When László Babai first announced his graph isomorphism in quasipolynomial time result, I wrote
We think of theory as a young person's game, most of the big breakthroughs coming from researchers early in their careers. Babai is 65, having just won the Knuth Prize for his lifetime work on interactive proofs, group algorithms and communication complexity. Babai uses his extensive knowledge of combinatorics and group theory to get his algorithm. No young researcher could have had the knowledge base or maturity to be able to put the pieces together the way that Babai did.
Babai's proof is an exceptional story, but it is exceptional. Most CS theorists have done their best work early in their career. I got myself into a twitter discussion on the topic. For me, I'm proud of the research I did through my forties, but I'll always be best known, research wise, for my work on interactive proofs around 1990. It would be hard to run a scientific study to determine cause and effect but here are some reasons, based on my own experiences, on why we don't see research dominated by the senior people in theory.
The field changes - Computation complexity has moved from a computational-based discipline to one now dominated by combinatorics, algebra and analysis. I'm not complaining, a field should evolve over time but it plays less to my strengths. It's hard to teach this old dog new tricks.
I don't really get the "fruit hanged lower" part. How does that justify young people proving more theorems?
ReplyDeleteMore why a particular individual proves better theorems in their youth.
DeleteYou are missing several factors that point in the other direction, e.g., there is a lot to be said for the broad overview of the field, and closely related fields, that one gets at a later age and the ease with which one can do novel, inter-disciplinary work.
ReplyDeleteI feel I have only done better work since turning 60, in 2017, and moving to UC Irvine that Fall.
I think it's a complex story, and there will be examples in both directions. I think you're missing several obvious issues, though:
ReplyDelete1) Regression to the mean: Some fraction of people who got good results when they were young just got lucky, and they regress back to their mean performance. (And since early success leads to positions/opportunities, you probably see less of this "luck"/success from people with less prominent beginnings who stay in the field.)
2) Other opportunities/boredom: Doing research for 20 or so years is mentally draining, and can get repetitive or otherwise lose its luster. Other opportunities (startups, consulting) beckon that seem exciting and new and take energy from research. (I suppose this is like your "thrill is gone" category or your "new jobs" category, but "administration" seems very limited in scope! On the plus side, sometimes these other opportunities lead to new and exciting research directions, bringing energy back to the research.)
3) Mentoring/students: Academic life seems to push the mentoring of graduate students rather than doing your own work. Arguably for many people their "best work" will come through their students, and that (probably mostly rightly) gets attributed mostly to the student and not the advisor. (I suppose a counter-argument is for many advisors their "best work" is indeed behind them and so advising/mentoring younger students is their best way to continue doing very strong work; I'm not sure how much that's true and how much is the academic culture. I've known systems faculty that leave academia precisely because they decide they'd prefer to build/code their own systems rather than manage a group of graduate students and postdocs.)
A truly top-shelf researcher once told me that you should completely change your research subject every 10 years or so, or otherwise your research will become too much the "same-old" for you and/or you'll miss out on the new, exciting stuff in the field. I think that's hard advice to follow, but I see the merit in it if you want to increase your chances of your best work increasing over time. (I try to follow more of an expanding balloon approach, never really leaving behind the base, but always trying to be willing to try a new direction and see where it goes.)
Most of the arguments in this post and the comments apply to any academic field, except possibly the part on "the field changes." So, what are the fast-changing and slow-changing academic fields? Are their best results obtained by young researchers?
ReplyDelete@Lance: As usual, I enjoyed this piece.
ReplyDeleteThe way you frame perspectives ignites debate organically.
I don't want to make it sound brutishly simplistic;
but at the very foundational core, it seems,
all is an emotional process!
We publish because we have something interesting to say;
we have found a more efficient way to do X; we improved the
upper bound Y in paper ZZZZ; we disproved this long-lasting conjecture by infamous X. But deep down, why the urge to do
all this?
In principle, we are a competitive bunch; results are driven
by the fact that "deep down", we think, we can do better.
Of course, we can frame this as being "truth seekers" of sorts;
but a truthful and critical self-reflection might provide a different response.
I will hopefully hear differently. That this viewpoint
is very myopic, doesn't reflect what the community thinks,
etc ... but I'd hope that the response (if there is one), is not
a diplomatic or politically correct response.