December 26th, 2017

On surviving in academia

Another couple of comments in the same MathOverflow thread:

"Publish-or-perish and the sense of survival present a quite different set of problems. It is my feeling that many people nowadays are working so hard to survive in the academia that they would be much less troubled (and better off, too) surviving outside of the academia. On a deeper (and perhaps more controversial) level, I would say that personal survival and doing important research in mathematics should be viewed as two almost incompatible aims, not in the sense that they cannot be both achieved, but that they cannot be pursued simultaneously.

The mathematics research academia is not there for you or me to survive in it. It is there for your and my ideas to survive in it. This presumes that we care about having mathematical ideas that would survive and prosper (being worthy of surviving and prospering) in other people's minds more than we do about our personal survival and prosperity. If we don't, we just don't belong here, and should be doing something else."

Research excellence

There is no way to avoid dangerous routes in one's research. The first thing that I think should be stressed about how the profession of a researcher differs from the "normal" occupations is that it is an inherently dangerous enterprise, in a particular way in which the normal occupations are not. One way to explain it is to point out that, as everyone has heard, a researcher is supposed to excel in his research, one's research must be excellent. What does it mean? That it should be better than everybody else's research, in some sense.

As a research mathematician, you are supposed to have some aspect to what your are doing, however possibly narrow, but still important enough to worth noticing, which is superior over what every other mathematician in the world is doing. There is no such requirement in non-research occupations.

If you are baking bread, your bread does not necessarily need to be the best bread in the world. Not even any particular narrow aspect of it needs to be the best in the world. Your bread does not even need to be the best in your town. The producer of a better bread would just price it higher. If you are a doctor treating people's kidneys, there does not necessarily need to be an aspect of treating kidneys that you do better than every other doctor in the world. If you are a lawyer advising your clients, you do not need to better at some aspect of it than every other lawyer in you jurisdiction. Those more skillful lawyers just have their clients, and you have yours.

But as a research mathematician, you are useless if you have not excelled, literally, over everybody else in the world, at least in some respect. It is in this sense, I think, that you either succeed or fail.

Thus the name of the game in research is that you are supposed to understand something that noone else in the world understands. And betting your fortunes on the proposition that you are in some way smarter than everybody else in inherently dangerous. You take some route which everybody believes is leading nowhere, but you know better than everybody else. You tackle a problem that everybody considers to be meaningless or unsolvable, or you approach a problem in a way which everybody thinks is clearly doomed to fail, but you see things deeper than they do.

Now, what is this notion that there are some certain, sure ways to excel over everyone else in the world? It is an illusion and nothing but an illusion. A researcher taking one or another dangerous route in one's research career -- what other people would consider to be a dangerous route, based on what they know and understand -- may indeed succeed or fail, depending on the quality of his vision of things. But a researcher systematically avoiding all such dangers is literally doomed to fail. There just isn't anything he can possibly succeed in.