anybody saw me when I was sweeping the floor, mopping up the messes and carrying buckets of waste from the darkroom, cleaning the machines, and doing other such stuff. I did those things because I wouldn't have dared to ask graduate students to do menial tasks that were beneath them.
I know that every large project has some things that are much less fun than others; so I can get through the tedium, the sweeping or whatever else needs to be done. I just do it and get it over with, instead of wasting time figuring out how not to do it. I learned that from my parents. My mother is amazing to watch because she doesn't do anything efficiently, really: She puts about three times as much energy as necessary into everything she does. But she never spends any time wondering what to do next or how to optimize anything; she just keeps working. Her strategy, slightly simplified, is, "See something that needs to be done and do it." All day long. And at the end of the day, she's accomplished a huge amount.
Putting this another way, I think that the limiting thing — the thing that determines a person's success in life — is not so much what they do best, but what they do worst. I mean, if you rate every aspect of what someone does, considering everything that goes into a task, a high minimum is much more important than a high maximum. The TeX project was successful in large part because I quietly did things like mop the floor. The secret of any success that I've had, similarly, is that in all the projects I've worked on, the weakest link in my chain of abilities was still reasonably strong."
A person’s success in life is determined by having a high minimum, not a high maximum. If you can do something really well but there are other things at which you’re failing, the latter will hold you back. But if almost everything you do is up there, then you’ve got a good life. And so I try to learn how to get through things that others find unpleasant.
https://news.ycombinator.com/item?id=31482116
Donald Knuth interviews are so interesting, but would like to particularly highlight this little piece of advice, out of this great playlist:
"Donald Knuth - My advice to young people": https://youtu.be/75Ju0eM5T2c
Complete Playlist - "Donald Knuth (Computer scientist)" [97 videos]:
https://www.youtube.com/playlist?list=PLVV0r6CmEsFzeNLngr1Jq...
Also the "Oral History of Donald Knuth" from the Computer History Museum is great.
"Oral History of Donald Knuth Part 1": https://youtu.be/Wp7GAKLSGnI
"Oral History of Donald Knuth Part 2": https://www.youtube.com/watch?v=gqPPll3uDa0
Plus..
"Donald Knuth Interview 2006": https://github.com/kragen/knuth-interview-2006
"An Interview with Donald Knuth": https://www.ntg.nl/maps/16/14.pdf
"Interview with Donald Knuth": https://www.informit.com/articles/article.aspx?p=1193856
This somewhat "colourful" page also tracks a few: http://www.softpanorama.org/People/Knuth/donald_knuth_interv...
PS: The story that he told Steve Jobs he was "Full of shit" is not true.
"Donald Knuth never told Steve Jobs that he was full of shit"