Another needull on Ramanujan. Ramanujan is an Indian mathematician who continues to fascinate me endlessly.
Using a long and complicated argument, we finally found a way to show that the truth of the generalized Riemann hypothesis implies that every odd number greater than 2719 can be written as x2 + y2 + 10z2 for some integers x, y, and z. The fact that almost every mathematician believes in the truth of the generalized Riemann hypothesis and the fact that every odd number greater than 2719 up to a very large number can be represented by Ramanujan’s quadratic form convinced us that we had found the law. But although the law is simple enough to state, it thus far defies a definitive proof. To be sure, if someone manages to prove the generalized Riemann hypothesis, then our conditional proof will at once become a genuine proof. But the generalized Riemann hypothesis is arguably one of the most difficult open problems in mathematics. So Ramanujan was right that the odd numbers do not obey a simple law, in the sense that they are constrained by one of the most difficult unsolved problems in mathematics.
I had no idea that I would see the number 2719 again ten years later, etched on a wall in the very spot where Ramanujan performed some of his first calculations.
The complete article
Ken Ono — IAS
This would probably be my third needull on Ramanujan. This mathematician fails to amaze me every time I read about him. Although, I do not understand many of his proofs and theorems (very few people do) but there is something very pristine about him. A natural talent like Mozart, we keep discovering in layers. It won’t be incorrect to say that he was touched by divine.
In the last months of his life, Ramanujan frequently asked his wife Janaki Ammal for loose sheets of paper to record new results. Following Ramanujan’s death, Janaki, who had no formal education, delivered the papers to the University of Madras. They were subsequently forwarded to Hardy, who passed them on to G. N. Watson, the world’s premier authority in the field of special functions. After Watson’s death in 1965, the papers, comprising eighty-seven pages of handwritten results and more than six hundred formulas, were placed in storage at the Trinity College Wren Library. Forgotten by the mathematical world, the papers became known as “The Lost Notebook.” They were rediscovered by George Andrews in 1976 and have been the focus of intensive research ever since. The Lost Notebook and Other Unpublished Papers was finally published in 1987, in honor of the Ramanujan Centennial.
The complete article
Krishnaswami Alladi — Inference
Today’s needull is a very neat article. The writer gives you three puzzles to solve. When you finally look at the solution, they don’t look very difficult. So, for people out there wanting to exercise their grey cells, this one is for you.
The mathematician Mark Kac divided all geniuses into two types: “ordinary” geniuses, who make you feel that you could have done what they did if you were say, a hundred times smarter, and “magical geniuses,” the working of whose minds is, for all intents and purposes, incomprehensible. There is no doubt that Srinivas Ramanujan was a magical genius, one of the greatest of all time. Just looking at any of his almost 4,000 original results can inspire a feeling of bewilderment and awe even in professional mathematicians: What kind of mind can dream up exotic gems like these?
The complete article
Quanta Magazine — Pradeep Mutalik
Reading about Ramanujan gives me goose bump. The sheer raw brilliance of this independent mathematician amazes me. I had read the book “The Man who Knew Infinity” a couple of years ago and had recommended it on my blog. Now, a movie is releasing based on the book.
Pure geniuses like Ramanujan come once in a century. People are still discovering the elegant mathematics behind his theorems. He found these theorems hundred years ago when there were no computers. Reading his story reminded me of the feeling I get while looking at the stars in the sky. A feeling of complete awe at the wonderful world and things our human brain can’t fathom.
Today’s needull has been written by Stephen Wolfram, a distinguished mathematician himself.
It’s taken the better part of a century for many of Ramanujan’s discoveries to be fitted into a broader and more abstract context. But one of the great inspirations that Ramanujan gives us is that it’s possible with the right sense to make great progress even before the broader context has been understood. And I for one hope that many more people will take advantage of the tools we have today to follow Ramanujan’s lead and make great discoveries in experimental mathematics—whether they announce them in unexpected letters or not.
The complete blog
What is it that makes biographies so fascinating? I read Ramanujan’s biography to understand the genius he was. Was it inborn, or was it through hard work or just something that we don’t have an answer for yet. I read biographies also to have a glimpse at the human side of the achievers, probably as a reassurance to myself that not all is lost for me.
A good article in OPEN
OPEN — Srinath Raghavan