Convergence of ideas
As a moderator on MathOverflow, I see a lot of interesting interactions between mathematicians. The occasional dramatic situations get discussed profusely by community but very few take the time talk about the pleasant exchanges they have had. Here is one that caught my attention today because it illustrates how it is not uncommon for two mathematicians from distant parts of the world can stumble upon the exact same set of ideas…
Today, Sean Eberhard asked two interesting questions: Intersecting group orbits and Intersecting group orbits, version 2. The first question was answered almost immediately by Andreas Blass with a carefully crafted argument. This is not unusual, Andreas is well-known for answering questions quickly and precisely, both on and off MathOverflow. However, Andreas’s comment after answering explains why he answered so fast:
This, along with the projective plane example, was actually going to be in a paper I’m writing. Fortunately, the main topic of the paper is something else, so the paper won’t lose much by omitting this.
After getting an answer from Andreas, Sean posted his second question. Andreas answered again, with another comment:
This is another piece of the planned paper that I mentioned in connection with Sean’s previous question. Maybe the whole paper will gradually appear on MO this way. It’s one way to get it written without my usual delays.
It appears that Sean and Andreas have been having a lot of common questions and ideas, even if they don’t appear to know each other and live on different continents. Let me conclude this anecdote by seconding one of Sean’s comments:
I look forward to reading this paper. :)
Peter Krautzberger wrote
What a wonderful post. This is why I think it is so urgent that we move beyond papers – this is exemplary research activity of the future – quick dissemination, immediate peer review. There is no reason to actually press this into a paper, really, if credit would be given (not that Andreas needs it, but for the younger generation, this might is a much saner way to build a track record).
Dana C. Ernst wrote
I agree with Peter. Great post.
Sean Eberhard wrote
I’m glad you enjoyed this exchange as much as I did!