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Why, at least as it seems to me, in past centuries mathematicians worked alone, while currently most of them work in pairs/groups? Reasons might be rooted in Mathematics, or Sociology, and so on..

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7 Answers 7

Mathematics is getting bigger and more complicated, so, although this depends heavily on what exactly you are doing, in general it is harder to complete projects alone and more beneficial to combine the expertise of multiple people.

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I think this is correct. In general, people work together on projects (of any nature) because what might be very hard or even impossible to do alone can be accomplished by working in a group, just because it reduces the labour required from each individual, or because of the necessity of pooling different kinds of expertise, or ... . While I agree that there are some institutional pressures towards collaboration, as other answers have noted, I don't think that those are the main force driving the move towards greater collaboration. –  Emerton Jul 8 '10 at 18:14
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Better communications must surely play a role. Travel is easier, faster and more convenient, and telecommunications helps to – not least the Internet, of course. Even today, I have the distinct impression that collaboration within a single department is relatively rare. Certainly most if not all of the long running productive collaborations I know of involve mathematicians in different countries, often on different continents.

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I think this is right on the money. Only one comment: the US is a big country, represents a substantial share of the mathematical world, and many of its citizens have the unattractive habit of forgetting that a world exists outside the US. I think of myself as a fairly "internationally aware" American: I have been to Europe several times and lived outside of the US (not far out, but it counts!) for more than two years. It is amusing for me to note that my first two collaborators were Catalan and Israeli, whereas the last five or so have all been American. –  Pete L. Clark Jul 8 '10 at 17:55
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Oh, and one more thing -- collaborations within departments of the senior/junior type are becoming far more common. Government funding like NSF's VIGRE program highly encourages this kind of collaboration. Universities are becoming increasingly interested in student research (even at the freshman/sophomore undergraduate level, which I confess I feel is usually misguided). –  Pete L. Clark Jul 8 '10 at 17:58
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Michael Nielsen describes how things have changed in http://michaelnielsen.org/blog/the-future-of-science-2/ and how Newton and the like would keep their discoveries secret and publish things only as anagrams so that they could claim priority. It was a different culture.

See also: http://whatisresearch.wordpress.com/2009/02/02/on-new-modes-of-mathematical-collaboration/

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Today mathematics is a profession with tens if not hundreds of thousands of mathematicians and mathematical scientists in the world.

Hundreds of years ago there were only small numbers of mathematicians at any time, so the opportunities for widespread collaboration just weren't there.

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From my (CS) perspective there are at least 2 forces which encourage working in pairs/groups. Teaching limits ones time and one has students, so one works with students. Secondly, funding schemes often encourages collaboration between various parties (I'm thinking large European projects here). Even local (Belgian) funding schemes favour consortia to individuals.

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At least part of the answer to your question will be hard to measure/document. For example, it's reasonable to believe that at least some of the mathematicians we think of as working alone in past centuries in fact discussed their ideas with, and received valuable insight from, their wives. Many people believe, for instance, that Mileva Maric collaborated on some of Albert Einstein's 1905 papers. Given that as late as the start of the last century top mathematicians had a hard time finding publishers if they were female (Emmy Noether spent many years where the only way she could give lectures was for David Hilbert to sign up as the official instructor), it's likely that some mathematicians let their husbands publish solely in order for the publication to happen at all.

But this is all rather speculative. I mean only to highlight one way that the historical record can be systematically distorted. There are bound to be others, and I, necessarily, don't know of a lot of examples to prove that it was.

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The supposed Maric-Einstein collaboration is doubted by most historians, but in any case, it was not out of the question for husband and wife to co-publish in those days. The first book on set theory, The Theory of Sets of Points (Cambridge University Press 1906), was written by the husband and wife team of W.H. Young and Grace Chisholm Young. –  John Stillwell Jul 8 '10 at 23:33
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This won't be a large reason, but some papers were probably jointly written so that someone could get a lower Erdos number.

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FWIW, I have been proud of my very high -- but finite -- Erdos number of 5. One of my slightly more junior colleagues who has collaborated only with me is currently the proud beneficiary of Erdos number 6. Alas, my own PhD student has written a joint paper (or two) with me and now all of a sudden with someone with Erdos number 1. Betrayal! –  Pete L. Clark Jul 8 '10 at 18:03
    
@Pete: According to the MathSciNet collaboration distance tool, your Erdos number is infinite. –  Boyarsky Jul 8 '10 at 18:28
    
@Boyarsky: I'm not sure what's happening on your end; when I do it I get 5 (I checked again just now). You did type in "Clark, Pete L.", right? Accept no substitutes... –  Pete L. Clark Jul 8 '10 at 20:53
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@Pete, in view of your student's paper shouldn't yours now be 3? –  Kiochi Jul 8 '10 at 22:37
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On a lighter note, my Copernicus number is 2: my coauthor collaborated with a person from Toruń, and due to a unique sequence of errors by the powers responsible, "Nicolaus Copernicus University" was listed as one of the authors of their paper! Oh yes, and MR collaboration distance tool is crazy: my distance to Carl Friedrich Gauss is 8 (the path goes through Einstein and Minkowski:) –  Victor Protsak Jul 9 '10 at 1:58
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