Friday, November 21, 2008

What is your best paper? Ambigous!

I sometimes ask people
What is your best paper?
This question is actually ambigous. Here are criteria that you can use.
  1. Most important to the public. E.g., a big breakthrough people care about.
  2. Most important in your view E.g., a big breakthrough on a problem that you care about, but perhaps others do not.
  3. Most citations. This might be the same as important to public but may take more time to be evident as such. This one is verifiable!
  4. You are personally attatched to it ind. of what the public things. E.g., you are delighted that it used theorms in p-adic cohomology to solve a problem in number theory, but nobody else cares.
  5. You had a big contribution to it.
  6. You liked how it evolved.
Hence, if someone asks what your best paper is, ask them to clarify the question. Or give them 5 answers. ~


  1. 7.(& 2) The ones with the most elegant proof(s) discovered by me.

  2. I meant to say "proofs" not "proof(s)".

  3. How is the paper that has been cited the most verifiable?

    In fact I would go so far as to conjecture that as probability that a paper will be widely cited goes up, the ability of the paper's author to know how many times the paper has been cited diminish to nothing.

  4. Anon 3: What are you talking about? Citations are carefully tracked by a number of organizations (including Google Scholar and citeseer). Sure, both are imperfect, and miss some citations and count some things that shouldn't count. But I would imagine that they both give very good approximations to the "actual" citation count.

  5. Many of the places to which I am applying this year ask applicants to attach PDFs of their "three most important papers." Given your discussion, now I have to wonder if they are seeking to learn about the candidate by observing which of these choices the candidate makes.

  6. Congratulations! This page is currently the #2 hit on Google for "ambigous"! Maybe this comment will push it up to #1.

    I'd call that an unambigous success!

  7. It is also possible that the same paper is the answer in all five cases.

  8. hmm, interesting question. But some papers/results that don't seem important now may be useful later.

  9. Maybe it's also fun to ask people about their worst papers --- the ones where you do all the work, struggle to get it published anywhere, and then no-one cites it.

  10. Don't worry about no one citing your papers (except for obvious reasons). Many important mathematics papers were "useless" until much later. For example, the notion of imaginary numbers took 200 years to be widely accepted.

    Popularity, I mean impact factor, is only a relatively recent phenomenon.

  11. Citations is the most commonly recognized measure, but it can also be a misleading one. To see what I mean, take a look at CiteseerX's list of most-cited papers across their entire database.;jsessionid=8D28776679FE9FA8AB90D45C461891B8

    Putting aside the Tarski Grothendieck set theory papers (which appear to have some odd citation convention) you'll notice a number of things. Longer works like books tend to get cited more - they cover more material, and they're frequently taken as the authority on classical matters, rather than the original publications. In a way, you know your work is most successful when people begin to take it for granted, like the earth they stand on, and think of it as undeserving of citation - there's a reason the original papers on linked lists aren't on this list.

    Citations is also peculiar as a relative measure. Is the genetic algorithms paper twice as important as the RSA paper? Are R-trees more important than C++? Not really. There are patterns and conventions to citations within certain subfields, and perception of the paper comes into play. A paper that, like the RSA paper, is recognized as the single authoritative original source for a sudden insight, may have an easier time getting cited than one of a long, incremental series of papers, such as the 20 papers required to prove the Robertson–Seymour theorem, or the many papers associated with the Human Genome Project.