tag:blogger.com,1999:blog-9004452969563620551.post6775063974891260365..comments2017-06-21T11:55:27.964+05:30Comments on Paramanand's Math Notes: Rogers-Ramanujan Identities: A Proof by Ramanujantesternoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-9004452969563620551.post-35274891401899696422017-06-21T11:55:27.964+05:302017-06-21T11:55:27.964+05:30@Unknown,
I consider a proof or presentation of ...@Unknown, <br /><br />I consider a proof or presentation of a mathematical fact as more elementary if it can be understood by having a lesser amount of mathematical education. Mathematical education has a cost in terms of time, money and biggest of all dealing with educational establishment, not to mention the pressure of exams and bearing with mostly uninspiring teachers. I am interested in mathematics to enjoy what has already been created and do not consider myself sufficiently able to create new stuff. And I want to enjoy the maximum with minimal cost.<br /><br />The term highbrow is not used these days. I read it from one of G. H. Hardy's books and instantly understood the meaning it conveyed. And I am happy to use to it here. Any mathematics which is unnecessarily difficult (possibly because the creators were not able to find simpler approaches) should be done away with. If Ramanujan suddenly becomes alive magically then he would probably laugh at those modular form guys and what they did to his beautiful theories of theta functions. Dr. Bruce C. Berndt echoes the same feelings in his books and says that modular forms can only help verify Ramanujan's identities, they can not be used to create/discover them and his words indicate a longing for the techniques with which Ramanujan obtained his results.<br /><br />By the way the proof of Prime Number Theorem via elementary methods (avoiding complex analysis) is so much convoluted that it falls in the same category of proofs of Ramanujan's identities via modular forms. To say in plain and simple words, it is boring and does not convey a sense of purpose. The proof via complex analysis is so much appealing.<br /><br />Mathematics has to be enjoyable and accessible to as many people as possible. Modern mathematicians are definitely not working in this manner. They are perhaps trying to restrict it to the elite few.<br /><br />Regards, <br />Paramanand Paramanand Singhhttp://www.blogger.com/profile/03855838138519730072noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-1427945298030907082017-06-16T10:13:45.983+05:302017-06-16T10:13:45.983+05:30Being "elementary" is not the same as be...Being "elementary" is not the same as being "simple" or "useful", if "elementary" means "depends on less high-powered"<br />There's an elementary proof of the Prime number theorem, but according to Terence Tao, the proof by Fourier analysis is more insightful and easier to understand, despite requiring more high-brow concepts and symbolisms.<br /><br />(I'm pretty sure you are trying to push a moral lesson here. The word "high brow" signals that you morally disapproves people who uses complicated structures)Unknownhttp://www.blogger.com/profile/06602052788668631388noreply@blogger.com