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I apologize if this question seems frivolous, but the motivation for it is quite serious. When I encounter the endless topic of the 'relevance' of mathematics, I am rather fond of referring to a network of knowledge. Before explaining this term, I should say that I'm not one who considers it very difficult to make a plausible direct case for the importance of mathematics to the general public, provided the context and tone of such a discussion is chosen with some care. Nevertheless, a little bit of thought makes it clear that the realistic value of any research assessed over time depends very heavily on the integrity of a network of related activity within which it sits. That is to say, a pure mathematician might occasionally speak to an applied mathematician who will speak to a physicist who will speak to an engineer who will speak to a biologist who will speak to a computer scientist who will speak to a mathematician, and so on. If we find sufficient coherence in the overall network of interaction, the individual components will frequently take on deeper significance than may have been noticed in isolated observation. Clearly, this isn't to imply that any obscure activity is as important as any other, but it seems to me an awareness of the network is critical in any discussion of relevance.

After making this point recently to some graduate students, it occurred to me to investigate more than casually a rather amusing measure of connectedness, the collaboration distance calculator. So here is a small but somewhat surprising list of (finite!) distances from myself I've found using mathscinet:

Albert Einstein 5

James Clerk Maxwell 6

Richard Feynman 5

Stephen Hawking 4

J.B.S. Haldane 7

Noam Chomsky 4

Willard Van Orman Quine 6

Nelson Goodman 5

Amartya Sen 7

Ilya Prigogine 4

Jean Piaget 6

Needless to say, this array of celebrity intellectuals says nothing about me in particular. Among mathematicians of comparable seniority, I have relatively few collaborators, and examining the specific bridges that make up the paths will quickly reveal that they have nothing much to do with the signficance of my own research. It's obvious then that the diversity of this list reflects nothing less than the centrality of mathematics, and perhaps the coherence of human scholarly endeavour as a whole.

Now to the question: Could you investigate a bit yourself now, and let me know of interesting research connections you find to people working outside mathematics, using mathscinet or otherwise? For the purposes of this question, what I would like to know about are concrete sequences of research links as might appear in the collaboration distance calculator, rather than an anecdotal discussion of some application of mathematics. Perhaps you could also add a word about your own area of research, so I can get some sense of surprise (or lack of it). By the way, I work on arithmetical algebraic geometry.

As mentioned at the beginning, I do think my motivation is serious: In grandiose terms, a general awareness of the connections is pretty important not just for reassuring students, but for cultivating ourselves a reasonably sophisticated sense of where we stand in the scheme of things.


As mentioned by Sonia Balagopalan in the comments below, it would be also interesting to hear of unlikely connections Mathematician A--Non-mathematician B. However, I did think people would be pleasantly surprised to experiment a bit and find out specifically about their personal connections. That is, I thought it would be fun to concretely illustrate my own generic answer to

'How connected are you?':

More than you expect!

I agree with most of the other comments, especially what Professor Milne writes about inaccuracy. But even with the few weak links that show up, the paths still seem to be interesting, and mostly illustrate my point. (Of course I can think of examples where they would be nearly uninteresting, such as a link created by two articles appearing in an encyclopedia.)

Felipe: Actually, I have the impression that my more unusual connections go through you!

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According to the ErdÅ‘s Number Project (oakland.edu/enp/trivia), out of the 401k authors in MathSciNet, 268k authors are in the largest connected component of the collaboration graph (the graph with authors listed in MathSciNet as vertices and an edge between two authors if MathSciNet reports they have co-authored). So it's not surprising that you have a finite distance from these people. –  Chris Phan Jul 29 '10 at 17:11
MR collaboration numbers aren't accurate. For example, MR claims my collaboration number with Gauss is an improbable 6. They get that number by claiming Landau and Riemann are coauthors and Riemann and Gauss are coauthors because works by them were included together in reprint collections. Similarly, they incorrectly give my Erdos number as 3 because they count me as a co-author of Gerardin when we only published articles in the same collection. –  JS Milne Jul 29 '10 at 18:10
Also, there are things not captured by collaborations. For instance, Fields medalist Laurent Lafforgue has no coauthor, and on top of that his papers are said to be quite technical: so the probability to see his own work being related to other topics outside math by a string of collaborations is zero, yet its place in "the scheme of things" from a pure math perspective is not that limited. Probably a better measure would be a notion of "greatly inspired by paper X" (i.e. not just a citation). –  Thomas Sauvaget Jul 29 '10 at 19:07
Links to Einstein are probably via the number-theorist Ernst Straus, who, as a young man, was employed by Einstein as a research assistant, and got a joint paper out of it. Through Straus, Einstein achieved Erdos number 2. –  Gerry Myerson Jul 29 '10 at 23:34
I am dubious that this question is appropriate for this forum, and I am not the only one: someone else has voted to close without comment already. Please take further discussion about whether the question is appropriate to meta: tea.mathoverflow.net/discussion/565/how-connected-are-you . This comments section should continue to have discussion about the content of the question, as it has above. –  Theo Johnson-Freyd Jul 30 '10 at 3:37
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closed as not a real question by Igor Pak, Theo Johnson-Freyd, Hailong Dao, Steve Huntsman, Victor Protsak Jul 30 '10 at 5:37

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