RAMANUJAN MATHEMATICS | STEPHEN WOLFRAM | 04.27.2016

|| TRUTH VERSUS NARRATIVE | EXCERPT ||

Ramanujan's way of working must have seemed quite alien . For Ramanujan was in some fundamental sense an Experimental Mathematician :

Going out into the Universe of Mathematical possibilities and doing calculations to find interesting and significant facts — and only then building theories based on them .

|| SEEING WHAT IS IMPORTANT | EXCERPT ||

Ramanujan was surely a great human calculator , and impressive at knowing whether a particular Mathematical fact or relation was actually true .

But Ramanujan's greatest skill was , I think , something in a sense more mysterious : an uncanny ability to tell what was significant , and what might be deduced from it .

|| A WAY OF DOING MATHEMATICS | EXCERPT ||

By the time of the scholarship , Ramanujan had started writing more papers , and publishing them in the Journal of the Indian Mathematical Society .

Compared to the big claims about primes and divergent series , the topics of these papers were quite tame . But the papers were remarkable nevertheless .

What is immediately striking about them is how calculational they are — full of actual , complicated formulas . Most Math papers are not that way . They may have complicated notation , but they do not have big expressions containing complicated combinations of roots , or seemingly random long integers .

In modern times , we are used to seeing incredibly complicated formulas routinely generated by Mathematica . But usually they are just intermediate steps , and are not what papers explicitly talk much about .

For Ramanujan , though , complicated formulas were often what really told the story .

And of course it is incredibly impressive that Ramanujan could derive them without computers and modern tools .

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|| PUBLISHED PAPERS & UNPUBLISHED NOTEBOOKS ETC LINKS | TBC . . . ||

http://plouffe.fr/simon/math/Ramanujan's%20Notebooks%20I.pdf
http://plouffe.fr/simon/math/Ramanujan's%20Notebooks%20II.pdf
http://plouffe.fr/simon/math/Ramanujan's%20Notebooks%20III.pdf
http://plouffe.fr/simon/math/Ramanujan's%20Notebooks%20IV.pdf
http://plouffe.fr/simon/math/Ramanujan's%20Notebooks%20V.pdf

http://www.math.tifr.res.in/~publ/nsrBook1.pdf
http://www.math.tifr.res.in/~publ/nsrBook2.pdf
http://www.math.tifr.res.in/~publ/nsrBook3.pdf

http://ramanujan.sirinudi.org/

http://www.imsc.res.in/~rao/ramanujan/contentindex.html

http://babel.hathitrust.org/cgi/pt?id=umn.319510002394343;view=1up;seq=773