Below, a few recent highlights.
From Hamming, “You and Your Research” (June 6, 1995).
The example I’ve given you already is working with the door closed or open. If you work the door closed, you won’t be interrupted and you get your work done. You work your door open, people come by and stop and chat and so on and so on. But I’ve noticed very clearly, at Bell Laboratories, those who work with door shut may be working just as hard ten years later but they don’t know what to work on. They are not connected with reality. Those who have the door open may very well know what’s important. Now I cannot prove to you whether the open door causes the open mind or whether the open mind causes the open door. I suspect it – I can only establish the correlation, and it was quite spectacular. Almost always the guy with the door closed were often very well able, very gifted, but they seem to work always on slightly the wrong problem. So you’ll have to get wide feeling for what is going on and the supreme example of this closure is the Institute for Advanced Study at Princeton. They take in people who’ve done something great. They give them luxury, a beautiful office a beautiful restaurant to dine in, a wonderful grounds and everything else like that. Adequate salary to live on. No cares, no worries, no nothing, you’re freed for life on anything at all. What happens? The bulk of ’em continue working on the problem they made that made them famous. They keep on elaborating and so on. Well, they’ve already made it famous. It doesn’t have to be added to. They got the thing going. Rarely do they change. Now, von Neumann was different. He was the Institute and he did go out in reality and turn up in Washington in other places. He traveled widely and was receptive of new ideas. But the bulk of the people got appointed the Institute for Advanced Study don’t keep the door open on life as it were. And they don’t do anything comparable to what they had done before. They are very able people, but the Institute in my opinion sterilized them a great extent. So what do you think are the ideal working conditions are not.
From David Hilbert and his mathematical work by Hermann Weyl. Found in Levels of Infinity – Dover Publications.
In his famous address, Mathematische Problème, delivered before the Paris Congress in 1900, he stresses the importance of great concrete fruitful problems. “As long as a branch of science,” says he, “affords an abundance of problems, it is full of life; want of problems means death or cessation of independent development. Just as every human enterprise prosecutes final aims, so mathematical research needs problems. Their solution steels the force of the investigator; thus he discovers new methods and viewpoints and widens his horizon.” “One who without a definite problem before his eyes searches for methods, will probably search in vain.”