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He credited his work to his family goddess. From wikipedia: "A deeply religious Hindu, Ramanujan credited his substantial mathematical capacities to divinity, and said the mathematical knowledge he displayed was revealed to him by his family goddess. "An equation for me has no meaning," he once said, "unless it expresses a thought of God.""
Earlier quoted context omitted.
Another fun fact: 1 + 7 + 2 + 9 = 19 ; 19 × 91 = 1729
This kind of coincidence is just cute, it doesn't imply anything useful mathematically right?
"Interestingness" is often as good a heuristic as any when looking for paths that lead to useful developments, although the path is often not a straight one or short one.
I also like the idea of secondary and tertiary effects. One simple example: By "playing" with cute yet fun ideas that are highly likely to not lead to anything immediately interesting, we can build up skillsets and capabilities that lead to very useful results for other problems. Perhaps this is somewhat akin to how the young of predator species "play" around in a way that prepares them to actually hunt when they are older.
Earlier quoted context omitted.
In fact, there seems to be a lot of interesting things about 1729: https://en.wikipedia.org/wiki/1729_(number)
I love how the article starts with the most boring facts about 1729: > 1729 is the natural number following 1728 and preceding 1730.
Therefore, these are not the most boring facts about 1729.
;)
[0] https://en.wikipedia.org/wiki/Interesting_number_paradox
How does that work? Who can explain this to me?
Ramanujan also claimed 1 + 2 + 3 + ... = -1/12. How does that work? Who can explain this to me?
Great read! When you first hear the taxicab number story, your initial impression is to be struck by Ramanujan's innate calculating capability. It's interesting to find out that the real coincidence here is that Hardy rode in a taxicab whose number had happened to show up in Ramanujan's investigations of Fermat's last theorem.
A lot of genius stories are like this. I was also under the illusion that these guys could just do things that fast, but at some point, I read Feynman's biography where he explicitly talks about how he used to solve homework problems or something beforehand and then he used to pretend that he found the solution while solving it if his classmates asked. That threw me for a loop and I started believing shit like no one…
The taxi cab story is easily a top-5 math story, and is quintessential Ramanujan. Has there been a genius of his kind since? Maybe Terry Tao, but his work also lacks the ease and lack of machinery that Ramanujan had. Truly amazing.
Yes definitely: Alexandre Grothendieck. And Terrence Tao can’t sit at his table (yet?). But honestly it’s kind of a silly game to rank mathematicians this way.
Ramanujan also claimed 1 + 2 + 3 + ... = -1/12. How does that work? Who can explain this to me?
The taxi cab story is easily a top-5 math story, and is quintessential Ramanujan. Has there been a genius of his kind since? Maybe Terry Tao, but his work also lacks the ease and lack of machinery that Ramanujan had. Truly amazing.