Historical basis and mathematical significance of Riemann surfaces - MathOverflow [closed]most recent 30 from http://mathoverflow.net2013-06-19T23:56:30Zhttp://mathoverflow.net/feeds/question/75504http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/75504/historical-basis-and-mathematical-significance-of-riemann-surfacesHistorical basis and mathematical significance of Riemann surfacesSadiq Ahmed2011-09-15T11:45:11Z2011-09-15T19:16:05Z
<p>It is written in <em><a href="http://www.amazon.com/dp/0199606749" rel="nofollow">Riemann Surfaces</a></em> (Oxford Graduate Texts in Mathematics) by Simon Donaldson, that:</p>
<p>"[t]he theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination of much of traditional calculus"</p>
<p>Can someone please provide an articulated commentary on this statement.</p>
<p>Specifically, the statement suggests, [or seems to suggest], that Riemann surfaces were the logical / mathematical outcome of many years of careful development and refinement of traditional calculus. But: (i) what was / were the major milestones(s) in this road? and (ii) when the author uses the word 'culmination' what specifically is it the culmination of, and what problems / issues did the introduction of Riemann surfaces help to solve / clarify / etc.?</p>
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<p>(This question was originally <a href="http://math.stackexchange.com/questions/64727/historical-basis-and-mathematical-significance-of-riemann-surfaces" rel="nofollow">posted</a> on Math SE, but I'm also posting it here because I'm seeking an expert's [in Riemann surface theory] feedback if possible.)</p>
http://mathoverflow.net/questions/75504/historical-basis-and-mathematical-significance-of-riemann-surfaces/75508#75508Answer by BSteinhurst for Historical basis and mathematical significance of Riemann surfacesBSteinhurst2011-09-15T12:30:52Z2011-09-15T12:30:52Z<p>From the wording of your question it is possible you are asking someone to write an entire historical overview for you. So instead what I did was spend a few minutes on Ye Olde Google and found this:</p>
<p><a href="http://store.doverpublications.com/0486470040.html" rel="nofollow">The Concept of a Riemann Surface</a> by Hermann Weyl. It is cheap and your local library might have it already it.</p>
http://mathoverflow.net/questions/75504/historical-basis-and-mathematical-significance-of-riemann-surfaces/75542#75542Answer by Margaret Friedland for Historical basis and mathematical significance of Riemann surfacesMargaret Friedland2011-09-15T16:44:59Z2011-09-15T16:44:59Z<p>If you are looking for an outline, check Chapter III of
"The Riemann legacy: Riemannian ideas in mathematics and physics"
By Krzysztof Maurin</p>
<p>Here is the link to Google Books, where you can view the table of content</p>
<p><a href="http://books.google.com/books?id=jlll448aDLEC&printsec=frontcover&dq=inauthor:Maurin&hl=en&ei=5CpyTr2-HOGusQLfz-X1CQ&sa=X&oi=book_result&ct=result&resnum=3&ved=0CDUQ6AEwAg#v=onepage&q&f=false" rel="nofollow">http://books.google.com/books?id=jlll448aDLEC&printsec=frontcover&dq=inauthor:Maurin&hl=en&ei=5CpyTr2-HOGusQLfz-X1CQ&sa=X&oi=book_result&ct=result&resnum=3&ved=0CDUQ6AEwAg#v=onepage&q&f=false</a></p>