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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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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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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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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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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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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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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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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