रामानुजम आणि रेमन झीटा

रामानुजम यांनी शोधलेली समिकरणं अगोदरच मांडली गेली होती. हार्डीने लंडनला नेऊन तो खजिना दाखवला. पण{दुर्दैवाने} नंतर नवीन काही मांडता आले नाही. हे बरोबर नाहीये. http://www-history.mcs.st-and.ac.uk/Biographies/Ramanujan.html Hardy, together with Littlewood, studied the long list of unproved theorems which Ramanujan enclosed with his letter. On 8 February he replied to Ramanujan [3], the letter beginning:- I was exceedingly interested by your letter and by the theorems which you state. You will however understand that, before I can judge properly of the value of what you have done, it is essential that I should see proofs of some of your assertions. Your results seem to me to fall into roughly three classes: (1) there are a number of results that are already known, or easily deducible from known theorems; (2) there are results which, so far as I know, are new and interesting, but interesting rather from their curiosity and apparent difficulty than their importance; (3) there are results which appear to be new and important...

कंजूस, रामानुजनने सुमारे शंभरेक संयुक्त संशोधने (=रीसर्च पेपर्स) प्रकाशित केली. इथे एक लेख आहे : https://qz.com/670254/the-unlikely-friendship-that-uncovered-an-untrain… उपरोक्त लेखानुसार रामानुजनला औपचारिक (फॉर्मल) गणिताची बैठक नव्हती. त्यामुळे त्याचं संशोधन घासूनपुसून लोकमान्य (=प्रेझेंटेबल) स्वरूपात प्रकाशित करावं लागे. त्यामुळे संयुक्त कागदांची संख्या वाढलेली दिसते. मला मात्र इथे उचलेगिरीचा वास येतोय. औपचारिक गणित आवाक्यात न येण्याइतका रामानुजन बावळट नक्कीच नव्हता. रामानुजन व इतर कोणी असा काही संयुक्त कागद दिसला की रविकिरण मंडळाची आठवण होते. रवि एकंच बाकी सगळे किरण. आ.न., -गा.पै.

हे वाचूनही तुम्हाला शंका असल्यास सांगा During his short life, Ramanujan independently compiled nearly 3,900 results (mostly identities and equations).[2] Many were completely novel; his original and highly unconventional results, such as the Ramanujan prime, the Ramanujan theta function, partition formulae, and mock theta functions, have opened entire new areas of work and inspired a vast amount of further research.[3] Nearly all his claims have now been proven correct.[4] The Ramanujan Journal, a peer-reviewed scientific journal, was established to publish work in all areas of mathematics influenced by Ramanujan,[5] and his notebooks – containing summaries of his published and unpublished results – have been analyzed and studied for decades since his death as a source of new mathematical ideas. As late as 2011 and again in 2012, researchers continued to discover that mere comments in his writings about "simple properties" and "similar outputs" for certain findings were themselves profound and subtle number theory results that remained unsuspected until nearly a century after his death and which relied on work published in 2006.[6][7] He became one of the youngest Fellows of the Royal Society and only the second Indian member, and the first Indian to be elected a Fellow of Trinity College, Cambridge. Of his original letters, Hardy stated that a single look was enough to show they could only have been written by a mathematician of the highest calibre, comparing Ramanujan to other mathematical geniuses such as Euler and Jacobi.